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ITEM POOL

Mathematics

Grade 8

Federal Democratic Republic of Ethiopia

Ministry of Education

Japan International Cooperation Agency

How to Use This Item Pool

LAMS

This Item Pool is a product of LAMS project.* A group of Ethiopian experts

have developed the question items stored in this Item Pool.

Good Items

The purpose of this Item Pool is to make a collection of “good” question items

freely available for teachers and educators throughout the country. The items

are “good” because the experts (item writers) wrote them strictly following the

guidelines and peer-reviewed them several times. Some of the items were

further field-tested on primary school students to ensure that the items have

statistically acceptable quality as well. At the final stage, all items were

rigorously reviewed and selected by representatives of the Ethiopian experts.

Only those items with satisfactory quality have been selected for this Item Pool.

Coverage

LAMS project has developed Item Pools for Grades 7 and 8, covering all the

Units as specified in the syllabus. It has also developed Sample Item Pools for

Grades 4 and 10, covering only two Units each.

About the Items

In the Pool, one item is indicated in one row. Each row has 10 columns: from

the left to the right, Serial number (S.N.), Competency number, Level (K or A),

Stem, Figure/Table, Option A, Option B, Option C, Option D and Key.

A serial number is given to each item. The series is confined to each Unit,

however. For a new Unit, a new series of numbers are given.

Competency number indicates the specific competency the item tries to test. The competencies are taken from the official syllabus (2008 version) but

numbered by LAMS. For the list of competencies, see the table attached below.

Level of items is a rough indication of the cognitive level that the item is trying

to assess. “K” means Knowledge Level, roughly corresponding to the

“knowledge” and “comprehension” levels as defined in Bloom’s taxonomy. “A”

means Application and Higher Level, referring to the “application” and higher

levels. This two-level classification of items is only meant to be a summative

indicator of the characteristics of the items and not to be a rigorous academic

exercise.

For What Purposes You Can Use This Item Pool

This Item Pool is a collection of “good” items. It can be used for following

purposes:

1. To compile term or year-end tests

You can compile term or year-end tests selecting items from this Item Pool

appropriate for your purposes and students’ level of performance.

2. To compile unit-end tests

At the end of each unit, you may give a test to students to see how well they have

understood the contents of the unit. Such unit-end tests can be easily compiled

using this Item Pool since it is organized unit-wise and according to the

competencies.

3. To give exercise problems to the students in the lesson

This Item Pool contains a full range of basic question items that are suitable for

students to work on after the teacher’s initial explanation. You can pick up such

basic-level question items and use them in your lesson to complement the

exercises given in the textbook.

Many other ways are possible. Please try your own ideas.

* LAMS project is a technical cooperation project jointly implemented by the Ministry of Education of Ethiopia

and the Japan International Cooperation Agency (JICA) for three years from 2014 to 2017. This project

produced the Item Pools for Mathematics, Biology, Chemistry and Physics for Grades 7 and 8 (and samples for Grades 4 and 10). The LAMS project also developed the Workbooks of the same subjects for Grades 7 and 8.

©2017 All rights reserved. Federal Democratic Republic of Ethiopia, Ministry of Education, and Japan

International Cooperation Agency (JICA)

Unit Sub-unit Competency No.

Calculate the square of a number 1

Find squares from a table of squares 2

Define the square root of a non-negative rational number 3

Calculate the square root of perfect squares 4

Extract the square root of a number by using square root table 5

Define the cube of a number 6

Determine the cubes of numbers 7

Define the cube root of a number 8

Determine the cube roots of perfect cubes 9

Use variables in expressing algebraic and geometric relations 10

Simplify algebraic expressions with and without brackets 11

Solve life related problems using variables 12

Determine the product of monomial by binomial 13

Determine the product of binomials 14

Find highest common factor of algebraic expressions 15

Factorize binomial 16

Solve linear equations involving brackets using equivalent transformation 17

Solve linear equations involving fractions 18

Solve real life word problems using linear equations 19

Use the inequality signs ≥ and ≤ properly, to give solutions 20

Solve linear inequalities with negative coefficients by applying the rule for transforming

linear inequalities

21

3.3 Cartesian coordinate

system

Draw the four quadrants of the Cartesian plane and mark the origin, x - axis and y - axis 22

Plot points on the Cartesian coordinate plane given their coordinates 23

Read the coordinates of any point on the Cartesian coordinate plane 24

(Blank) 25

Draw straight lines in the coordinate plane whose equations are of the form y = a 26

Draw straight lines in the coordinate plane whose equations are of the form x = b 27

Draw straight lines in the coordinate plane whose equations are of the form y = mx 28

3.2 Further on linear

inequalities

2. Further on working

with variables

2.1 Further on algebraic

terms and expressions

2. 2 Multiplication of

binomials

2.3 Highest common factors

3. Linear equation and

inequalities

3.1 Further on solutions of

linear equations

Mathematics G8

Table of Competencies

1. Squares, square

roots, cubes and cube

roots

1.1 The squares of a number

1.2 The square root of a

rational number

1.3 Cubes and cube roots

1


Determine the equation that relates the coordinates in a given set of ordered pairs 29

Determine the equation of a line that contains points whose coordinates are given 30

4. Similar figures Identify figures that are similar to each other 31

Explain the concept of similar figures 32

Draw an enlarged figure of a given real object by enlarging factor 33

Draw reduced figure of a given real object by reducing factor 34

Explain facts about two similar triangles 35

4.2 Similar triangles Apply the definition of similarity of two triangles to solve related problems 36

Apply the SSS, SAS and AA similarity tests for triangles to determine the similarity of two

triangles

37

Explain how the perimeters of two similar triangles are related 38

Explain how the areas of two similar triangles are related 39

Identify major arc and minor arc 40

Identify sector and segment of a circle concepts 41

Describe the concepts "tangent" and "secant" of a circle 42

Determine the centre of a circle by construction 43

Identify central angles and inscribed angles 44

Calculate the measure of central angle or inscribed angle or the intercepted arc based on the

given information

45

Prove that an angle formed by two chords intersecting inside a circle is equal to half the

sum of the intercepted arc by measurement

46

Solve problems related to angle formed by two intersecting chords inside a circle 47

Define "cyclic quadrilateral" 48

Describe property of "cyclic quadrilateral" 49

Prove theorem on the opposite interior angles of a cyclic quadrilateral 50

Calculate the unknown angle of cyclic quadrilateral 51

6.1 The concept of

probability

Identify certain, and impossible outcomes 52

Identify experiment, event and sample space 53

Determine the probability of simple events 54

Express probability using fractions, decimal and percentage 55

Apply Euclid's theorem and its converse for solving related problems 56

Apply Pythagoras' Theorem and its converse for solving related problem 57

7. Geometry and

measurement

7.1 Theorems on the right

angled triangle

4.1 Similar plane figures

5. Circles 5.1 Further on circles

5.2 Angles in the circle

6. Introduction to

probability 6.2 Probability of simple

events

2


Describe the trigonometric ratios, the sine, cosine and tangent using right angled triangle 58

Determine the value the trigonometric ratios for 30°, 45° and 60° angles 59

Apply the trigonometric ratios for 30° and 60° in solving related problems 60

7.3 Solid figures Identify parts of a pyramid 61

Prepare models of pyramid 62

Name different types of pyramids based on their bases 63

7. Geometry and

measurement

7.2 Introduction to

trigonometry

3

LAMS Item Pool, Mathematics, G8 Unit 1

S.N. Com-

peten-

cy No.

Level

(K or

A)

Stem Figure/Table A B C D Key

1 1 K In the expression 62=36 we call 2 is _________. Base Power form Exponent Standard form C

2 1 K Which one is the correct form of 62? 6

2=2x6 6

2=6+6 6

2=6x6 6

2=6x2 C

3 1 K Which one of the following is NOT true? 22=4 3

2=6 4

2=16 5

2=25 B

4 1 K Which one of the following is true? (20)2=20x20 -(5)

2=5x5 (-6)

2=-6x6 (20)

2=2x20 A

5 1 K 72 is equal to ________. 9 14 49 72 C

6 1 K If x=9 then the square of x is ______. 3 18 81 512 C

7 1 K 122 is equal to _________. 12 24 122 144 D

8 1 K Which one of the following is the square of 12? 24 48 96 144 D

9 1 K The square of 13 is ________. 19 26 169 196 C

10 1 K The square of 14 is _______. 28 196 256 2744 B

11 1 K Which one of the following is the square of 16? 4 32 64 256 D

1


S.N. Com-

peten-

cy No.

Level

(K or

A)


12 1 K What is the square of 17? 34 49 170 289 D

13 1 K Which of the following is true? 8=42

14=72

169=132

256=142 C

14 1 K 252 is equal to ________. 50 225 425 625 D

15 1 K What is the value of x2 if x=100? 100 200 1000 10000 D

16 1 K If x=2 and y=3, then what is the value of x2+y

2? 5 7 11 13 D

17 1 K If x=1.7, the value of x2 is ________. 2.89 3.4 28.9 34 A

18 1 K (2.3)2 is equal to _________. 4.29 4.6 4.9 5.29 D

19 1 K Which of the following is the square of 2.9? 4.82 5.82 8.41 8.52 C

20 1 K Which one is correct? (3.5)2= 12.96 (2.4)

2= 5.76 (3.52)

2= 12.40 (2.51)

2= 6.3 B

21 1 K Find the square of 5.2 25.4 27.04 25 27 B

22 1 K If x=1.52 then find the value of x2=_______. 0.23 2.38 2.5 2.31 D

23 1 K Let x=2.31 then x2 is

equal to ________. 5.3361 5.4101 5.6101 5.8001 A

2


S.N. Com-

peten-

cy No.

Level

(K or

A)


24 1 K (0.03)2= ________ 0.09 0.009 0.0009 0.00009 C

25 1 K If x=5/7, then find x2. 5/49 10/14 25/49 25/7 C

26 1 K If x=4/3 what is the value of x2? 64/27 16/9 8/6 9/16 B

27 1 K The square of 3/7 is _________. 9/7 6/7 6/14 9/49 D

28 1 K If x=-30/7 then what is the value of x2? -900/49 -90/49 90/49 900/49 D

29 1 K On the table given, what is the value of x2? 6 8 9 12 C

30 1 K From the table below, what is the value of C? 23 25 64 65 C

31 1 K Which of the following is a perfect square? 80 90 100 110 C

32 1 K Which one of the following is a perfect square? 6 8 12 16 D

33 1 K Which one is a perfect square? 8 9 12 27 B

x

x2

2

4

3

x 1 2 3 4 8 9 10

x 1 4 9 16 C 81 100

3


S.N. Com-

peten-

cy No.

Level

(K or

A)


34 1 K Which of the following is a perfect square? 8 16 27 32 B

35 1 K From numbers given below, identify a perfect

square.

40 24 48 81 D

36 1 K Which of the following is a perfect square? 8 27 48 81 D

37 1 K Which of the following is a perfect square? 99 88 81 60 C

38 1 K Which one of the following is a perfect square? 72 125 144 200 C

39 1 K Which one of the following is a perfect square? 2.24 2.25 2.5 2.6 B

40 1 K Which one of the following decimals is a perfect

square?

0.064 0.144 0.81 0.025 C

41 1 K Which of the following numbers is NOT a perfect

square?

1/36 9/225 1/144 25/6 D

42 1 K The square of 9 is found between the squares of

_____ and ______

6 and 7 6 and 8 8 and 10 10 and 11 C

43 1 A What is the next non-negative rational number? 0,

1, 4, 9, 16, 25, 36, ___

47 49 44 64 B

4


S.N. Com-

peten-

cy No.

Level

(K or

A)


44 1 A If (2.54)2=6.452 then find (25.4)

2. 64.52 645.16 645.2 6452 C

45 1 A If (25.4)2=645.16, then find (254)

2. 6451 645.16 6451.6 64516 D

46 1 A If (2.12)2= 4.494, then (21.2)

2= ________. 42.4 44.94 449.4 4494 C

47 1 A From the square root table (1.83)2=3.349, then

(18.3)2=_________.

3.349 33.49 334.9 3349 C

48 1 A If (1.3)2=1.69 then (0.13)

2=________. 16.9 1.69 0.169 0.0169 D

49 1 A If (1.42)2≈2.016 from the table of squares, then

(14.2)2≈ __________.

20.16 201.6 2016 20160 B

50 1 A If 22+3

2+6

2=7

2

32+4

2+12

2=13

2

42+5

2+20

2=21

2 then 6

2+7

2+42

2=________.

432

442

552

562 A

51 3 K The product of a number by itself is ________. The square root of

a number

The square of a

number

The cube root of a

number

The cube of a

number

B

52 4 K What is the square root of 16? 2 4 8 256 B

53 4 K The square root of 25 is ________. 5 50 12.5 625 A

54 4 K is equal to ______. 4.9 7 23 24.5 B49

5


S.N. Com-

peten-

cy No.

Level

(K or

A)


55 4 K If x=64, the value of √x is ________. 32 16 8 4 C

56 4 K is equal to _______. 8.1 9 18 40.5 B

57 4 K What is the square root of x, if x is 81? 8 9 18 27 B

58 4 K Tthe square root of 121 is _________. 12 11 10 9 B

59 4 K √225=________. 15 25 35 45 A

60 4 K What is the square root of 289? 17 16 15 13 A

61 4 K is equal to ________. 22 44 121 242 A

62 4 K The square root of 625 is _________. √15 √25 15 25 D

63 4 K What is the square root of 625? 15 25 35 45 B

64 4 K If x=625 then the square root of x is ________. 15 14 25 35 C

65 4 K Find the square root of 900. 90 80 60 30 D

66 4 K Find the prime factorization of 324. 23

x 53

23

x 35

23

x 34

22

x 34 D

484

6


S.N. Com-

peten-

cy No.

Level

(K or

A)


67 4 K Let

The value of y is _________.

6 7 8 9 A

68 4 K The square root of 1/4 is _________. 1/16 1/8 1/6 1/2 D

69 4 K If x=4 and y=9, the square root of x/y is

_________.

8/18 2/3 4/9 3/2 A

70 4 K If x2=9/16, what is the value of x? 8/9 3/8 3/4 18/32 C

71 4 K a2=16/81, then a is equal to _______. 4/81 8/81 4/9 8/9 C

72 4 K Find the square root of 121/144. 12/11 11/12 D

73 4 K If x=361/100 then √x=________. 19 10 1.9 0.09 C

74 4 K Which one of the following is the square root of

225/625?

5/15 25/15 3/5 5/25 C

75 4 K Find the square root of D

76 4 K The simplified form of is: 40 16 4 2 C

12

11

x 4 9 25 36

2 3 5 yx

11

12

25

400

529

361

23

19

23

19

23

19

23

19

7


S.N. Com-

peten-

cy No.

Level

(K or

A)


77 4 K The value of is: 16/25 4/25 4/5 16/5 C

78 4 K Which one of the following is true? C

79 4 K Which one of the following is true? A

80 4 K If x=0.0361 then √x=_________. 0.019 0.19 1.9 19 B

81 4 K =___________. 2 √20 √10 20 D

82 4 K If x=144, then what is the value of 4√x? 24 48 144 288 B

83 4 A The simplified form of is: 0.12 1.2 2 3 B

84 4 A What is the simplified form of ? 1/8 1/32 1/64 1/128 C

85 4 A Simplify 3x 3x2 9x 9x

2 B

2.02.7 X

50

32

0005.00005.00025.0

005.0005.00025.0

05.005.00025.0

0.0025 = 0.5´0.5

22

1636

2

64

1

x

x

27

729 7

1.001.0 05.025.0 012.0144.0 2.04.0

8


S.N. Com-

peten-

cy No.

Level

(K or

A)


86 4 A If x=4 and y=9, then the value of is

________.

2 3 6 36 C

87 4 A Let a=3 and b=4, then

=__________.

6/4 5/4 7/4 9/4 B

88 4 A If x=7 and y=9, find

=__________.

14 16 18 63 B

89 4 A Evaluate if x=2 and y=-2. √3 0 √2 √8 A

90 4 A If the distance

X

and Let x1=10, x2=6, y1=12, y2=9 find the value

of d=________.

1 3 5 7 C

91 4 A If x=4 and y=5, then the value of

is:

9 27 81 243 C

92 4 A If a=13 and b=-12, what is the value of 4 25 50 100 D

2yx

yx.

2

2

1b

a

221

2

21 yyxxd

23 yx

2222 ba

9


S.N. Com-

peten-

cy No.

Level

(K or

A)


93 4 A Which of the following is true? C

94 4 A -√53 is between which two numbers? -7 and -6 -8 and -7 -54 and -52 7 and 8 B

95 4 A If √2x =6 find the value of x. 2 12 18 36 C

96 5 K The given table contains square values. What is

the result of √4.494?

2.01 2.12 2.2 2.31 B

97 5 K From the square root table √17.89≈4.23, then

√178.9=________.

0.423 42.3 423 4230 B

98 6 K The expression a x a x a = _________. 3a √a a3 3

√a C

99 6 K Which of the following is correct about 73? 7

3=7x3 7

3=7x7x7 7

3=7+7+7 7

3=3+3+3+3+3+3

+3

B

100 6 K From the following numbers, identify a perfect

cube number.

10 25 27 81 C

101 6 K Which of the following is a cubic number? 36 27 100 121 B

x

2.0

2.1

2.2

0 1 2

4.00

4.410

4.840

4.04

4.452

4.884

4.080

4.494

4.928

10


S.N. Com-

peten-

cy No.

Level

(K or

A)


102 6 K From the given numbers, which one is a perfect

cube?

5 8 25 216 B

103 6 A Which of the following is true about cubic

numbers?

C

104 7 K 53 is equal to _________. 3+3+3 3x3x3 5x5x5 5+5+5 C

105 7 K 93=_______. 3+3+3 3x3x3 9+9+9 9x9x9 D

106 7 K The expression of 43=________. 4+4+4 3+3+3+3 3x3x3x3 4x4x4 D

107 7 K Which expression below has the same value as a3? 3a a/3 axaxa 3ax3ax3a C

108 7 K 223 is equal to _________. 22x22 44x22 66x22 484x22 D

109 7 K When x=2, what does x3 equal to? 6 8 9 23 B

110 7 K The value of (5)3 is _________. 15 25 125 243 C

111 7 K What is the cube of 6? 18 36 216 256 C

112 7 K Which of the following expresses 512? 63

73

83

93 C

b

a

b

a 33

baab 33

3

33

b

a

b

a

33aaa

11


S.N. Com-

peten-

cy No.

Level

(K or

A)


113 7 K If x=2.1 then what is the value of x3? 4.41 6.51 9.261 19.448 C

114 7 K If (4.37)3=83.453, then find (43.7)

3. 834.53 8345.3 83453 83453.453 C

115 7 K (2/3)3= _________. 2/3 4/9 6/9 8/27 D

116 7 K The value of (-3/4)3

is: -9/12 -27/64 -9/64 27/64 B

117 7 K What is the volume of a cube whose side is 2 cm? 4cm3

6cm3

8cm3

12cm3 C

118 8 K Which expression is true? (3/4)3=27/28 (-3)

3=2.7 (4/3)

3=64/125 B

119 8 K Which one is true about ? 3 is radicand Its value is 4 64 is the index It is square root of

64

B

120 9 K What is the cube root of 64? 2 4 8 16 B

121 9 K The cube root of 125 is _________. 5 25 225 475 A

122 9 K Calculate

=__________

5 7 9 11 B

3 64

4643

3 343

12


S.N. Com-

peten-

cy No.

Level

(K or

A)


123 9 K What is the cube root of 729? 8 9 11 12 B

124 9 K The cube root of 1000 is ________. 10 100 10000 100000 A

125 9 K The cube root of 0.064 is: 0.3 0.4 0.6 0.8 B

126 9 K is equal to _________. 0.0002 0.002 0.02 0.2 D

127 9 K The cube root of 1/27 is equal to ____________. 3 9 1/3 1/9 C

128 9 K The cube root of 1/27 is ________. 1/9 1/6 1/3 1/2 C

129 9 K What is the cube root of 1/64? 1/3 1/4 1/8 1/12 B

130 9 K The simplified form of is: 1/4 1/8 1/16 1/32 A

131 9 K Find the cube root of -1/1000. -1/1000 -1/100 -1/10 -1 C

3 008.0

3

64

1

13


S.N. Com-

peten-

cy No.

Level

(K or

A)


132 9 K Which of the following is the correct statement? D

133 9 K If x=27 and y=64, then the value of is

_______.

64/27 4/3 3/4 27/64 C

134 9 K The simplified form of is: 1/3 1/4 3/4 4/3 D

135 9 A The volume of a cube is 216cm3. What is the

length of each edge?

18cm 14.7cm 12cm 6cm D

136 9 A The volume of a cube is 27cm3. What is the length

of its edge?

27 18 9 3 D

137 9 A If the cube of a number is 64, what is its square

root?

16 8 4 2 D

3

y

x

3

3

64

1

27

1

9

1

27

13

8

1

64

13

5

1

25

13

36

1

216

13

14


S.N. Com-

peten-

cy No.

Level

(K or

A)


138 9 A Simplify x4

x3

x2 x D

139 9 A The simplified expression of is

___________.

D

140 9 A Find the value of y, if 12 9 6 5 D

312

15

x

x

233 y

15


S.N. Com-

peten-

cy No.

Level

(K or

A)


1 10 K Which one of the following is an algebraic

expression?

4x - 5 = 36 x+10<10 x+4>3x+10 9x+4+5x D

2 10 K From the given algebric expressions, which one is

monomial?

y-6 -6 x2+4xz B

3 10 K Which pair is unlike terms? -2yz and -3zy 8x3

and 12x3

6p3q

2and 4p

2q

34x

2y and 2yx

2 C

4 10 K What is the square of 6a? 6a2

62a 12a

236a

2 D

5 10 K The sum of a number (n) and 6 is 32. Which

equation shows this relation?

6+n=32 32n=6 6-n=32 32+n=6 A

6 10 K Semira has 5 more birr than Abebe. If Abebe has

P birr, which expression represents Semira's

amount?

P-5 P+5 5-P 5P B

7 10 K Five more than half of a number is _______. x+5 D

8 10 K The cube of a number decreased by 3 is ______. x3+3 x

3-3 x

3+a x

3-a B

9 10 K The difference between a mother’s age (x) and her

son (y) is 25. Which one is the correct relationship

between x and y?

x+y=25 y-x=25 x-y=25 x-2y=25 C

2

5x

2

5x 52

x

yx

1


S.N. Com-

peten-

cy No.

Level

(K or

A)


10 10 K The perimeter of a rectangular field with sides x

and x+2 is ______________.

4(x+1) 2(x+2) x2+2x 2x

2+4x A

11 10 K What is the length (l) of a rectangle if it is six less

than twice the width(w)?

2w+6 2w-6 6w+2 6w-2 B

12 10 K The perimeter of a rectangular field is 200 m. If

the length is y and width x, find the width x in

terms of y.

x =200 - y x = 100 - y x = 50 +y x = 50 - y B

13 10 K The sum of two consecutive even natural numbers

devided by three is equal to 6. Which of the

following is the correct representation of the

statement?

B

14 10 K Evaluate

where a=1 and b= -1

-1/8 1/8 8 -8 B

15 10 K The simplified form of

where a=-2

b=1 and c=4 is:

-8 8 12 16 B

16 10 A Abebe went to a shop to buy 6 packets of chewing

gum of the same kind with 3 birr each. He has 50

birr at hand. What is the expression that shows the

change (C)?

C = (6 × 3) + 50 (6 × 3) - C = 50 C = 50 - (6 × 3) C - (6 × 3) = 50 C

ba

ba

24

1

4

2 2

abc

ba2

2

4 2

63

2

n6

3

22

n6

3

12

n6

3

1

n

2


S.N. Com-

peten-

cy No.

Level

(K or

A)


17 10 A Desie bought 5 shirts and 4 ties. The cost of a tie

is 10 birr and the cost of a shirt is 15 birr. Which

equation can be used to find the total cost (c) of

the 5 shirts and 4 ties?

c=5x15 +4x10 c=5x10 +4x15 c=5x4 +10x15 5x5+4x4 A

18 10 A How much water is needed to fill a plastic cube

with length of sides x m?3x

3 m x m

3x

3m

3x

3m C

19 10 A ABCD is a rectangular field whose perimeter is

30m. If the length is given as x in the figure

below, express the width in terms of x.

w=15-x w=15+x w=30-x w=30+x A

20 10 A Each side of a square measures (3k+5) units.

Which of the following expresses the perimeter?

3k+9 7k+9 12k+5 12k+20 D

21 10 A The perimeter of the rectangle shown at the right

is 8a+4b. The width of the rectangle is 2a-2b.

Which of the following expressions represents the

length of the rectangle?

2a 2a+4b 4a+2b 6a+6b B

22 10 A Almaz squared a number 'x' and increased the

result by 12. The correct algebric expression is

_____________.

(x+12)2

x2-12 2x+12 x

2+12 D

3


S.N. Com-

peten-

cy No.

Level

(K or

A)


23 10 A A volleyball field is shaped like a rectangle. It has

a width of x meters and a length of 2x meters.

Which expression gives the area of the field?

3x square meters 6x square meters 2x2 square meters 3x

2 square meters C

24 10 A If mgh +5h2

= 5h, find the value of m in terms of g

and h.

D

25 10 A The parallel sides of a trapizium are b1 and b2

units long. Its area is A square units. What is its

height (h) in terms of area (A) and bases?

D

26 10 A From a given trapezium below, A=(b1+b2)h/2. b2

is expressed in terms of the other variables in the

formula for A(area) is ________.

D

27 10 A Which algebraic expression describes the area of

the square ABCD?x

2 + 2xy + y

2x

2 - 2xy + y

2x

2 - xy + y

2x

2 + 4xy + y

2 A

g

hm

1

h

gm

)1(5

h

gm

)1(5

g

hm

)1(5

123

5

n

4


S.N. Com-

peten-

cy No.

Level

(K or

A)


28 10 A Dividing a number by 3 and adding 5 to the result

give 12. Which of the following equations

matches the statement?

5=12+n/3 n/3 +5=12 3/n= 5 B

29 10 A The lengths of the sides of a triangle are

consecutive odd integers. If the perimeter of the

triangle is 27cm, what are the lengths of the sides?

9, 9, and 9 7, 9, and 11 8, 9, and 10 5, 7 and 15 B

30 11 K For x=12, 5(x-36)=_________. -120 24 36 120 A

31 11 K For c=4, 9c2=__________. 324 144 72 36 B

32 11 K If a=2, b=3, then what is the value of ? 14/2 7/2 7/4 14/6 B

33 11 K a-(b-c)=________. -ab+ac a-b-c a-b+c a+b+c C

34 11 K The simplified form of a(b+c) -ac is ________. ab ab-ac bc ab + ac A

35 11 K What is the product of 4a and 2ab? 4a/2ab 2ab/4a2

8a2b 2a(b+2) C

36 11 K Which one of the following is true for any three

rational numbers x, y, and z?

-x-(y-z)=-x-y-z x-(y+z)=x-y-z x-(y-z)=x-y-z x+(y-z)=x+y+z B

37 11 K The simplified form of x + (-x) + r is

__________.

2x + r r -xr + x xr + x B

a

ba

2

24

123

5

n

5


S.N. Com-

peten-

cy No.

Level

(K or

A)


38 11 K Simplify (3x+7y)+(2x-5y). 5x+2y 5x+12y 5x-2y 5x-12y A

39 11 K The simplified form of the expression 2x - 3(8x -

3) + 20x is _______.

2x - 9 46x - 9 -2x + 9 -4x - 9 C

40 11 K The simplest form of 3x + 4(7x + 5) is ______. 31x + 5 31x + 20 25x + 20 11x + 9 B

41 11 K The simplified form of 2x -5(3x + 2) is

_________.

-13x + 2 -13x -10 -23x -13x + 10 B

42 11 K Which expression is equivalent to the expression

2(4x + 2y) - 3(x + y) + 2(x - y)?

7x 7x - y 7x - 5y 7x + y B

43 11 K 2x-(8x-6w-6)-6w equals to _________. 6(w-1) 6(x-1) 6(1-w) 6(1-x) D

44 11 K Simplify 4(3a+b)-3(a+2b) = _________. 15a-10b 15a+10b 9a-2b 9a+10b C

45 11 K Simplified form of 3(2m+5n)+4(3m-2n) is

___________.

18m+23n 18m+7n 18m+3n 18m+7 B

46 11 K The simplified form for (2x-3)-(3x-9)+6 is

___________.

-4-x 12-x 5x-16 5x-4 B

47 11 K The simplified form of 5(x+1)-3(x-2) is

__________.

2x-1 8x-1 2x+11 8x+11 C

6


S.N. Com-

peten-

cy No.

Level

(K or

A)


48 11 K The simplified form of (2x-5y)-(3y+7x)-4y is

___________.

-5x-2y -5x-12y 9x-2y 9x-8y B

49 11 K The simplified form of 4(x-1)+3(x+2)=5(x-4) is

__________.

-12 -11 10 11 B

50 11 K When the expression 5k-(5k-[2k-(4k-8k)]) is

simplified, it gives ____________.

-6k -4k 4k 6k D

51 11 K What is the simplified form of 3x-5 [(2x+1)-(4-

x)]?

2x-15 15-2x 12x-15 15-12x D

52 11 K The simplified form of x/3 - [(x/5 + 1) - x] is

_______.

B

53 11 K The simplified form of -19b2a+9+14ab

2-3 is

______________.

ab2+1 -5ab

2+6 5ab

2+6 -5ab

2-6 B

54 11 K x2-8y

3+2x

2+5y

3 equals to _________. 3(xy)

23(xy)

33(x

2-y

3) 3(x

3-y

2) C

55 11 K (4x2-2x+8)-(x

2+3x-2)=__________. 3x

2+x+6 3x

2+x+10 3x

2-5x+6 3x

2-5x+10 D

56 11 K What is the simplified form of the following

equation?-2x

2/2 + 2x

2 + 10 10 + x x

2 + 10 -1/2x + 10 C

c

ab

2

2

15𝑥

17

15𝑥 − 1

−7

15𝑥 − 1

17

15𝑥 + 1

1022

20 2

2

x

x

7


S.N. Com-

peten-

cy No.

Level

(K or

A)


57 11 K For a, b, and c≠0, simplify A

58 11 K Which one of the following is the simplest form of

3x + (-6x/2) + (-12x/2) ?

12x -6x -3x - (12x/2) C

59 11 K Simplify x(y+z) y(x+z) z(x+y) A

60 11 K The simplified form of is: 2x4 B

61 11 K The simplified form of is

_____________.

x+3 x+2 6 3 A

62 11 K What is reduced to lowest term? a/2 D

63 11 A If x≠0, the quotient of (15x2

+ 30xy) ÷ 5x is

_______.

9xy 90y 3x + 6y D

ababbc

ab

2

1

2

4 3

c

ab2c

ab 2

c

ab

2

3

c

ab

2

44

3

4

3

4

xzxyxz

xy 4

yzx

aa

aa

816

20122

23

12

53

a

a

a

a

24

2

122

53

a

aa

7

3

10

5

x

x42

1

x 45

1

x 5

4x

x

yx

5

63

12

1266 xxx

8


S.N. Com-

peten-

cy No.

Level

(K or

A)


64 11 A Evaluate values from the table into the expression

and simplify

= ______

72 82 92 94 C

65 11 A Solve the value of Z, if x=3 and y=1. 0 1 2 4 A

66 11 A Add 7 to x, double what you get, then subtract 3

from the result. The simplified form of this

expression is _________.

2x+14 2x+11 x+11 2x-11 B

67 12 A A 12 meter rope is to be cut into two pieces so that

the longer piece is 3 times the shorter. Find the

length of the shorter rope.

3 meter 4 meter 6 meter 9 meter A

68 12 A The sum of two consecutive odd integers is 20.

Then find the two numbers.

7 and 13 5 and 15 9 and 11 3 and 17 C

69 12 A The sum of two consecutive odd integers is 44.

Find the integers.

13 and 31 11 and 33 21 and 23 5 and 39 C

70 12 A If the sum of two consecutive even integers is 90,

what are the integers?

40 and 50 45 and 45 44 and 46 42 and 48 C

2222 yxz

d

bca 2

a b c d

4 5 6 2

9


S.N. Com-

peten-

cy No.

Level

(K or

A)


71 12 A The sum of three consecutive integers is 63. What

is the smallest of the three integers?

21 20 19 18 B

72 12 A If the sum of three consecutive intergers is 153,

then what are the integers?

47, 52 and 54 48, 51 and 54 49, 50 and 54 50, 51 and 52 D

73 12 A The cost to rent a car is given by the expression

20x + 0.75y, where x is the number of days and y

is the number of kilometers. If Mr. Abedela rents

the car for 6 days and drived 1200 kilometers,

what will be the cost in birr?

920 birr 1,000 birr 1,020 birr 1,040 birr C

74 12 A Ahmed is 8 years older than Belete. Seada is 2

years younger than Belete. If the sum of the three

ages is 36, how old is Belete?

8 9 10 12 C

75 12 A The age of a mother is 20 years more than her

daughter's age. What is the age of the mother

when her daughter is 11 years old?

9 20 31 42 C

76 12 A The father's and his son's ages are in the ratio of

5:2 now. If the age of the father at the time of son's

birth was 18 years, then find the age of son.

18 16 15 12 D

77 12 A The sum of two numbers is 45 and their difference

is 25. What are the numbers?

20 and 25 35 and 10 30 and 15 40 and 5 B

10


S.N. Com-

peten-

cy No.

Level

(K or

A)


78 12 A The perimeter of a rectangular football playing

field is 400m. If the length is given by a, then find

the width in terms of a.

400-2a 400-a 200-2a 200-a D

79 12 A If the perimeter of a football field is 360m and the

length is 40m longer than the width, what are the

length and the width?

90m and 40m 110m and 70m 120mand 60m 150m and 10m B

80 12 A Ato Tolessa's monthly expenses in terms of x are;

Birr x for house rent, Birr 2x for household and

Birr

for recreation. How much does he spend for house

rent if his salary is Birr 6500?

Birr 3,250 Birr 2,167 Birr 2,000 Birr 1,625 C

81 12 A A shop keeper buys 25kg of Potato at Birr x per

kg. If he sells 15kg at Birr (x+1/2) per kg and the

rest at Birr (x+2) per kg, how much did he profit?

Birr 17.50 Birr 25.00 Birr 27.50 Birr 37.50 C

82 12 A A 120 meter-long rope is cut into 3 pieces. The

first piece of the rope is twice as long as the

second piece of the rope. The third piece of the

rope is three times as long as the second piece of

rope. What is the length of the longest piece of

rope?

20m 40m 60m 80m C

83 12 A If a, b and c are odd integers, which of the

following expressions must be an even integer?

a+b+c a(b+c) b(a+c)+ac a(b+c-a) B

x4

1

11


S.N. Com-

peten-

cy No.

Level

(K or

A)


84 12 A The following isosceles triangle has 16cm

perimeter. Then solve for x.

4cm 6cm 8cm 12cm B

85 12 A Three metal rods with lengths of R1=x+4, R2=x-

1, and R3=x are arranged as below. What is the

length 'y'?

x+3 x+5 2x+4 3x-3 B

86 12 A What is the volume of a cube shown below? x2-3x

2+3x-1 x

3-3x

2+3x-1 x

3+3x

2-3x-1 x

3+3x

2+3x-1 B

87 13 K The product of 2x and 4x+3 is ________. 8x+6 8x+6x 8x2+6 8x

2+6x D

88 13 K Simplify the following product (2ab2)(2a-3b). 4a

2b

2+6ab

24a

2b

2+6ab

34a

2b

2-6ab

34a

2b

2+2ab C

89 13 K The product of 3x(2x2-1) is _________. 6x

2-3x 6x

2-1 6x

3-3x 6x

3-1 C

12


S.N. Com-

peten-

cy No.

Level

(K or

A)


90 13 K The products of 3x(2y-4x) is __________. 6xy-12x2

5xy-7x2

3xy-4x2

2xy-3x2 A

91 13 K The product of (-4+2a)(-3ab2) is _________. 12ab

2+6a

2b

212ab

2-6a

2b

26a

2b

2-12ab

2 -3ab

2 + 2a B

92 13 K The simplified form of 4x(y-x) -3y(x-y) is: -4x2-3y

2+xy -4x

2+3y

2+xy 4x

2+3y

2+7xy 4x

2-3y

2+xy B

93 13 K The simplified form of 4(3x+y)+3(2x-5y) is: 18x-11y 18x+11y 12x-4y 12x+4y A

94 13 K Find the product of x2 and (xy)

3. (xy)

5x

3y

5x

5y

3 xy C

95 13 K The product of (x3) and (xy

4) equals to ______. x

3y

4x

4y

4x

4y

7x

3y

7 B

96 13 K The product of (3x4) and (y

2+x) is: 3 x

2y

2+3x

43 x

4y

2+3x

53 x

6y

2+3x

43 x

8y

2+3x

5 B

97 13 K The product of 2x and is

_________.xy

2+x x

2y+x xy+x xy+y C

98 13 K The product of (3/4x2) (2x+4) is _________. 3/2x

2 +4 2x

3 +3 3/2x

3 +3x

23/2x

3 +4x

2 C

99 13 A The product of 6p2 and 9abp-6a

2bp is

__________.

54p3-36p

3a

2b 54p

3ab-36p

3a

2b 54p

3a+36p

3a

2b 54p

3ab+36p

3a

2b B

100 13 A The result of

is:

16x5

+ 4x3

4x6

+ 2x2

4x5 +2x

34x

5 + 4x

3 C

2

1y

2x2 8x3 + 2x( )

13


S.N. Com-

peten-

cy No.

Level

(K or

A)


101 13 A The length of a rectangular plot of land is x meters

and its width is 3 meters less than the length.

What is the area of the land?

(x2

- 3x)2m

2(x

2 - 3)m

2(x - 2)

2m

2(x

2 - 3x)m

2 D

102 13 A The length of a football field is P meters and its

width is 30 meters less than the length. What is the

area of the field in m2 if P = 100 meters?

10000 m2 9970 m2 9910 m2 7000 m2 D

103 13 A The height (h) of a parallelogram is 6 less than its

base (b). What is the area (A) of the

parallelogram?

6b2

+ b 6b2

- b b2

+ 6b b2

- 6b D

104 13 A A rectangular assembly hall has a dimention of its

length to its width is 2:3. The perimeter of the hall

is 30 units. What is its area?

15sq. units 36sq. units 54sq. units 60sq. units C

105 14 K The product of (3x+4) and (2x-3) is

___________.6x

2-x-12 6x

2+x-12 6x

2-x+12 6x

2-17x-12 A

106 14 K Multiply (2x-18) by (x+3). 3x-15 2x2-12x-54 2x

2-18x+54 2x-21 B

107 14 K The product of (3x-2)(2x+6) is ___________. 6x2+14x -12 6x

2+12x 6x

2+18x -12 6x

2 -12 A

108 14 K The product of (2x+1)(1-x) is _________. -2x2-x+1 -2x

2+x-1 -2x

2+x+1 -2x

2+3x+1 C

109 14 K The equivalent algebric expression of (3a+2b)(2a-

3b) is ____________.-5a

2b

26a

2 -6b

26a

2+13ab+6b

26a

2-5ab-6b

2 D

14


S.N. Com-

peten-

cy No.

Level

(K or

A)


110 14 K Which of the following is the correct product of (-

3x +2y)(3x-2Y)?9x

2-4y

2+12xy -9x

2 + 4y

2 + 12xy -9x

2-4y

2+12xy -9x

2-4y

2-12xy C

111 14 K The product of (x2-5) and (2x+4) is

___________.

2x3+4x

2+10x+ 20 2x

3+4x

2-10x+ 20 2x

3+4x

2-10x- 20 2x

3+3x

2-3x+ 1 C

112 14 K Find (5/4 + 3a/4) (2a+3). 5a2/4 + 7a + 15/4 3a

2/2

+ 14a/4 +

15/4

3a2/2

+ 19a/4 +

15/4

3a2/2

+ 14a/6 +

15/4

C

113 14 K Which one of the following is a product of D

114 14 K The product of is _______. B

115 14 K (x+1) (x-1)=_________ x2+2x+1 x

2-2x+1 x

2+1 x

2-1 D

116 14 K What is the product of (a+2) and (a-2)? a2+4 4-a

2a

2-4 (a-2)

2 C

117 14 K Which one is the product of (3x+3y)(3x-3y)? 9x2+9y

29x

2-6y

29x

2-9y

29x

2+6y

2 C

x

4+x

4

æ

èç

ö

ø÷x

4-x

2

æ

èç

ö

ø÷

8

x

8

2x

8

x

8

2x

4222

xxxx2

2x

2

2x

4

2x

4

2x

15


S.N. Com-

peten-

cy No.

Level

(K or

A)


118 14 K When (x/4 + x/2) is multiplied by (x/4-x/2) the

result is __________.

C

119 14 K Simplify (a2-ab)(a

2+ab). 2a

2- a

2b

22a

2- ab a

4- ab a

4- a

2b

2 D

120 14 K What is the product of 3a-b and b+3a? 9a2-6ab-b

29a

2-b

23a

2-6ab-b

23a

2-b

2 B

121 14 K If A=(x+y) and B= (2x3-y) then AB=________. 2x

3+x 2x

4 - y

22x

3y - xy 2x

4 + 2x

3y - y

2 -

xy

D

122 14 A If p2+q

2=25 and pq =12 then (p+q)

2 is

_________.

5 24 37 49 D

123 14 A If a2+b

2=80 and (a-b)

2=16 then what is the value

of ab?

12 24 32 64 C

124 14 A If ab = 12 and a² + b² = 25, then what is the value

of (a-b)²?

1 13 37 49 A

125 14 A If (a+b)=6 and (a-b)=-2 then a2

- b2=________. -12 4 8 12 A

16


S.N. Com-

peten-

cy No.

Level

(K or

A)


126 14 A The figure to the right represents a rectangle with

lengths of sides shown. What is its area if x = 3?

25 30 36 54 B

127 14 A School A has a rectangular shape compound with

length x + 2 and width .

What is the area (A) of the school compound?

C

128 14 A The length of a rectangular floor is x meters and

its width is y meters. What will be area of the

floor, if the length is increased by 3 meters and the

width by 2 meters?

(xy + 5xy + 6) m2 (xy + 2x +3y +5)

m2

(xy2

+ 2x + 3y + 6)

m2

(xy + 2x + 3y + 6)

m2

D

129 14 A The total surface area of a box with sides x, x+2,

and x+3 is __________.6x

2+20x+12 8x

2+10x+12 24x

2+20x+12 6x

2+10x+12 A

130 14 A The sum of two binomials is 5b2-6b. If one of the

binomials is 3b2-2b, what is the other binomial?

2b2-4b 2b

2-8b 8b

2+4b 8b

2-8b A

131 15 K Find the HCF of the numbers 24 and 18? 4 6 8 12 B

2

1x

17


S.N. Com-

peten-

cy No.

Level

(K or

A)


132 15 K Find the highest common factor of the following

termss: 233

2 and 2

23

3

24 18 36 72 C

133 15 K The highest common factor of 3x2 and 9x is

_________.

x3

3x2 27x 3x D

134 15 K What is the highest common factor of x4 and 4x? x x

2x

3x

4 A

135 15 K What is the highest common factor of the

expressions 15x³ and 5x?

5x 5x² 5x³ 5 A

136 15 K The highest common factor of 8a2 and 12b

2 is

_________.

2 4 2ab 4ab B

137 15 K The highest common factor of 20x3 and 4x

2 is

__________.

1 5x 4x2

20x3 C

138 15 K The highest common factor of the algebraic

expressions of 6x³ and 9x² is __________.

3x 3x² 6x 6x² B

139 15 K The highest common factor of x3/4 and x

5/6 is

__________.

x/2 x2/3 x

2/2 x

3/2 D

18


S.N. Com-

peten-

cy No.

Level

(K or

A)


140 15 K Which one of the following is HCF of 6x, 15x²

and 18x³?

18x 15x 6x 3x D

141 15 K Find the highest common factor of the following

terms. 4x3y, 6xy

3

2x2y 2xy 2xy

22x

3y

3 B

142 15 K Which of the following is the HCF of 4a2x

2y

3 and

8ax3y

2?

ax2y

22ax

2y

23ax

2y

24ax

2y

2 D

143 15 K Find the Highest Common Factor of 6ab4c

3 and

2a4b

2c

2.

2ab2c

2 2abc 2a2b

2c

22a

4b

4c

3 A

144 15 K What is the highest common factor of 6a2b

2 and

15ab2?

3ab2

5a2b

26a

2b

39ab

2 A

145 15 K The highest common factor of 27x3y

2z and 9x

2y

5

is __________.

9x2y

29x

2y

2z 27x

3y

527x

3y

5z A

146 15 K Find the Highest Common Factor of 6ab4c

3 and

2a4b

2c

2.

2ab2c

2 2abc 2a2b

2c

22a

4b

4c

3 A

19


S.N. Com-

peten-

cy No.

Level

(K or

A)


147 15 K The highest common factor of

and

D

148 15 K Which of the following is the Highest Common

Factor of 9x2-3y and 3x+3y?

-9 -3 3 9 C

149 15 K The highest common factor of 8(m+5) and -

3n(m+5) is ____________.

8-3n m+5 3mn 24n B

150 15 K The highest common factor of 21a(a-3) and 7a2(a-

3) is ____________.

(a-3) (3-a) 7a(a-3) 7a(3-a2) C

151 15 A The simplified form of is ______. 16 32 64 128 D

152 15 A If LCM (x, 20)=60 and GCF (x, 20)=x-4, then

what is the value of x?

6 10 30 40 A

153 16 K Factorize 6x2+3x. 3x(2x+1) 3x(2x-1) 3x(-2x-1) 3x(-2x+1) A

154 16 K The expression 3a2b

2+4a

3b

3 is equivalent to: a

2b(3+4ab) b

2(3a+4ab) a

2b

2(3+4ab) a

2b

2(3a+4ab) C

aca

19

12

acb

19

32

a2

19

b2

19

3

19

2

4

33

2

1

2

1.2.4

20


S.N. Com-

peten-

cy No.

Level

(K or

A)


155 16 A The expression a2(a+2)-a(a+2) is equivalent to the

expression:

(a+2)(a-1) a(a+1)(a-1) a(a+2)(a-1) a(a+2)(a+1) C

156 16 A The expression x2(x+4)-x(x+4) is equivalent to

the expression ______________.

(x+4)(x-1) x(x+1)(x-1) x(x+4)(x-1) x(x+4)(x+1) C

157 16 A Which pair of binomials are factors of x2-1? (x+1) and (x+1) (x-1) and (x-1) (x+1) and (x-1) (x+1) and (1-x) C

158 16 A The factor form of x2 + x - 6 = _______. (x+3) (x-2) (x+3) (x+2) (x-3) (x-2) (x+2) (x+1) A

159 16 A Which one is a factor of a2-11a+24? a+3 a-3 a+4 a-4 B

160 16 A Which is the factorized form of 3a2-24ab+48b

2? (3a-8b)(a-6b) (3a-16b)(a-3b) 3(a-4b)(a-4b) 3(a-8b)(a-8b) C

161 16 A If the area of a rectangle is given as x2

+ 3x for

x>0, what are the dimensions of the rectangle in

terms of x?

x2

and 3x x+3 and x+3 x and x+3 x2

and 3 C

162 16 A Gebru's solution to an equation is shown below.

given: x2+5x+6=0

step 1: (x+2)(x+3)=0

step 2: x+2=0 or x+3=0

step 3: x= -2 or x= -3

Which property of rational numbers did Gebru use

to move from step 1 to step 2?

Multiplication

property of

equality

Zero product

property of

multiplication

Communicative

property of

multiplication

Distributive

property of

multiplication

B

21


S.N. Com-

peten-

cy No.

Level

(K or

A)


1 17 K The value of x in 2(x-3)=6 is _________. 6 2 3 -6 A

2 17 K The solution set of the equation 8+2(x-5) = 14 is

_______.

{11/2} {6} {8} {17/2} C

3 17 K Solve the equation 5(x-3)=35. -10 10 12 14 B

4 17 K If -(2x+1)=3 then what is the value of x? -1 -2 1 2 B

5 17 K Solving the equation 4(3x-8)=-8, the solution is

____________.

x=-1 x=-2 x=1 x=2 D

6 17 K The solution set of the equation 2(3-4x)=5(7-3) is

________.

{-4/7} {-7/4} {4/7} {7/4} B

7 17 K In the equation 5x-10-2x=12x-3x-4, the value of x

is _______.

x=2/3 x=8/3 x=-1 x=4 C

8 17 K Find the solution of 2(3-x)=3(2x-10). -9 -9/2 9/2 9 C

9 17 K The solution set of the equation 3(x+2)+14=5(x-4)

is ________.

{13} {17} {18} {20} D

10 17 K The solution set of the equation 5x+5(4-2x)=0 is

_______.

T.S={18} T.S={12} T.S={5} T.S={4} D

11 17 K Solve the equation 3(3k-6)=2(2k-4). 1 -1 2 -2 C

12 17 K Solve the equation 5(2x-3)-6x=9 for x. x= -6 x= -3/2 x= 3/2 x= 6 D

13 17 K The value of x for the equation 2x+2(2x-2)=2-

3(x-1) is ________.

1 3 4 9 A

1


S.N. Com-

peten-

cy No.

Level

(K or

A)


14 17 K Solve the following equation using the

transformation rule. What is the value of x?

x+3(x-1)=4-2(x+2)

x=2 x=1 x=1/2 x=1/3 C

15 17 K Solving the equation 10(1-2x)-6(4x+4)=0 gives

x=_____.

x=-17/2 x=-7/2 x=-7/22 x=17/22 C

16 17 K Solve the equation 3(7-2x)=14-8(x-1). 1/2 2/3 5/2 7/2 A

17 17 K The value of x for the equation 5(x-1) + 3(x+3) =

6(x+5) is _______.

-17 -13 13 17 C

18 17 K Solve the linear equation -2(x+2)-3(1-x)=7x-(4-

3x).

1/3 3 -1/3 -3 C

19 17 K What is the solution of 2(3x-1/2)-1/4(8-4x)=-2? {1/7} {5/7} {5} {7} A

20 17 K The solution set of the equation 1/4(2x-4) +

1/8(4x+8) = 2x+3 is ________.

{3} {2} {-2} {-3} D

21 17 K Which one of the following is true if A=B? A+C=B+C A-C=B+C AC=B+C A/C=BC C≠0 A

22 17 A The solution set of the equation ax+b=0 is

_________.

{x:ax=-b} {x:x=-b/a} {x:x=a/b} {x:x=b/a} B

23 17 A In the formula below, find a formula for F in terms

of C.

C

2


S.N. Com-

peten-

cy No.

Level

(K or

A)


24 17 A Solve for x in terms of a and b, if a≠b.

a(2x-3)-bx=3b(1-x)

3/2 2/3 C

25 17 A Girma solved the equation 2(3x-7)=10 using the

following steps.

Given 2(3x-7)=10

Step 1: 6x-14=10

Step 2: 6x=24

Step 3: x=4

To move from step 2 to step 3 Girma

_______________.

added 6 to both sides subtracted 6 from both

sides

multiplied both sides

by 6

divided both sides by

6

D

26 17 A In the fiigures shown below, the rectangle and

equilateral triangle both have the same perimeter.

Determine the value of x.

6 5 4 3 D

27 18 K If x/4=5/2, then what is the value of x? 1/10 5/8 10 20 C

28 18 K If what will be the value of x? 15 16 21 26 B

29 18 K Find the solution set of {1} {1/2} {-1} {-1/2} C

30 18 K Evaluate the value of x in the equation 5/2 x - 1/3

= 6.

5/2 2/5 15/38 38/15 D

ba

ba

42

33

ba

ba

42

33

73

5

x

3


S.N. Com-

peten-

cy No.

Level

(K or

A)


31 18 K Which one is the value of x in the equation

-x/2+10=20?

-10 -20 10 20 B

32 18 K What is the least common denominator of : 6 18 36 216 C

33 18 K Given x/8 + x/6 = 1, what is the value of x? 1/14 14 7/24 24/7 D

34 18 K Solve the following equation: -5/6 -6/7 -3 -5/3 B

35 18 K Solve the following equation -4 -2 2 4 A

36 18 K What is the solution to the equation x= -10 x= -3 x= 6 x= 9 A

37 18 K Solve -3 -1 1 3 A

38 18 K Solve -8 -7 5 8 C

61812

1

xx

55

2

10

4

5

2 xx

44

32 xx

?43

22

3

1

xx

4


S.N. Com-

peten-

cy No.

Level

(K or

A)


39 18 K The solution set of the equation

is ___________.

{3/2} {2/3} {3} {4} A

40 18 K Solve 10 12 14 15 A

41 18 K Solve for x. -12 -4 4 12 C

42 18 K The solution set of the equation

is

{-31/3} {-25/3} {5/3} {14/3} C

43 18 K The solution of the equation

is

x=51/7 x=69/7 x=83/7 x=59/2 C

44 18 K If

then what is the value of x?

-33 -25 25 33 A

45 18 K Find the solution set of the equation: {-1} {1/2} {1} {3/2} C

05

2

4

5

xx

2

4

3

12

xx

65

4

2

3

xx

23

52

5

23

xx

x

3+

7+ 4x

2= 7

5


S.N. Com-

peten-

cy No.

Level

(K or

A)


46 18 K Solve -2/3 -3/2 2/3 3/2 D

47 18 K Solve the following equation: -50 -25 -25/2 25 D

48 18 K Solve the equation 7/2 7/3 7/5 7/6 B

49 18 K Solve {1/3} {-1/3} {-1/2} {1/2} C

50 18 K Find the solution of the equation: -16/5 -8/7 8/7 16/5 D

51 18 A What is the value of h, if -2 -1 1 2 D

52 18 A In the equation below, what is the value of b when

a = 9?

63/8 6 27/4 9 A

53 18 A The equation 2x+7+x= 4x-x+25 has __________. one solution two solutions no solution infinitely many

solutions

C

132

12

4

12

xxx

1842

3 ba

4

4

4

6

2

212

xxx

6


S.N. Com-

peten-

cy No.

Level

(K or

A)


54 18 A If I solve as follows.

Step 1. 2-x/2-x=-3/2

Step 2. -3/2x= -3/2 -2

Step 3. -3/2x= -7/2

Step 4. x=-7/3

In which step does my work become wrong

(incorrect)?

Step 1 Step 2 Step 3 Step 4 D

55 19 A A machine takes a minute to produce 60 mobile

phones. How long would the machine take to

produce 300 mobile phones?

3 min 4 min 5 min 6 min C

56 19 A A machine grinds 5 kilograms of coffee in 2 ½

minutes. How many minutes will it take to grind

50kgs of coffee?

12 min 20 min 25 min 30 min C

57 19 A Eight less than half of a number is 16 . What is the

number?

12 16 24 48 D

58 19 A Six times a number increased by seven times the

number equals to 39. What is the number?

9 6 4 3 D

59 19 A When you multiple a number eight times and then

add 4, you obtain 60. What is the number?

6 7 8 9 B

60 19 A Subtracting 5 from a number x and multiplying

the result by 7 gives 14. What is the number x?

-3 -7 7 19/7 C

2

32

22

xx

7


S.N. Com-

peten-

cy No.

Level

(K or

A)


61 19 A 67 decreased by twice a number is 39. Then what

is the value of that number?

28 21 14 13 C

62 19 A I thought of a number, doubled it then added 2.

The result multiplied by 2 becomes 24. What is

the number I thought of?

2 3 4 5 D

63 19 A I think of a number. I multiply it by 4 and subtract

6. My answer is 14. What number am I thinking

of?

4 5 6 8 B

64 19 A Find a number such that ten times the number

equals four times the number increased by 12.

2 4 10 12 A

65 19 A A number is doubled and then increased by seven.

The result is ninety three. What is the original

number?

40 42 43 48 C

66 19 A 24 less than 3 times a number itself is equal to the

number. What is the number?

8 12 21 27 B

67 19 A Find the sum of three consecutive odd numbers

whose sum is 45.

9, 13, 19 13, 15, 17 13, 15, 19 13, 17, 19 B

68 19 A Half the sum of two consecutive even natural

numbers is 13. What is the smallest number?

10 12 14 26 B

69 19 A The sum of three consecutive odd numbers is 81,

then what are the numbers?

13, 15, 17 25, 27, 29 23, 25, 27 15, 17, 19 B

8


S.N. Com-

peten-

cy No.

Level

(K or

A)


70 19 A The sum of the three consecutive odd numbers is

69. What is the largest among the three?

25 27 29 33 A

71 19 A The sum of three consecutive numbers is 180.

What are the numbers?

57, 58, 59 58, 59, 60 59, 60, 61 60, 61, 62 C

72 19 A x is the largest of four consecutive odd integers.

What is their sum in terms of x?

4x+12 4x+8 4x-8 4x-12 D

73 19 A The sum of five consecutive integers is 270. What

are the integers?

49, 53, 55, 56 and 57 50, 51, 54, 55, and 60 50, 52,54, 56 and 58 52, 53, 54, 55, and 56 D

74 19 A Find three consecutive even integers whose sum is

-12.

-2, -4, -6 -4, -6, -8 2, 4, 6 4, 6, 8 A

75 19 A Two third of the sum of two consecutive natural

nymbers is 6. What are the numbers?

2 and 3 4 and 5 5 and 6 6 and 7 B

76 19 A The sum of two natural numbers is 30 and one

number is 6 more than the other. Then what are

the numbers?

10 and 20 11 and 19 12 and 18 13 and 17 C

77 19 A The sum of two numbers is 45 and their difference

is 13. Then what are those numbers?

25 and 20 32 and 13 29 and 16 26 and 19 C

78 19 A The sum of two numbers is 36. If the bigger

number is divided by the smaller one, the quotient

is 3. Then the product of the numbers is

________.

243 324 423 432 A

9


S.N. Com-

peten-

cy No.

Level

(K or

A)


79 19 A The sum of two numbers is 45. If the biggest of

the two numbers is divided by the smaller one, the

quotient is 2. What is the multiple of these two

numbers?

450 600 675 1350 A

80 19 A In a class there are 65 students. The number of

boys is 5 more than 3 times the number of girls.

How many boys are there in the class?

15 45 50 55 C

81 19 A How many boys are there in a class of 36 students,

if the number of girls is 6 more than the boys?

6 15 21 42 B

82 19 A The sum of the ages of a father and his son is 48

years. The father is 22 years older than his son.

How old is the father?

28 years 32 years 35 years 40 years C

83 19 A Amare is 8 years older than his wife. The sum of

their ages is 60 years. How old is his wife?

26 years 30 years 34 years 52 years A

84 19 A The sum of the ages of a boy and his sister is 56

years. The boy is 8 years older than his sister.

How old is he?


85 19 A The sum of ages of a boy and a girl is 49. The boy

is 3 years older than the girl. How old is the girl?

20 years 23 years 26 years 46 years B

86 19 A The age of a boy is 2 times a girl's age and the sum

of their ages is 27. What is the age of the girl?

27 years 18 years 13 years 9 years D

10


S.N. Com-

peten-

cy No.

Level

(K or

A)


87 19 A At present, a man is 3 times as old as his son. In

11 years time he will be twice as old as his son

will be. What is the man's present age?


88 19 A A man has a weight of x kg and his wife's weight

is 2/3 of him. If the weight of his wife is 48kg then

the weight of the man is ______.

48kg 72kg 88kg 96kg B

89 19 A Henok goes to supermarket to buy two things.

Their prices are in the ratio of 7:2. The price of

one good is greater than the second one by 20 birr,

then what are the prices of the goods?

20 and 8 28 and 8 28 and 20 40 and 8 B

90 19 A The length of a rectangle below is 2cm longer than

the width. If the perimeter of the rectangle is

16cm, what is the length of the rectangle?

3cm 5cm 6cm 7cm A

91 19 A The length of the sides of a triangle are y, y+1,

and 7 cm. If the perimeter is 56cm, what is the

value of y?

24 25 31 32 A

92 19 A The length of the rectangle is twice its width. If

the perimeter is 36 cm, find its length (l) and

width (w).

l=4 w=12 l=6 w=12 l=12 w=6 l=14 w=8 C

93 19 A Semira divided a number by 8 and subtracted 11

from the result. Her answer is 4. Which equation

did Semira use?

B

48

11

n411

8

n411

8

n4

811

n

11


S.N. Com-

peten-

cy No.

Level

(K or

A)


94 19 A The linear equation y = 6x represents the total km,

y, Abel runs after 'x' number of days. How many

kilometers Abel runs after 3 days?

3 km 6 km 12 km 18 km D

95 19 A The total cost (c) in Birr of renting a car for n days

is given by the equation c=120+60n. If the total

cost was 360 Birr, how many days was the car

rented for?

2 4 6 8 B

96 19 A The cost in Birr for a farmer to buy "X" number of

chickens is given by the equation C= 2x+30.

How much does it cost to buy 76 chickens?

68 152 182 212 C

97 19 A A man buys 30 kg of salt at birr x per kg and sells

20kg at birr(x+1/2) per kg and the rest at birr

(x+3/4) per kg. Find his profit in Birr.

5/4 15/2 25/2 35/2 D

98 19 A In Semera the temperature at noon was 40 degree

celcius (oC). What was the temperature in degree

fahrenheight (oF)? [

oF=9/5

oC +32]

40 78.4 104 129.5 C

99 20 K What is the solution for the inequality 2x>5? {x: x>5/2} {x: x>- 5/2} {x: x<5/2} {x: x< -5/2} A

100 20 K If x+1≥3 then what is the value of x? x≥1 x≥2 x≤1 x≤2 B

101 20 K The solution set of the inequality 2x-7 <5 is

___________.

{x: x<1} {x: x<-1} {x: x<6} {x: x<10} C

12


S.N. Com-

peten-

cy No.

Level

(K or

A)


102 20 K The solution set of the inequality 8x+1<-7 is

________.

{x>1} {x<-1} {x>-1} {x<1} B

103 20 K Solve the inequality 3x-8≤30. x≥ 38/3 x≥ -38/3 x≤ 38/3 x≤ -38/3 C

104 20 K Find the solution set of 12-4x≤30. {x: x≥ 4} {x: x≥ -4} {x: x≥ -4.5} {x: x≤ -4.5} C

105 20 K If 8y+3>9y-14, then y is _______. y=17 y≥17 y<17 y>17 C

106 20 K Solve 3x-2(2x-7)≤2(3+x)-4. x≤4 x≥4 x≥-4 x≤-4 B

107 20 K What is the value of x if 3(x+2)-(5x-1)≤ (5x-1)-

2(x+6)?

x< -4 x≤ -4 x> 4 x≥ 4 D

108 20 K What is the solution to -x/2 -4 >16? x> -24 x>40 x<24 x<-40 D

109 20 K The solution set of the inequality 2(x-5) ≥ 1/4(3x-

5) is ________.

{x: x≤-5} {x: x≥0} {x: x≥7} {x: x≥9} C

110 20 K Find the solution set of 1/3(2x-1)<1/2(x-1). {x| x<1} {x| x>1} {x| x< -1} {x| x> -1} C

13


S.N. Com-

peten-

cy No.

Level

(K or

A)


111 20 K What is the value of x, if ? x≥4/5 x≤4/5 x≥5/4 x≤5/4 A

112 20 K Which one is the solution of 4x-1≥-13, xЄ N? {-3, -2, -1, 0, 1 ...} {0, 1, 2, ...} {1, 2, 3, ...} { -2, -1, 0, 1, 2 ...} C

113 20 K What is the solution set of the inequality 5t+5≤35,

tЄW?

{0, 1 ,2, 3, 4, 5} {1, 2, 3, 4, 5, 6} {0, 1, 2, 3, 4, 5, 6} {0, 1, 2, 3, 4, 5, 6, 7,

8}

C

114 20 K The solution set of the inequality x-4≥1, xЄZ, is

________.

{4, 5, 6, 7, …} {5, 6, 7, 8, ….} {6, 7, 8, 9, …} {7, 8, 9, 10, …} B

115 20 K What is the solution set of 6x+4 < 4x+12?

Domain= {… -1, 0, 1,…}

{1, 2, 3} {…, 1, 2, 3} {5, 6, 7} {5, 6, 7, …} B

116 20 K Solve the inequality 11x-8≥ 12+x, xЄZ {3, 4, 5, ….} {2, 3, 4, …} {…, 0, 1, 2} {-2, -1, 0, 1 ,2, ….} B

117 20 A Solve the inequality {0, 1, 2, 3, 4, 5} {…-2, -1, 0, 1, 2, 3,

4}

{…-2, -1, 0, 1, 2, 3, 4,

5}

{0, 1, 2, 3, 4} D

118 20 A What is the solution set of {0, 1, 2, 3} {0, 1, 2} {1, 2, 3} {1, 2} D

119 20 A The solution set of the inequality x/2-(x-1)≥

3/2(x-1) in xЄW is ________.

{0, 1} {1} {0, 1, 2} {0, 1, 2, 3, ….} A

3

1

21

xx

Zxxxx

,4

2

32

5

14


S.N. Com-

peten-

cy No.

Level

(K or

A)


120 20 A What is the solution set of the inequality 4(3x-

0.25) ≥15x, xЄW?

{0} {0, 1} {1} ᴓ D

121 20 A The solution set for 2x-11<5 in graphic form is

__________.

C

122 20 A Eight less than three times a number is greater

than fifteen. Which inequality is correct?

3x-8>15 3x-8<15 8-3x>15 8-3x<15 A

123 20 A Pass mark of mathematics subject is 50 out of 100.

If the first test' score was 15 out of 40, what

should be the final test's mark out of 60 to pass?

Use x out of 60.

x≥50 x≥40 x≥35 x≥33 C

124 21 K Given -2 (2x-7) >2,

step 1: -4x+14>2

step 2: -4x >2-14

step 3: -4x> -12

step 4: x> 3

Which operation is NOT CORRECT?

Between Given and

step1

Between step1 and

step2

Between step2 and

step3

Between step3 and

step4

D

125 21 K If -2x≤6 then what is the value of x? x≤-3 x≥-3 x≤3 x≥3 B

126 21 K Solve -3x-3<6. {x: x> -3} {x: x< -3} {x: x≥ 3} {x: x≤ 3} A

127 21 K Which value of x is in the solution set of the

inequality -4x+2 > 10?

3 2 -2 -4 D

128 21 K What is the solution of 2-4x>3x-5? x<1 x<7 x>1 x>7 A

15


S.N. Com-

peten-

cy No.

Level

(K or

A)


129 21 K What is the solution of 4x-3≤4x+2-x? {x: x≤5/2} {x: x≤5} {x: x≥5/4} {x: x≥5} B

130 21 K Solve the following inequality

-6x-15≤9+2x

{x: x>3} {x: x<3} {x: x≥-3} {x: x≤-3} C

131 21 K What is the solution set of x(1/2 -3)≤ 4(1/2+x)- x? {x: x≤ -10/7} {x: x≤ -4/11} {x: x≥ -10/7} {x: x≥ -4/11} D

132 21 K What is the value of x in the inequality x > 13/3 x < 13/3 x < 13 x > 13 B

133 21 K If

then what is the value of x?

x> 36/7 x> - 36/7 x<-36/7 x< 36/7 D

134 21 K The value of x for -1/3x +1/3≤1-x is _______. x≥1 x≤-1 x≤1 x≥-1 C

135 21 K Find the solution set of linear inequality x<-1/3 x>-1/3 x<1/3 x>1/3 A

136 21 K Which one is the solution set of the inequality -

8x+4≤4, xЄQ?

{x| xЄQ and x≥0} {x| xЄQ and x≤0} {x| xЄQ and x≥1} {x| xЄQ and x≤1} A

82

3

6

54 xx

2

15

4

1

3

13

xxx

?54

26

x

x

16


S.N. Com-

peten-

cy No.

Level

(K or

A)


137 21 K The solution set of the linear inequality 2-1/2x ≥

3/2x+1, where x Є W is _________.

{1/2} {0} {1} {1/2, 0} B

138 21 K Which one is the solution set of the linear

inequality

{m| m>0} {m| m≤0} {m| m≥0} {m| m<0} D

139 21 K {-1, 0, 1} {0, 1} {-1, 0} { } D

140 21 A One of the following equations has a solution set

of x < -2. Which one is it?

C

141 22 K In which quadrant does a point (-2, 1) lie? Quadrant IV Quadrant III Quadrant II Quadrant I C

142 22 K On which quadrant does point p(3, -2) lie? 1st quadrant 2nd quadrant 3rd quadrant 4th quadrant D

143 22 K In which quadrant does the ordered pair (-2, 4)

lie?

I II III IV B

144 22 K In which quadrant does the point (-4, 2) lie? Quadrant I Quadrant II Quadrant III Quadrant IV B

Zmwheremm

...4

4

21

15

2

3

1

xx

3

410

2

43 xx

4

4

32

x

x

5

4

5

332

x

x

17


S.N. Com-

peten-

cy No.

Level

(K or

A)


145 22 K Which of the following ordered pairs is found in

quadrant 2?

(-3, 4) (4, 6) (-3, -2) (5, -3) A

146 22 K Which of the following points is in quadrant

three?

(3, 1) (3, -1) (-2, -1) (-2, 1) C

147 22 K A(-1/2, -2) belongs to Quadrant ______. I II III IV C

148 22 K From the Cartesian coordinate shwon below, point

B is found in ________.

Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 D

149 22 K In the coordinate plane below, which one is

correct about point P?

a<0 and b<0 a<0 and b>0 a>0 and b<0 a>0 and b>0 B

18


S.N. Com-

peten-

cy No.

Level

(K or

A)


150 22 K Name the quadrant in which the point of P(x, y)

lies when x<0, y>0.

1st quadrant 2nd quadrant 3rd quadrant 4th quadrant B

151 22 K In which quadrant are the ordered pairs (-, +)

found?

IV III II I C

152 23 K Which one is the coordinate point for (-3, 4)? C

153 23 K Which of the following rectangular coordinate

systems represents the coordinate of p(2, 0)?

C

154 23 K Which letter indicates the order pair (-3, 0)? Point P Point Q Point R Point S A

19


S.N. Com-

peten-

cy No.

Level

(K or

A)


155 23 K Which graph indicates the coordinates of A(2, 1)

and B(-2, 2)?

D

156 23 K In the coordinate plane below, which point is

marked correctly?

P Q R S D

157 23 K Which one of the following graphs indicates the

coordinate points of (-1, 1) and (1, -1)?

C

20


S.N. Com-

peten-

cy No.

Level

(K or

A)


158 24 K In the following Cartesian plane, what is the

coordinate of A?

(-2, 2) (2, -2) (2, 2) (-2, -2) B

159 24 K In the coordinate plane below, which one is the

coordinate of p?

(0, 4) (0, -3) (-3, 4) (4, -3) C

160 24 K From the graph shown below, point Q represents

ordered pair _______.

(3, -4) (-4, 3) (-3, 4) (-3, -4) A

21


S.N. Com-

peten-

cy No.

Level

(K or

A)


161 24 K Based on the given figure below which one is the

coordinate of point B?

(3, 3) (-2, 3) (2, -2) (-1, -3) C

162 24 K Which one is the coordiante of point A plotted on

the Cartesian coordinate plane?

(1, 1) (-1, -2) (-3, 2) (2, 1) B

163 24 K In the figure below, the coordinate of point T is

_________.

(2, 2) (-2, 2) (-2, -2) (2, -2) C

22


S.N. Com-

peten-

cy No.

Level

(K or

A)


164 26 K Which of the following is the graph of y=3? A

165 26 K Which one of the following graphs shows y=3? C

166 26 K Which one of the following is the graph of y= -1? C

167 26 K Which one of the following graphs shows y= -2? A

23


S.N. Com-

peten-

cy No.

Level

(K or

A)


168 26 K Which one is the graph of y+2=0? D

169 26 K Through which quadrants does the line y= -3

pass?

I and II III and IV II and III I and IV B

170 26 K Which one of the following is true? A line parallel to the

y-axis is horizontal

A line perpendicular

to the x-axis is vertical

A line parallel to the

x-axis is vertical


to the y-axis is vertical

B

171 26 K Which quadrants does the graph of y=-3 pass

through ?

first and third first and fourth second and third second and fourth D

172 27 K Which of the following is the correct coordinate

representation of the line x=-5?

C

24


S.N. Com-

peten-

cy No.

Level

(K or

A)


173 27 K Which one of the following is the graph of x=-2? B

174 27 K Which of the following graph shows the line x= –

3?

C

175 27 K Which one is the graph of x= –3? A

25


S.N. Com-

peten-

cy No.

Level

(K or

A)


176 27 K Which one of the following is the graph of x=-4? C

177 27 K The graph of a line x -1=0 is ________. A

178 27 K Which of the following is true about the graph of

x=2?

A line parallel to x-

axis

A line parallel to y-

axis

A line pass through

the origion


to y-axis

B

179 27 K What is the equation of a line given in the figure

below?

y=3 y= -3 x=3 x= -3 C

26


S.N. Com-

peten-

cy No.

Level

(K or

A)


180 27 A Which of the following graphs indicates the

equation 2y+3x+5=2(x+y+1)?

A

181 28 K Which of the following is the graph of y=x? A

182 28 K Which of the following is the graph of y=x? C

27


S.N. Com-

peten-

cy No.

Level

(K or

A)


183 28 K Which one is the graph of y= -x? B

184 28 K Which of the following is the graph of the

equation y=4x?

B

185 28 K Which coordinate plane represents the line y= -5x

correctly?

C

28


S.N. Com-

peten-

cy No.

Level

(K or

A)


186 28 K The equation of the graph is: y=2x y= -2x y=x y= -x B

187 28 K Which of the following is true about the graph of

y= -3x?

When x=-1, y=-3 When x=0, y=-3 When x=1, y=3 When x=2, y=-6 D

188 28 A Helen walks 2km every day. Which linear

equation represents the total km, Y, she walks

after x-days?

B

189 29 K Which one of the following graphs has a negative

slope?

D

190 29 K Find the slope of the line passing through points

P(3, 3) and Q(-1, -1).

-1 1 -3 1 D

29


S.N. Com-

peten-

cy No.

Level

(K or

A)


191 29 K Find the slope of a line which passes through

points (1, 2) and (3, 4).

-2 -1 1 2 C

192 29 K What is the slope of the line passing through

points P(0, 30) and Q(15, 0)?

-1/2 -2 1/2 2 B

193 29 K Find the slope of the line passing through points (-

2, 5) and (4, -10).

-5/3 -5/2 5/3 5/2 B

194 29 K What is the slope of a line passing through points

P(-6, 3) and Q(10, -5)?

-1/4 -1/2 1/4 1/2 B

195 29 K What is the slope of a line passing through point

(4, -3) and (2, 1)?

2 1/2 -2 -1/2 C

196 29 K What is the equation of a line that passes through

(-1, 4) and (1, -4)?

y=4x y=-4x y=4x+4 y=-4x+4 B

197 29 K Determine the equation of a line that passes

through A(1, 0) and B(0, -1).

y=1-x y=x+1 y=x-1 y=- x-1 C

198 29 K Which of the following is the equation of the line

that passes through points (2, 3) and (-1, 3)?

x=3 y=3 y=2x+3 y=-x +3 B

199 29 K What is the equation of a line which passes

through points (0, 1) and (-3, -2)?

y=-x+1 y=x-1 y=x+1 y=-x-1 C

200 29 K What is the equation that passes through the

ordered pairs of (1, 3) and (2, 1)?

y=2x+5 y=2x-5 y= -2x+5 y= -2x-5 C

30


S.N. Com-

peten-

cy No.

Level

(K or

A)


201 29 K What is the equation of a line passing through

points P(1, -2) and Q(2, 3)?

y=5x+13 y=x+13 y=5x-7 y=x-7 C

202 29 K Find the equation of a line that passes through the

points A(-1, 0) and B(-3/4, 1/2).

y-2x-2=0 2x-y-2=0 2x+y+2=0 y+2x-2=0 A

203 29 K The table below shows values for x and

corresponding values for y. Which of the

following represents true relationships between x

and y?

y=x/5 y=5x y=x-5 y=x+5 A

204 29 A If the slope of a line passing through (4, 1) and (3,

a) is -4, find the value of a.

a=5 a=4 a=-5 a=-4 A

205 30 K Which of the following points lies on the line

y+x=0?

(-2, 2) (-2, -2) (0, 2) (2, 2) A

206 30 A Among the given points, which point does the line

y=3x-1 pass through?

(0, 1) (1, 3) (2, 6) (3, 8) D

207 30 A Which point lies on the line given below? (0, 0) (0, 1) (2, 0) (1, 0) D

208 30 A Which equation contains the coordinate (-5, 1)? y-2x+9=0 y+2x-9=0 y-2x-9=0 y+2x+9=0 D

x

y

30 2

5

20

4 3 2 1

51 10

6

31


S.N. Com-

peten-

cy No.

Level

(K or

A)


209 30 A Which equation contains points A(-2, 1) and B(1,

-2)?

y+x+1=0 y-x-3=0 y-2x-5=0 y-2x+4=0 A

210 30 A Find the equation of the given line in the graph. y= x+1 y= -x+1 y= x y=-x D

211 30 A For the line of equation y=x+2, the slope is

________.

-1 -2 1 2 C

212 30 A Find the value of a if point (2, 4) lies on the line

ax+2y=10.

1 2 3 4 A

213 30 A Which one is the equation of a line that passes

through (a,b) and (b,a) if a=2b?

y=3x+b y=x+3b y=-3x+b y=-x+3b D

214 30 A The equation of a line is ax-by=4 and points (1,3)

and (2,-2) lie on the line. What are the values of a

and b?

-2 and 5 -2 and 2/5 5/2 and -1/2 1/2 and -5/2 C

215 30 A If the slope of a line passing through (4, 1) and (3,

a) is -5, find the value of a.

8 6 5 4 B

32


S.N. Com-

peten-

cy No.

Level

(K or

A)


216 30 A Which of the following graphs represents y=x+1? A

217 30 A Which of the following graphs represents the

graph of y= –3x-1?

C

218 30 A Which of the following represents the equation of

the following line given on the following graph?

y=2x+2 y=2x-2 y=-2x+2 y=-2x-2 C

219 30 A For the line of equation y=x+2, the slope is

________.

-1 -2 1 2 C

Following items deal with competencies beyond Grade 8. (For example, the general form of y=ax+b and the concept of intercept are taught at Grade 9.) Therefore,

these items are shown here for reference purposes only. (Competency number is tentatively set at 30 and level is A.)

33


S.N. Com-

peten-

cy No.

Level

(K or

A)


220 30 A Which one of the following have the same slope to

the equation 4x+6y=10 ?

B

221 30 A What is the y-intercept of the graph of 4x+2y=12? -2 -1/2 3 6 D

222 30 A The y-interciept of the line with equation x-3y=12

is _________.

(0, -4) (12, 0) (0, 4) (-12, 0) A

223 30 A What are the coordinates of the x-intercept of the

line 2x+4y=12?

(0, 3) (3, 0) (0, 6) (6, 0) D

224 30 A Which of the following is true about the equation

2y=4x+2?

The slope is -4 The y-intercept is 2 The line passes

through the origion

Point (1, 3) is on the

line

D

225 30 A What is the equation of a line with slope 3 and y-

interciept 0?

y= -3x y= -3x/2 y=3/2 x y=3x D

226 30 A Find the equation of a line that passes through the

given point (0, 1) and m= -2.

y=-2x-2 y=2x+2 y=-2x-1 y=-2x+1 D

227 30 A Which of the following equations represents the

line whose slope is -3 and on which lies point (1,

3)?

y=3x-6 y=3x+6 y+3x=6 y-3x=6 C

228 30 A The equation of a line which has slope -3 and pass

through the point (2, 0) is __________.

y=3x y= -3x+6 y= 3x+6 y= -3x B

229 30 A Which of the following ordered pairs satisfies the

equation y= -2x-4?

(-1, -2) (-1, -1) (-2, -4) (0, 4) A

230 30 A Which of the following points lies on the line

?

(0, 4) (3/2, 13/4) (3, 5/2) (36, 0) C2𝑥

3+ 4𝑦 = 12

𝑦 =3𝑥

2+ 4 𝑦 =

−2𝑥

3+ 6 𝑦 =

2

3𝑥 + 5 𝑦 =

−3

2𝑥 + 3

34


S.N. Com-

peten-

cy No.

Level

(K or

A)


231 30 A If point (-2, 1) lies on the line ax+3y=4, what is

the value of a?

-7/2 -5/2 1/2 10 B

232 30 A If point (b, b) lies on the graph of the equation

3y=2x-4, then what is the value of b?

-4/3 -4 4/3 4 B

233 30 A The point (2, 1) lies on the line 5x+by =20. What

is the value of b?

10 15/2 5 7/2 A

234 30 A If point (3, 2) lies on the line ax+2y=10, then what

is the value of a?

1 2 3 4 B

235 30 A What is the intersection point of equations

y=3x+1 and y=-2x-4?

(1, 2) (-1, 2) (1, -2) (-1, -2) D

35


S.N. Com-

peten-

cy No.

Level

(K or

A)


1 31 K The figure given at the right is similar to ______. C

2 31 K Which of the following pairs of triangles are

similar?

A

3 31 K Which of the following figures are similar?

and and and and

D

1


S.N. Com-

peten-

cy No.

Level

(K or

A)


4 31 K Which parallelogram is similar to parallelogram

EFGH?

C

5 31 K Consider the figures given below. Which plane

figures are similar?

I and II I and III II and III I, II and III A

6 31 K Which pair of triangles are similar but not

congruent?


2


S.N. Com-

peten-

cy No.

Level

(K or

A)


7 31 K Which one is similar to the indicated figure

below?

Rhombus with

sides 3 by 3

Trapezium with

base 3 and 6

Rectangle with

sides 6 and 3

Square with sides

2 by 2

D

8 31 K Which of the following plane figures are always

similar?

Any two squares Any two

rectangles

Any two

parallelograms

Any two isoceles

triangels

A

9 31 K Which of the following plane figures are always

similar to each other?

Two triangles Two rectangles Two squares Two rhombuses C

10 31 K Which of the following figures are similar? Any two

rectangles

Any two line

segments

Any two triangles Any two squares D

11 31 K Which of the following are always similar? Any two

rectangles

Any two circles Any two

quadrilaterals

Any square and

rectangle

B

12 31 K Which of the following polygons are always

similar?

Any two

rectangles

Any two

rhombuses

Any two squares Any two triangles C

13 31 K Identify figures that are similar to each other. Square Rhombus Rectangle Trapezium A

14 31 K Which plane figures are similar to each other? Any two

rectangles

Any two isoceles

triangles

Any two

parallelograms

Any two

equilateral

triangles

D

15 31 K Which polygons are similar? Any two

rectangles

Any two squares Any two

rhombuses

Any two

trapeziums

B

16 31 K Which pair of plane figures is always similar? A square and a

rhombus

A rectangle and a

parallelogram

Any two issoceles

triangles

Any two squares D

17 31 K Which one of the following is NOT true? Any two

equilateral

triangles are

similar

Any two squares

are similar

Any two circles

are similar

Any two isoceles

triangles are

similar

D

3


S.N. Com-

peten-

cy No.

Level

(K or

A)


18 31 A In the figure shown below, which one is correct? ∆ABD~ ∆ABC ∆ABD~ ∆BCD ∆ABC ~ ∆BAD ∆DCB~∆BAC B

19 32 K If ∆PQR is similar to ∆XYZ, then which of the

following is true?

<P≡<Q <Q≡<R <R≡<Z <P≡<Y C

20 32 K Which of the following is correct about two

similar triangles or quadrilaterals?

They have the

same size

Their

corresponding

sides are equal

Their

corresponding

angles are equal

Their

corresponding

angles are

proportional

C

21 32 K If ∆LMN~∆OPR, which one shows the

corresponding sides?

LM and PR LN and OP MN and PR LM and PO C

22 32 K Two triangles are similar if _______. their

corresponding

sides are not

proportional

their

corresponding

angles are

proportional

their

corresponding

sides are

proportional

their

corresponding

angles are not

congruent

C

23 32 K If ∆DEF is the image of ∆ABC with scale factor k,

then what is the value of DF/AC?1/k

2 1/k k k2 C

24 32 K If two triangles ABC and DEF are similar with the

ratio of their corresponding sides AB:DE=k, then

what will be the ratio of their corresponding

angles m(<A):m(<D)?

k 1/k k2 1 D

4


S.N. Com-

peten-

cy No.

Level

(K or

A)


25 32 K In the figure below, if ∆ABC is an image of ∆

PQR, what is the proportionality constant?

1/2 1 2 3 A

26 32 K When the image of the object figure becomes

smaller than the object figure, the scale factor k is

______.

-1<k<0 0<k<1 k=1 k>1 B

27 32 K Find the scale factor from ABCD to EFGH, given

that ABCD~ EFGH?

2/5 5/2 3/5 5/3 A

28 32 K Which of the following is/are always correct?

I. Similar triangles are congruent

II. Congruent triangles are similar

I II I and II Both are incorrect B

29 32 K Suppose ∆ABC ~∆XYC as shown in the figure

below. Which statement is true?

I. AB/XY=BC/YC

II. YC/BC=XC/AC

III. AB/XY=XC/AC


5


S.N. Com-

peten-

cy No.

Level

(K or

A)


30 33 K In the figure below, triangle A'B'C' is the image of

triangle ABC under enlargement. Which pair of

sides is parallel to each other?

AC is parallel to

A'C'

AC is parallel to

A'B'

AC is parallel to

C'B'

AC is parallel to

itself

A

31 33 K Point A is the center of enlargement of ∆ABC. If

you enlarge it by scale factor 2, then what figure

do you obtain?

D

32 33 K If ∆PQR has lengths PQ=3cm, PR=4cm and

QR=5cm, which one is true about the sides of the

enlarged triangle by scale factor 2?

P'Q'=5cm P'R'=6cm P'Q'=3cm Q'R'=10cm D

33 33 K Which of the following is true about central

enlargement?

Lines are not

parallel

Angles are not the

same

Lines and their

images are parallel

Lines and their

images are not

parallel

C

34 34 K Point A is the center of enlargement of ∆ABC. If

the figure is reduced by a factor of 1/2, then what

figure do we obtain?

B

35 34 K What is the length of the image of 24cm long

segment after central stretching with scale factor

k=2/3?

8cm 12cm 16cm 18cm C

36 34 K Triangle ABC is similar to triangle DEF. The

scale factor from triangle ABC to triangle DEF is

1/3. If DE=6cm, what is the length of AB?

1/18cm 1/2cm 2cm 18cm D

6


S.N. Com-

peten-

cy No.

Level

(K or

A)


37 35 K ∆ABC~ ∆DEF if _________. <A ≡<D, <B≡ <E,

<C≡ <F

<A ≡<F, <B≡ <E,

<C≡ <D

AB/DE=BC/EF=

AC/DE

AB/EF=AC/DF=

BC/DE

A

38 35 K If figure 1 and figure 2 are similar, then which one

is true?

∆CAB~∆EDF ∆CBA~∆EDF ∆BAC~∆EDF ∆ACB~∆EDF C

39 35 K If ∆MNO and ∆HIJ are similar, which one is true? <MNO=<HJI <MON=<JHI <OMN=<JHI <NOM=<HIJ C

40 35 K If ∆DEF~∆OPQ, which of the following is NOT

true?

<D=<O <F=<Q DE/OP=EF/PQ DF/OQ=OP/DE D

41 35 K In the figure below, if ∆ABC~∆DEF, then which

of the following sides are proportional?

AB and DE BC and DE AC and DE BC and DF A

42 35 K In the figure below, if ∆ABC~∆XYZ, then which

of the following angles are congruent?

<A≡<Z <C≡<X <B≡<X <A≡<X D

7


S.N. Com-

peten-

cy No.

Level

(K or

A)


43 35 K Which one is the correct similarity statement for

the triangles?

∆CDE~∆FHG ∆CED~∆FGH ∆CDE~∆FGH ∆EDC~∆FGH C

44 35 K In the figure below <R =<V. Which sides of the

triangles are proportional?

RS and BS RW and VS SW and SB WS and WR C

45 35 K If ∆ABC~∆DEF and ∆DEF~∆HMK with

m(<ABC)=60o

and m(<HKM)=70o, then which

one is true?

m(<HMK)=50o

m(<DEF)=60o

m(<BAC)=70o

m(<EDF)=70o B

46 35 K If ∆BAC~ ∆DEF and ∆DEF~ ∆XYZ, then to

which triangle is ∆ABC similar ?

∆ACB ∆DFE ∆YXZ ∆ZXY C

47 35 A If ∆ABC~∆DEF with the ratio of corrosponding

sides 3:4:5=9:y:15, find the value of y.

9 10 12 13 C

8


S.N. Com-

peten-

cy No.

Level

(K or

A)


48 36 K Which angles of triangles given below are

corresponding angles?

<B and <E <B and <F <C and <F <B and <D D

49 36 K If ∆ABC ~∆DEF given below, which of the

following is true?

AB/DE=EF/BC AC/DF=BC/EF m(<F̂)=60o m(<F)=m(<A) B

50 36 K Given ∆ABC~ ∆XYZ as shown in the figure

below, what is the degree measure of (<XYZ)?32

o46

o72

o102

o A

51 36 K If ∆ABC~∆XYZ, and AB=8cm, AC=10cm and

XY=4cm, then find the length of XZ.

10cm 1/5cm 1/10cm 5cm D

9


S.N. Com-

peten-

cy No.

Level

(K or

A)


52 36 K If ∆ABC~∆XYZ and AB=4cm, AC=5cm and

XY=2cm as shown in the figure below, then find

the length of XZ.

5cm 5/2cm 2cm 2/5cm B

53 36 K Given that ∆ABC~∆DEF, if AB=4cm, DE=6cm

and BC=2cm, then find EF.

3cm 8cm 10cm 12cm A

54 36 K In the figures shown below ∆ABC~∆DEF. What

is the length of side DF?

12cm 16cm 18cm 20cm B

55 36 K In the figure below, if ∆ABC~∆DEF with

AB=8cm, BC=6cm, AC=10cm, DE=4cm and

EF=3cm, then what is the length of DF?

5cm 6cm 8cm 10cm A

10


S.N. Com-

peten-

cy No.

Level

(K or

A)


56 36 K For ∆ABC and ∆XYZ shown below, <B = <Y,

<C = <Z, AB=4cm, AC=6cm and XY=2cm as

shown in the figure below. Find the length of XZ.

2cm 3cm 4cm 6cm B

57 36 K ∆ABC ~∆PQR with AB=4cm, BC=3cm and

PQ=12cm. Find the length of QR.

1/16cm 1/9 cm 9cm 16cm C

58 36 K If ∆ABC~∆ADE, AB=20cm, and AD=30cm, then

what is the value of AC/AE?

2/3 3/2 20 30 A

59 36 A Triangle ABC is similar to triangle XYZ and

<A=72o, <B=38

o. What is the measure of <Z?

38o

70o

72o

110o B

60 36 A The sides of a triangle are 3cm, 7cm and 9cm.

What is the length of the longest side of a similar

triangle whose shortest side is 8cm?


11


S.N. Com-

peten-

cy No.

Level

(K or

A)


61 36 A In the figure below, DE||BC, AE=10cm, EC=5cm

and DB=4cm. What is the length of AB?


62 36 A In ∆ABC, DE is parallel to BC, AD=6cm,

DB=8cm and AE=9cm. How long is AC?


63 36 A Given PQ||BC, find the length of AQ. 9cm 11cm 12cm 18cm A

64 36 A In the figure, ∆HLT~∆UWT with UW=3cm,

TW=2cm and HT=6cm as shown below. Then

WL=_______.

3cm 4cm 6cm 8cm B

12


S.N. Com-

peten-

cy No.

Level

(K or

A)


65 36 A In the figure below, what is the length of BC? 15cm 15/2cm 4cm 2cm B

66 36 A In the figure below, if AE is parallel to BD, what

is the lelngth of AB?

9cm 12cm 27cm 30cm A

67 36 A In the figure below ∆ABC~∆ADE. If AD= 5cm,

AE=6cm and AB=15cm, then find the length of

AC.

14cm 15cm 16cm 18cm D

68 36 A In the figure below MN||YZ. If XN=10cm,

NZ=5cm an MY=4cm, then what is the length of

XY?


13


S.N. Com-

peten-

cy No.

Level

(K or

A)


69 36 A Given ST||QR, find ST:QR. 5/2 3/2 2/3 2/5 D

70 36 A In the figure below XY||PQ. If OX=4 cm, XP=6

cm and YQ= 3 cm, then what is the length of OY?

2 5 7 8 A

71 36 A In the figure shown below, if ∆ABC ~ ∆ZBX with

XB=4cm, BZ=3cm, CX=4cm and AC=6cm, find

the length of XZ.

3cm 4cm 6cm 8cm A

72 36 A In the following figure if ∆ABC~∆DEC and if

AB=8cm, EC=3cm and DE=2cm then what is the

measure of BE?


14


S.N. Com-

peten-

cy No.

Level

(K or

A)


73 36 A In the figure below, ∆DEF~ ∆MNF. If MF=6,

NF=5 DM=3 and DE=8, then find MN.

3/16 16/3 48 9 B

74 36 A Triangles PQR and XYZ are similar. If PQ=6,

PR=4cm and XY=9cm, what is the length of side

XZ?

8/3cm 4cm 6cm 27/2cm C

75 36 A In the figure below AB||CD. What is the length of

OB?

2/5cm 5/2cm 3cm 5cm B

76 36 A A football field measures 100m by 72m. A school

marks a football field similar in shape to the

fullsize football field but only 30m long. What is

its width?

240m 108/5m 5/108m 5m B

77 36 A If ∆DEF~∆KLM, then find the length of ML in

the figure below.

2cm 4cm 6cm 8cm A

15


S.N. Com-

peten-

cy No.

Level

(K or

A)


78 36 A In the figure below ∆ABC is a right-angled

triangle at B and BD⊥AC. What is the value of

BD, if AD=3cm and DC=4cm?

2√3cm 3√2cm 7cm 12cm A

79 36 A Find the value of x in the figure below. 3cm 3√3cm 9cm 27cm B

80 37 K Among the given alternatives, which one is NOT

in similarity theorem?

SSS similarity

theorem

SAS similarity

theorem

SS similarity

theorem

AA similarity

theorem

C

81 37 A In the figure below, ∆ABC and ∆DEF are given

where m(<A)=m(<D)=55o, AB=30cm,

AC=100cm, DE=15cm and DF=50cm. Then by

what theorem, are the two triangles similar?

ASA SAS SSS AA B

82 37 K In the figures given below, ∆CAB~∆FDE because

of __________.

AA ASA SAS SSS C

16


S.N. Com-

peten-

cy No.

Level

(K or

A)


83 37 K Which theorem is NOT used to show the

similarity of the triangles shown below?

AA similarity SSS similarity SAS similarity ASS similarity D

84 37 K In the figure below, <M=<X and ∆MNO~∆XNY.

Then which theorem makes them similar?

SAS ASA SSS AA D

85 37 K Which one of the theorems is used to prove that ∆

PQR~∆SQT?

AA similarity SAS similarity SSS similarity SSA similarity A

86 37 K In the figure below, PQ⊥QT, ST⊥QT, and P, R

and S are on the same line. If ∆PQR~∆STR, then

which of the following theorems supports your

answer?

SAS theorem SSS theorem ASS theorem AA theorem D

17


S.N. Com-

peten-

cy No.

Level

(K or

A)


87 37 K In the following figure if <D=<C=50o, then which

similarity theorem shows that ∆DEA is similar to

∆CEB?

SAS AA SSS ASA B

88 37 A In the figure below, the steps used to show

similarity of ∆ABC~∆EBD.

i. <ABC=<EBD…Vertical opposite angles

SSS Similarity AA similarity SAS similarity SSA similarity C

89 37 K In the figure below, DE||BC. If ∆ABC ~ ∆ADE,

then which one of the following similarity

theorems supports your answer?

SAS similarity

theorem

AA similarity

theorem

SSS similarity

theorem

ASA similarity

theorem

B

90 37 K Which of the following conditions is true for two

similar triangles?

They have one

equal side as well

as one equal angle

They have only

one pair of

proportional sides

They have three

equal angles and

proportional sides

They have two

proportional

angles

C

18


S.N. Com-

peten-

cy No.

Level

(K or

A)


91 37 A In ∆ABC, let D be on AB and let E be on BC such

that <BAC≡<BED, then ∆ABC~∆EBD by

___________.

SSS theorem AA theorem SAS theorem ASA theorem B

92 37 A If ∆PQR~∆XYZ by SAS theorem, then which of

the following is true?

PQ/XY=PR/XZ <P≡<Z and

PQ/PR=XZ/XY

<P≡<Z and

PQ/XY=PR/XZ

<P≡<X and

XY/PQ=XY and

PR=YZ

A

93 37 A For a triangle ABC if <A=<B then which

statement is true?

∆ABC~∆BCA ∆ABC~∆ACB ∆ABC~∆CBA ∆ABC~∆BAC D

94 37 A In the figure below, find the length of BC. 6cm 6.92cm 7cm 7.44cm A

95 37 A Using the given figure at the right, find CE. 5/18cm 18/5cm 5cm 6cm B

19


S.N. Com-

peten-

cy No.

Level

(K or

A)


96 38 K If the ratio of the corresponding sides of similar

triangles is k, then the ratio of their perimeters is

given as __________.

C

97 38 K The corresponding sides of two similar triangles

measure 12cm and 16cm long. What is the ratio of

their perimeters?

2:3 3:4 4:5 5:6 B

98 38 K If ∆ABC~∆DEF and the perimeter of ∆

ABC=18cm and AB/DE=2, find the perimeter of

∆DEF.


99 38 K ∆HIJ~∆PQR. If perimeters of ∆PQR is 24cm and

proportional constant PQ/HI=4, then the perimeter

of HIJ is ________.


100 38 K The ratio of the corresponding sides of two similar

triangles ABC and DEF is 1:3. Which statement

is true about the perimeter of ∆DEF?

Perimeter( ∆

ABC)=Perimeter

(∆DEF)

P (∆DEF)= 2P(∆

ABC)

P (∆DEF)= 3P(∆

ABC)

P (∆DEF)= 9P(∆

ABC)

C

101 38 K The side length of a triangle is 7cm, 9cm and 4cm.

The perimeter of a similar triangle is 60cm. What

is the length of the largest side of the second

triangle?


102 38 K The lengths of the sides of a triangle are 5cm, 6cm

and 7cm. The perimeter of a similar triangle is

54cm. What is the lelngth of the longest side of

the second triangle?


103 38 A If ∆ABC and ∆DEF are equilateral triangles and

the perimeter of ∆ABC=12cm with EF/BC=2,

then find the perimeter of ∆DEF.


20


S.N. Com-

peten-

cy No.

Level

(K or

A)


104 38 A The sum of the perimeters of two similar polygons

is 28cm. The ratio of the corresponding side is

3:4. The perimeter of the larger polygon is

________.


105 38 A Rectangle ABCD is similar to rectangle PQRS.

Given that AB=14cm, BC=8cm and PQ=21cm,

calculate the length of QR.


106 38 A The lengths of the sides of a rectangular

swimming pool are 20m and 60m. If the perimeter

of the fence which is similar to the swimming pool

is 240m, then the length of the sides of the fence

are: ___________________.

30m and 90m 40m and 80m 50m and 70m 60m and 60m A

107 39 K If the ratio of two corresponding sides of similar

triangle is 1:2, then what is the ratio of their areas?

1:4 1:3 2:5 2:1 A

108 39 K If the ratio of the corresponding sides of two

similar polygons is k, what is the ratio of their

areas?

k/2 k 2k k2 D

109 39 K Given ∆ABC~∆DEF with AB/DE=3/2, then find

area(∆ABC)/area(∆DFE).

6:4 9:4 4:6 4:9 B

110 39 K Triangle ABC is similar to triangle XYZ. If

AB/XY=1/4, then a(ΔABC)/a(ΔXYZ) = ______.

1/16 1/4 4 16 A

21


S.N. Com-

peten-

cy No.

Level

(K or

A)


111 39 K The ratio of the perimeter of two similar polygons

is 3:5. The area of the smaller polygon is 36cm2.

What is the area of the larger polygon?

9cm2

25cm2

36cm2

100cm2 D

112 39 K If ∆ABC~∆DEF with the area of ∆ABC=16cm2

and AB/DE=2, find the area of ∆DEF.

4cm2

8cm2

32cm2

64cm2 A

113 39 K If ∆ABC~ ∆DEF with AB/DE=3, then what is the

area of ∆ABC in terms of the area of ∆DEF?

a(∆ABC)=1/9a(∆

DEF)

a(∆ABC)=1/3a(∆

DEF)

a(∆ABC)=3a(∆

DEF)

a(∆ABC)=9a(∆

DEF)

D

114 39 K The ratio of the sides of two similar triangles is

2:3. The area of the larger triangle is 81cm2. What

is the area of the smaller triangle?

36cm2

54cm2

81cm2

96cm2 A

115 39 K If ∆ABC~∆DEF with AB=3DE and area of ∆

ABC=6cm2, then a(∆DEF) is _______.

2/3cm2

18cm2

36cm2

54cm2 A

116 39 K The diagram below shows two similar triangles.

The smaller triangle has an area of 16cm2. What is

the area of the larger triangle?

16cm2

24cm2

36cm2

48cm2 C

117 39 A ∆ABC ~∆PQR. The ratio of the perimeter of ∆

PQR to ∆ABC is 2. If the area of ∆ABC is 8cm2,

then a(∆PQR)=________.

16cm2

24cm2

32cm2

48cm2 C

22


S.N. Com-

peten-

cy No.

Level

(K or

A)


118 39 A The areas of two similar triangles are 96cm2 and

6cm2. If a side of the smaller triangle is 3cm, find

the length of the corresponding side of the larger

triangle.

4cm 9cm 12cm 16cm C

119 39 A The aeras of two similar triangles are in the ratio

of 25:16. Find a side of the larger triangle if the

corresponding side of the smaller triangle is 40.

16 25 40 50 D

120 39 A Two similar triangles have an area of 6cm2 and

24cm2 respectively. If one side of the smaller

triangle is 4cm, what is the length of the

corresponding side of the larger triangle?

6cm 8cm 10cm 12cm B

121 39 A The ratio of the areas of two similar triangles is

9:4. What is the ratio of their perimeters?

2:3 3:2 4:9 9:4 B

122 39 A The areas of two similar polygons are 64cm2 and

4cm2. If a side of the larger polygon is 4cm, find

the corresponding side of the smaller polygon.

1cm 4cm 8cm 16cm A

123 39 A The ratio of corresponding sides of two similar

polygons is 5:2. The area of the smaller polygon is

8cm2, then what is the area of the larger polygon?

20cm2

40cm2

50cm2

60cm2 C

23


S.N. Com-

peten-

cy No.

Level

(K or

A)


124 39 A The area of two similar triangles are 18cm2 and

32cm2. If a side of the first triangle is 9cm, what is

the corresponding side of the second triangle?


125 39 A The areas of two similar triangles ABC and XYZ

are in the ratio of 4:25. If BC=5cm, what is the

length of YZ?

2cm 4/5cm 25/2cm 125/4cm C

126 39 A The ratio of the areas of two similar triangles ABC

and PQR is 16:25. What is the ratio of their

corresponding sides, AC:PR?

4:5 5:4 16:25 25:16 A

127 39 A The figure below is a rectangle. If the rectangle is

enlarged by a scale factor of 3, then what is the

area of the enlarged rectangle?

24cm2

72cm2

96cm2

216cm2 D

128 39 A If two pieces of triangular plots of land have the

same shape and the ratio of the length of the

corresponding sides is 1/2, which of the following

is true?

The ratio of their

areas is 2

The ratio of their

areas is 1/2

The area of the

bigger land is 4

times as much of

the smaller land

The area of the

bigger land is

twice as much of

the smaller land

C

129 39 A The figure indicated below shows a park

surrounded by a recreational area. The area of the

park is 4000m2. What is the area of the

recreational area if they are similar with length

proportion of 1:2?

1000m2

4000m2

8000m2

12000m2 D

24


S.N. Com-

peten-

cy No.

Level

(K or

A)


130 39 A For two similar trapeziums, the area of the larger

trapezium is 4 times the area of the smaller

trapezium. What is the ratio of the sides of the

larger trapezium to the smaller one?

1:2 2:1 8:1 16:1 B

131 39 A If the ratio of the circumferences of two circles is

4:9, what will be the ratio of their areas?

2:3 4:9 8:18 16:81 D

25


S.N. Com-

peten-

cy No.

Level

(K or

A)


1 40 K In the figure to the right, O is the center of the

circle and AB the diameter. Then which one of the

following is a minor arc?

arc ABC arc ACB arc AXC arc AYB C

2 40 K In circle O shown to the right, A, X, B and Y are

points on the circle. What do you call the part

AYB of the circle?

Minor arc Major arc Semicircle Sector B

3 40 K Which of the following is true about circle O

given below?

AFC is major arc DFB is minor arc FAD is minor arc DEB is major arc C

4 40 K Given circle O with diameters AD and BE, then

which one is a minor arc?

ABD ABC BED AED B

1


S.N. Com-

peten-

cy No.

Level

(K or

A)


5 40 K In the circle below, which are minor arcs? ABC and BEF BCD and ABF ABD and ADF CDE and FAB D

6 40 K In the circle given below, which arcs are minor

and major, respectively?

GFE and CDE ADE and DEF BCD and BDF CEF and EFG C

7 40 K In the following circle, if O is the center, which

one shows a minor arc of the circle?

D

8 40 K In circle O with diameter AD as shown below,

which one is a major arc?

ABD ACE ABC BCD B

2


S.N. Com-

peten-

cy No.

Level

(K or

A)


9 40 K In the figure below, RS and TU are two diameters

of circle O. Which one of the following is a major

arc?

D

10 40 K An arc whose length is less than a semi-circle is

__________.

semi circle major arc minor arc sector of a circle C

11 40 K In a circle, if the measure of an arc is 120o, then

the arc is __________.

minor arc major arc semicircle segment A

12 40 K Which of the following can be the degree measure

of a minor arc?145

o180

o245

o270

o A

13 41 K The region bounded by two radii of a circle and

the intercepted arc of the circle is ________ of the

circle.

a chord a tangent a sector a segment C


circle. Then the shaded region represents

__________.

arc segment sector chord B

3


S.N. Com-

peten-

cy No.

Level

(K or

A)


15 41 K The figure at the right is a circle with center at O.

What does the shaded region represent?

Minor arc Major arc Sector Segment C

16 41 K Part of a circle bounded by AO, OB and arc AXB

is __________. (Hint: O is the center)

secant sector chord minor arc B

17 41 K In the figure given below, what is the segment of

circle O?

MON PON MPN QOM C

18 41 K Which of the following figures of a circle shows a

sector?

D

4


S.N. Com-

peten-

cy No.

Level

(K or

A)


19 41 K Which one of the following figures indicates a

sector of a circle?

B

20 41 K Which of the shaded parts of the following circles

represents a segment?

A

21 41 K O is the center of the circle. Which one of the

following regions shows the segment of a circle?

B

22 41 K The region bounded by two radii of a circle and

the arc they intercept is __________.

a segment of a

circle

a sector of a circle a quarter of a

circle

a semicircle B

23 41 K What is the part of a circle bounded by a chord

and an arc of the circle?

Diameter Chord Segment Sector C

24 41 K Which one of the following statements is true? A sector contains

a chord as one of

its sides

A sector of a circle

is a region bound

by an arc and two

radii

A sector of a circle

is a triangular

region

A segment of a

circle is a region

bounded by an arc

and two radii

B

5


S.N. Com-

peten-

cy No.

Level

(K or

A)


25 42 K In the figure to the right, line CD is ________. chord secant segment tangent B

26 42 K A line that intersects a circle at two points is

_________.

segment sector tangent secant D

27 42 K A line which cuts a circle at two points is

_______.

tangent radius secant sector C

28 42 K A straight line on a plane of a circle meets the

circle at most ____ points.

2 3 4 5 A

29 42 K In the circle below, line AB passes through it by

touching at point p. What is line AB with

reference to the circle?

Diameter Radius Secant Tangent D

30 42 K A line which touches a circle exactly at one point

is __________.

a secant line a tangent line diameter radius B

31 42 K Which line touches a circle exactly at one point? Chord Secant Segment Tangent D

6


S.N. Com-

peten-

cy No.

Level

(K or

A)


32 42 K What is the name of a line that touches a circle at

one point?

Arc Radius Secant Tangent D

33 42 K Which one of the following is true about tangent

of a circle?

It can pass through

the center of the

circle

Its end point can

lie on the circle

It can be the

diameter of a

circle

It intersects the

circle exactly at

one point

D

34 42 K Which of the following is true about tangent of a

circle?

A line intersects a

circle at two

points

A line intersects a

circle at exactly

one point

A line passes

through at the

center of a circle

A line does not

intersect a circle at

any point

B

35 42 K Which of the following describes the difference

between secant and tangent lines of a circle?

Secant line

touches a circle at

one point whereas

tangent line

touches a circle at

two points

Secant line forms

radius of a circle

whereas tangent

line forms

diameter of a

circle

Secant line crosses

a circle at two

points whereas

tangent line

touches a circle at

a point

With reference to

a circle, tangent

line is shorter than

secant line

C

36 42 K Which one is correct about Circle Q? AB is tangent to

circle Q

FG is tangent to

circle Q

CD is secant to

circle Q

E is a point of

tangency

D

37 42 K The figure below is a circle with center at O and A

is an exterior point. What kind of line can you

draw through points A and O?

Tangent Secant Chord Arc B

7


S.N. Com-

peten-

cy No.

Level

(K or

A)


38 42 K Line AB passes through the center of a circle.

What is this line called?

Arc Radius Secant Tangent C

39 42 K Which one of the following lines or line segments

is NOT possible to draw through the center of the

circle?

A secant A chord A tangent A diameter C

40 42 K In the figure below, point O is the center of the

circle. Which one is the correct statement?

You can draw a

tangent line

through point A

Point O is a point

of tangency

Point C is a point

of tangency

You can draw a

secant line through

points O and B

D

41 42 K Given the figure below, which one of the

following is correct?

AB is a secant line

of the circle

CD is a line of

tangency

Point P is a point

of tangency

OP is the secant

line of the circle

C

42 42 A Let A, B, and C be the three points not on the

same straight line. Then which one of the

following is true?

We can draw

many circles

which pass throuth

all the three points

A, B, and C

The perpendicular

bisector of AB and

BC can meet at

point C

We can draw a

secant line through

point A only

We can draw a

tangent line either

at point A or point

B or point C

D

43 42 A The maximum degree of an arc of a circle formed

by secant line is ______.45

o90

o180

o360

o C

8


S.N. Com-

peten-

cy No.

Level

(K or

A)


44 43 K Which of the following is the first step to

construct the center of a circle?

Drawing chords of

the circle

Drawing the circle Drawing

perpendicular

bisectors of a

chord

Drawing a tangent

line to the circle

B

45 43 K Which step is important to determine the center of

a circle by construction?

Drawing a tangent

line

Drawing a chord

of the circle

Drawing a point

inside the circle

Drawing a point

outside the circle

B

46 44 K An inscribed angle is an angle whose

_______________.

vertex lies on the

center of the circle

vertex lies on any

point on the circle

and subtended by

an arc of the circle

sides are tangents

to the circle

sides are tangents

to the circle and its

vertex lies outside

the circle

B

47 44 K The vertex of an angle lies on the circle and its

sides contain chords of the circle. This angle is

called ___________.

angle formed by

two inscribed

chords

central angle cyclic

quadrilateral angle

inscribed angle D

48 44 K In the figure to the right, if O is the center and A,

B, and C are points on the circle, which of the

following is true?

<AOB is a central

angle

<AOB is an

inscribed angle

<AOC is an

incribed angle

<ABC is a central

angle

A

49 44 K In circle O at the right, <AOC is _______. right angle obtuse angle inscribed angle central angle D

9


S.N. Com-

peten-

cy No.

Level

(K or

A)


50 44 K An angle inscribed in an arc whose degree

measure is less than 180o is ________.

acute obtuse right semicircle A

51 44 K An angle inscribed in an arc greater than a semi-

circle is ___________.

obtuse angle acute angle right angle reflex angle A

52 44 K In the figure below, O is the center of the circle.

Then which one of the following is a central angle

of the circle?

<ABC <BAO <AOC <BCO C

53 44 K Given a circle with center at O as shown below, if

<AOB is a central angle, which of the following is

NOT true?

m(<ACB)=1/2m(<

AOB)

m(<AOB)=m(AX

B)

m(<ACB)=1/2m(

AXB)

m(<AOB)=1/2m(

AXB)

D

54 44 K In the figure below, <AOB is a central angle of the

circle. Which one is an inscribed angle of the

circle?

AB <AOB <ACB C

10


S.N. Com-

peten-

cy No.

Level

(K or

A)


55 44 K If O is the center of the following circle, which

angle represents the inscribed angle?

<BCD <AOD <BCF <DCE A

56 45 K If O is the center of the circle shown, which one of

the following is true?

C


circle. What is the measure of <AOC?30

o60

o90

o120

o D

58 45 K In the figue given below, O is the center of the

circle. If m(<ABC)=70o, then what is m(<AOC)?

35o

70o

110o

140o D

11


S.N. Com-

peten-

cy No.

Level

(K or

A)


59 45 K O is the center of the circle in the figure below. If

m(<XOY)=60o, what is m(<XZY)?

30o

120o

180o

300o A

60 45 K In circle O at the right, m(<ABC)=35o. What is

m(<AOC)?

120o

90o

70o

35o C

61 45 K If O is the center of the following circle and if

m(<ABC)=80o, then what is m(<AOC)?

40o

80o

120o

160o D

62 45 K In the figure below, O is the center of the circle. If

m(<ABC)=50o then what is the degree measure of

the central angle?

25o

75o

100o

120o C

12


S.N. Com-

peten-

cy No.

Level

(K or

A)


63 45 K In the figure below, O is the center of the circle . If

m(<ABC)=80o, then what is the value of

m(<AOC)?

80o

100o

150o

160o D

64 45 K In the figure given below, find the measure of

central angle ROZ.35

o40

o70

o80

o C

65 45 K If O is the center of the circle, what is the value of

m?30

o60

o75

o80

o A


Then what is the measure of <ABC?15

o30

o45

o60

o B

13


S.N. Com-

peten-

cy No.

Level

(K or

A)



m(<AOC)=50o, what is m(<ABC)?

25o

50o

75o

100o A

68 45 K The measure of the central angle SOR is 80o. Then

find m(<SPR).

30o

40o

60o

80o B

69 45 K For a given circle O, determine the value of x. 35o

55o

70o

125o C

70 45 K In the figure below, O is the center of the circle

and m(<AOC)=110o. What is m(<ADC)?

45o

55o

90o

110o B

14


S.N. Com-

peten-

cy No.

Level

(K or

A)


71 45 K If the measure of the central angle AOB is 56o,

then what is the measure of angle ACB?

28o

56o

112o

124o A

72 45 K O is the center of the circle. If m(<AOC)=56o then

what is m(<ABC)?

28o

56o

84o

112o A

73 45 K The measure of the central angle AOB=64o. Then

what is the measure of angle APB?

32o

36o

42o

48o A

74 45 K In the figure, if m(<ACD)=24o, what is

m(<ABD)?

12o

24o

45o

48o B

15


S.N. Com-

peten-

cy No.

Level

(K or

A)


75 45 K Find the values of x and y. 12o and 16

o24

o and 32

o36

o and 48

o48

o and 64

o B


m(<B)=120o, then what is the measure of angle

ADC?

60o

110o

120o

240o A

77 45 K In circle O at the right, if AC is the diameter of

circle O, what is m(<ABC)?180

o120

o90

o60

o C

78 45 K What is the measure of an angle inscribed in a

semi-circle?

60° 90° 120° 150° B

16


S.N. Com-

peten-

cy No.

Level

(K or

A)


79 45 K In the figure below O is the center of the circle . If

m(<ACB)=48o, what is the measure of angle

ABC?

24o

42o

48o

96o B


What is the value of x?308

o128

o52

o26

o D

81 45 K In circle O with diameter AB as shown in the

figure to the right, m(<BAC)=55°. What is the

degree measure of arc AXC?

55° 70° 110° 125° B

17


S.N. Com-

peten-

cy No.

Level

(K or

A)


82 45 K In the figure shown below, O is the center of the

circle. Which of the following is true?m(AB)=45

o m(<BCA)=m(<A

OB)m(<AOB)=90

o m(<AOB)=1/2

m(<BCA)

C

83 45 K In the figure below, O is the center of the circle,

where m(ADC)=60o. Then which one is the

correct statement?

m(<ABC)=30o

m(<AOC)=60o m(ABDC) is twice

of m(AC)

m(AC) is twice of

m(ABDC)

C


Which of the following is true?m(<RPQ)=52

om(<ROQ)=52

om(<POQ)=52

o m(SR)≡m(RQ) C

18


S.N. Com-

peten-

cy No.

Level

(K or

A)


85 45 K If the figure below is a circle with center at O and

m(arc AXB)=120o, then m(<AOB) is:

60o

120o

180o

240o B


circle. If m(<AOC)=40o, then what is m(arc AC)?

20o

40o

80o

320o B

87 45 K In the figure, O is the center of the circle and

m(<BOC)=60o. What is m(<BDC)?

30o

60o

90o

120o A


and m(<BOC)=100o. Then what is m(<ADC)?

40o

50o

80o

100o A

19


S.N. Com-

peten-

cy No.

Level

(K or

A)


89 45 K In the figure given below, O is the center of the

circle and m(<HOR)=120o. What is m(<SPR)?

30o

60o

80o

120o A

90 45 K In the circle below, if m(<ABC)=80o, what is the

measure of arc AC?

40o

80o

160o

200o C


and m(arc AC)=60o. Then find the central angle P.

100o

120o

130o

140o B

92 45 K In the figure below, if <B=30o, then what is the

value of arc ADC?

15o

30o

60o

300o C

20


S.N. Com-

peten-

cy No.

Level

(K or

A)


93 45 K In the figure to the right, m(<BAC)=45o. What is

the measure of arc BXC?

120o

90o

75o

45o B

94 45 K In circle O, if the major arc ACB=280o as shown

in the figure, then what is the value of X?

160o

120o

80o

40o C

95 45 K In circle O shown bellow, if the measure of the

major arc ACB= 2800, what is the measure of the

angle marked by x?

80o

60o

40o

20o A


m(<QOR)=70o and m(arc QR)=x

o+ 55

o, then

what is the value of x in degrees?

15o

20o

70o

125o A

21


S.N. Com-

peten-

cy No.

Level

(K or

A)


97 45 K In the figure below, find the value of α. 34o

36o

70o

72o A

98 45 K O is the center of a circle and m(arc AB)=135o.

Then what is m(<AOP)?

17.5o

22.5o

35o

45o D

99 45 K If O is the center of the following circle and

m(<BOC)=70o then what is m(arc AB)?

35o

70o

110o

140o C

100 45 K Which of the following is true about the figure to

the right if O is the center?m(<AOB)=35

om(<ACB)=35

om(<DBC)=70

om(<ACB)=70

o B

22


S.N. Com-

peten-

cy No.

Level

(K or

A)


101 45 K In the figure below, O is the center of a circle and

m(<ABC)=55o. Then find the central angle AOB.

50o

60o

70o

80o C

102 45 A In circle O at the right, m(arc AYB)= 90o. Which

of the following is true?

m(<AOB)≠

m(<BOC)

m(<ABD)≠

m(<CDB)

m(arc AYB)≠

m(arc DXC)

m(arc

ABC)=m(arc

BCD)

D

103 45 A In circle O at the right, m(<BAC)=30o. What is

m(<AOB)?

60o

70o

120o

140o C

104 45 A In the figure given below, O is the center of the

circle and m(<SPT)=42o. Then find the measure

of central angle POT.

84o

94o

96o

100o C

23


S.N. Com-

peten-

cy No.

Level

(K or

A)


105 45 A If O is the center of the circle below and if

m(<ACD)=50o, what is the measure of arc DB?

25o

50o

80o

100o C

106 45 A In the figure below, O is the center of the circle

and measure of arc RPQ is 2400. Find m(<RPQ).

30o

60o

120o

180o B

107 45 A In circle O at the right, m(arc AXB)=1100. Find

the measure of <ABC.

70o

60o

45o

35o D

24


S.N. Com-

peten-

cy No.

Level

(K or

A)



and m(<POQ)=40o. What is m(<RSQ)?

35o

70o

140o

28o B

109 45 A In the figure below, O is the center of the circle. If

m (<XYZ)=120o then find m(arc XYZ).

60o

120o

180o

240o B


and m(<BOC)=120o. Then m(<BDC )=

__________.

360o

240o

120o

60o C

25


S.N. Com-

peten-

cy No.

Level

(K or

A)


111 45 A In the figure to the right, O is the center and

m(<ABC)=120o, then what is m(arc ABC)?

59o

60o

118o

120o D

112 45 A In the figure to the right, O is the center and

m(<ABC)=100o. Then what is m(<AOC)?

20o

40o

80o

160o D

113 45 A O is the center in the figure to the right and

m(<BCD)=160°. What is the degree measure of

<BAD?

20° 30° 40° 60° A

26


S.N. Com-

peten-

cy No.

Level

(K or

A)


114 45 A In the figure below, m(<ABC) = 1400. Then what

is m(<ADC)?

40o

70o

80o

140o A

115 45 A Given circle O with m(<ABC)=160o, what is

m(<ADC)?

20o

40o

80o

100o A

116 45 A Given circle O bleow, what is m(arc ACB)? 20o

40o

320o

340o C

27


S.N. Com-

peten-

cy No.

Level

(K or

A)


117 45 A Given the circle below where m(<AEB)=70o and

m(<CDE)=40o. What is m(arc AD)?

40o

70o

80o

140o D

118 45 A In the figure below, O is the center of the circle.

Then what is m(<APB)?112

o126

o140

o160

o B

119 45 A In the figure, if O is the center of the circle and

m(<BAC)=30o, then what is m(<ABC)?

40o

60o

80o

100o B

120 45 A In the figure, O is the center of the circle. If m(arc

AC)=80o, what is m(<BAC)?

40o

50o

80o

100o B

28


S.N. Com-

peten-

cy No.

Level

(K or

A)


121 45 A In the circle below, if O is the center, m(BC)=70o

and AB||DC, then what is m(<DBA)?

35o

55o

70o

110o A

122 45 A In the figure to the right, Arc AB is one half of arc

DC. The measure of <ADB is ________.100

o80

o(200/3)

o(100/3)

o D

123 45 A In the figure below, if m(<AED)=90o and

m(<BAC)=35o, what is m(<ABD)?

50° 55° 60° 70° B

124 45 A In the figure to the right, if AB is perpendicular to

CD and m(arc DB)=60o, what is m(<ABC)?

60° 80° 90° 120° A

29


S.N. Com-

peten-

cy No.

Level

(K or

A)


125 45 A In the figure below DE⊥FG and m(arc GE)=60o.

Find m(<DEF).

30o

60o

90o

120o B

126 45 A In the figure to the right, m(<ABD)=600 and

m(<APB)=900. What is m(<AXB)?

60o

80o

90o

120o D

127 45 A In the figure below, find m(arc BXC). 35o

45o

55o

90o A

30


S.N. Com-

peten-

cy No.

Level

(K or

A)


128 45 A In circle O at the right, chords AC and BD

intersect at Q, m(arc DA)≡m(arc CD)=xo and

m(arc AB)≡m(arc BC)=yo. If x=2y, find

m(<AQB).

120o

90o

60o

30o B

129 45 A In the figure below, if m (arc AB)=45o and

m(<AEB)=34o, which of the following is the

measure of arc CD?

68o

38o

23o

9o C

130 45 A If in the figure to the right, m(<DAX)=580,

m(<BXC)=480, and m(<DCX)=26

0. Then what is

m(<ACB)?

64o

74o

84o

116o B

31


S.N. Com-

peten-

cy No.

Level

(K or

A)


131 45 A In the circle below, if AC is tangent to the circle at

B and m(<DBA)=78o and m(DE)=62

o, then find

m(<BDE).

71o

124o

142o

156o A


where m(<BAE)=70o and m(<BOD)=70

o. Find

m(<ECD).

35o

70o

105o

140o A

133 45 A Given circle O, m(<BOC)=120o and

m(<ACO)=42o. What is the value of m(<ABO)?

18o

20o

22o

24o A

32


S.N. Com-

peten-

cy No.

Level

(K or

A)


134 45 A In the figure below, O is the center of the circle.

m(<BAC)=57o, then what is the value of

m(<BOC)?

57o

76o

114o

95o C

135 45 A In the figure below, if O is the center of the circle

and m(<AOB)=90o, then which of the following is

true?

m(<ACB)=270o

m(arc ADB)=180o m(<ACB)+m(<A

DB)=130o

m(<ACB)+m(<A

DB)=180o

D

136 45 A In the circle O given below, if m(<AEB)=70o and

m(<ADB)=50o then what is m(arc DC)?

40o

60o

70o

85o A

33


S.N. Com-

peten-

cy No.

Level

(K or

A)


137 45 A In the figure to the right, O is the center of the

circle, AB||DC, m(arc AB)=1100, and m(arc

DC)=500. Then the value of m is ________.

50o

110o

160o

200o A

138 45 A In the following circle, O is the center and

m(<ABC)=42o and m(<ECB)=38

o, then what is

m(<DOC)?

38o

42o

84o

96o D

139 45 A If O is the center of a circle and if m(<CDB)=30o

and m(<ACD)=100o then find m(<BFC).

60o

65o

130o

200o C

34


S.N. Com-

peten-

cy No.

Level

(K or

A)


140 45 A If O is the center of the circle in the figure to the

right and it represents the cross section of a pipe,

what is the measure of arc ABC in degrees?

40o

80o

280o

320o C

141 45 A In the figure below OA and OB are radii of circle

O, then which of the following is true?

A

142 46 K If chords AB and CD intersect at P inside a circle

as shown below, which of the following is true

about this circle?

m(<APC)=1/2m(

AYD)+1/2m(CSB

)

m(<APC)=1/2m(

AYC)+1/2m(BXD

)

m(<APC)=1/2m(

AYC)

m(<APC)=1/2m(

AZD)

B

143 47 K In the given circle , if m(arc AB)=76o and m(arc

BC)=36o, what is the measure of angle x?

18o

36o

56o

73o C

35


S.N. Com-

peten-

cy No.

Level

(K or

A)


144 47 K What is the measure of <CAD if m(arc CD)=60o

and m(arc BE)=100o as given below?

30o

60o

80o

120o C

145 47 K In the figure to the right, if m(DXC)=60o and

m(BYA)=100o, what is m(<AQD)?

120o

100o

80o

60o B

146 47 K If O is the center of the circle and chords AB and

CD intersect at E as shown below, what is

m(<CEB)?

48o

60o

72o

120o B

147 47 K In the following circle, O is the center and chords

AB and CD intersect at E. If m(<CEB)=80o and

m(arc AD)=90o, then what is m(arc CB)?

40o

45o

70o

90o C

36


S.N. Com-

peten-

cy No.

Level

(K or

A)


148 47 K What is the measure of <DEA in the figure

below?84

o96

o168

o192

o A

149 47 K In the figure given to the right, O is the center of

the circle, m(arc AB)=60o and m(arc DC)=40

o.

Then what is m(<AOB)?

40o

50o

60o

100o B

150 47 K In the figure below, find the degree measure of

<AXD.32

o40

o72

o90

o C

151 47 K If m(arc AB)=52o and m(arc CD)=36

o as shown in

the figure below, what is the value of β?

16o

44o

88o

136o D

37


S.N. Com-

peten-

cy No.

Level

(K or

A)


152 47 A In the figure below, m(arc AD) is 165o and m(arc

BC) is 55o. What is the value of angle Ɵ?

55o

70o

110o

220o B

153 47 K In the figure to the right, QS and PR are chords

and m(<PTQ)=50o. What is the measure of <PTS?

50o

100o

130o

260o C

154 47 K In the figure to the right, if m(<APD)=50o and

m(arc BRC)=40o, what is the measure of arc

DSA?

60o

50o

40o

30o A

155 47 K In the figure below, if m(<XPS)=30o and m(arc

SX)=40o, what is the measure of arc TY?

60o

50o

40o

20o D

38


S.N. Com-

peten-

cy No.

Level

(K or

A)


156 47 K In the circle below, the measure of <APC=65o

and

m(arc BD)=36o. What is m(arc AC)?

36o

65o

94o

130o C

157 47 K In the figure shown below, O is the center of the

circle. If m(BC)=60o and m(<BPC)=40

o, find

m(AD).

20o

40o

60o

80o A

158 47 K In the figure below, if m(WX)=a and m(YZ)=b

and m(<XPW)=β, which one of the following

statements is correct?

a-b=β a+b=β (a+b)/2=β a+b=β/2 C

159 47 A Two chords AC and BD intersect at point E in a

circle. If m(<ACB)=30o

and m(arc CXD)=120o,

what is the measure of <AEB?

30o

60o

75o

90o D

39


S.N. Com-

peten-

cy No.

Level

(K or

A)



and m(<AOC)=70o. Which of the following is

NOT true?

m(<ABC)=35o

m(<ACB)=55o

m(<BCD)=35o

m(<ADC)=70o D

161 47 A In the circle given below, O is the center and

m(BC)=40o, m(<AOE)=120

o. Then what is

m(<EFC)?

80o

100o

120o

140o B

162 47 A Given circle O where m(arc AB)=120o, m(arc

DC)=60o and m and n are parallel secant lines.

What is m(<BOC)?

45o

60o

90o

180o C

40


S.N. Com-

peten-

cy No.

Level

(K or

A)


163 47 A O is the center of the circle given below and AC

and BE interesect at F. If m(<BAC)=50o and

m(CDE)=140o, then find m(<AFB).

50o

70o

80o

110o D

164 48 K A quadrilateral inside a circle is called a cyclic

quadrilateral if _______________.

all its angles are

right angles

all its vertices lie

on the circle

one of its sides

passes through the

center

the diamonds meet

at the center

B

165 48 K If four different points on the circle are joined end

to end without crossing each other, what kind of

figure can be formed?

A rhombus A rectangle A parallelogram A cyclic

quadrilateral

D

166 49 K Which one is correct about a cyclic quadrilateral? Opposite sides of

a cyclic

quadrilateral are

congruent

All sides of a

cyclic

quadrilateral are

equal

A cyclic

quadrilateral is

inscribed in a

circle

Adjecent angles of

a cyclic

quadrilateral are

supplementary

C

167 49 K Which of the following is true about a cyclic

quadrilateral?

Opposite sides are

congruent

Opposite angles

are congruent

Opposite sides are

parallel

Opposite angles

are supplementary

D

41


S.N. Com-

peten-

cy No.

Level

(K or

A)


168 49 K In the figure to the right, ABCD is a quadrilateral

inscribed in a circle with center at O. Which is

correct about the inscribed quadrilateral ABCD?

<DBA is inscribed

in Arc CD

<ADC is a right

angle

<DAC and <ABC

are supplementary

<DAB and <DCB

are supplementary

D

169 49 K In the figure shown below, ABCD is a

quadrilateral inscribed in a circle. Which one is

the correct statement?

m(<ABC)=180o-

m(<ADC)/2

m(<ABC)+m(<A

DC)=180o

m(<ABC)+m(<C

BA)=180o

m(<ABC)/2+m(<

ADC)/2=180o

B

170 49 K In the figure below, ABCD is a quadrilateral

inscribed in a circle. Then which one of the

following is true about the cyclic quadrilateral?

m(<D)+m(<C)=18

0o

m(<A)+m(<C)=18

0o

m(<D)+m(<B)=36

0o

m(<A)+m(<B)=36

0o

B

171 49 K In circle O at the right, AC is the diameter of the

circle. Which of the following is always correct

about quadrilateral ABCD?

m(<BAC)=m(<B

CA)

m(<ABC)=m(<A

DC)

m(AD)+m(DC)=9

0o

∆ABC is an

isoceles triangle

B

42


S.N. Com-

peten-

cy No.

Level

(K or

A)


172 49 K From the following figures which one is a cyclic

quadrilateral?

A

173 49 K Which one of the following figures represents a

cyclic quadrilateral?

D

174 49 A In circle O and quadrilateral KLMN, if

m(<KLM)=q, then which of the following is NOT

true?

m(<KNM)=180o-

q

m(<KOM)=2q m(arc NM)=q m(<LKN)+m(<L

MN)=180o

C

175 51 K ABCD is a cyclic quadrilateral. If m(<DAB)=75o,

then m(<BCD) = _______.

15o

75o

105o

285o C

43


S.N. Com-

peten-

cy No.

Level

(K or

A)


176 51 K In the figure to the right, if m(<QRS)=980, find

m(<QPS).

108o

98o

82o

72o C


m(<BCD)=128o, find m(<BAD).

52o

64o

90o

116o A

178 51 K If ABCD is a cyclic quadrilateral as shown below

and if m(<A)=95o and m(<D)=75

o, then what is

m(<B)?

75o

85o

95o

105o D

179 51 K If ABCD given below is a cyclic quadrilateral and

if m(<A)=70°, m(<D)=85° then find m(<C).

85° 95° 110° 155° C

44


S.N. Com-

peten-

cy No.

Level

(K or

A)


180 51 K In the figure given below, PQRS is a cyclic

quadrilateral. Then find the value of Z.120

o140

o150

o160

o A

181 51 K In the figure below, ABCD is a cyclic

quadrilateral. E is on CD. If m(<ADE)=83o, what

is m(<ABC)?

83o

97o

166o

194o A

182 51 K In the following figure, PQRS is a cyclic

quadrilateral and T is on RS. If m(<PST)=110o,

then what is m(<PQR)?

35o

55o

70o

110o D

183 51 K In the circle below, if points A, B, C, and D are on

the circle and m(<BAE)=130o, then find

m(<DCB).

50o

65o

100o

130o D

45


S.N. Com-

peten-

cy No.

Level

(K or

A)


184 51 K In the figure to the right, ABCD is a cyclic

trapezium with AB||DC. If <ADC=85o, what is

the measure of <DAB?

85o

95o

135o

275o B

185 51 A In the figure to the right, ABCD is a cyclic

quadrilateral and m(ABC)=210o. What is

m(<ABC)?

105o

80o

75o

60o C

186 51 A In the figure below, m(arc ABC)=160o. Then what

is m(<ABC)?

80o

100o

160o

200o B

187 51 A In the figure to the right, ABCD is a quadrilateral.

If m(<DCB) is 3 times larger than m(<DAB),

what is the measure of <DCB?

180o

135o

90o

45o B

46


S.N. Com-

peten-

cy No.

Level

(K or

A)


188 51 A The measure of the opposite angles of a cyclic

quadrilateral are in the ratio 2:3. What is the

measure of the smallest of these angles?

36o

54o

72o

108o C

189 51 A In the figure below, ABCD ia a cyclic

quadrilateral and O is the center of the circle.

What is m(<BAD)?

114o

123o

132o

246o B

190 51 A Given circle O and cyclic quadrilateral ABCD, if

m(<AOC)=168o then what is m(<ABC)?

84o

96o

168o

180o B

191 51 A In the following figure, if ABCD is a cyclic

quadrilateral, what is the value of x?60

o80

o100

o120

o A

47


S.N. Com-

peten-

cy No.

Level

(K or

A)


192 51 A If ABCD is a cyclic quadrilateral as shown, find

the value of x.

11 14 18 48 A

193 51 A ABCD is a cyclic quadrilateral in the figure

below. Then what is the value of x?20

o80

o100

o43

o A

194 51 A In the figure below, find the value of x. 140o

110o

55o

35o C

48


S.N. Com-

peten-

cy No.

Level

(K or

A)


195 51 A ABCD is an inscribed cyclic quadrilateral as

shown in the figure below where O is the center of

the circle. Find m(<ADC).

20o

60o

90o

120o B

196 51 A If in the figure, ABCD is a cyclic quadrilateral,

then find the value of x.10

o15

o20

o25

o B

197 51 A ABCD is an inscribed quadrilateral as shown in

the figure below. What is the value of m(<BAD)?20

o80

o100

o180

o B

49


S.N. Com-

peten-

cy No.

Level

(K or

A)


198 51 A In the fiogure to the right, ABCD is a cyclic

quadrilateral and m(<DAB)=110o, m(<CDE)=30

o

and ∆DCE is isoceles. Then the value of x and y

respectively are __________.

60o and 120

o70

o and 110

o70

o and 120

o80

o and 100

o C

199 51 A In the figure below, ABCD is a cyclic

quadrilateral and PQ is tangent to the circle at

point A. If m(<C)=115o and m(AB)=144

o, what is

the value of x?

43o

50o

65o

72o A

50


S.N. Com-

peten-

cy No.

Level

(K or

A)


1 52 K Which of the following is a certain event? If a night falls, a

day dawns

Every day your

school ends at 3

pm sharp

You go home from

office by bus

You always get

above 90% in

Math exam

A

2 52 K Which one is a certain event? By tossing a coin

once, we can get

both head and tail

Getting hot ice

cube in

refrigerator

The sun sets in the

west

A month with 7

days

C

3 52 K Which of the following is a certain event? When water boils,

it changes to milk

December will

follow November

next year

You will grow to

be 30 meters tall

It will rain

tomorrow

B

4 52 K If tomorrow is Tuesday, then yesterday was

Sunday. This is an event which could be said

___________.

a certain event an impossible

outcome

1/3 chance to

happen

50% chance to

happen

A

5 52 K Which of the following is an example of

impossible outcomes?

Landing on the

moon

Raining next week Winning a lottery Walking on the

sun

D

6 52 K A bag contains 2 green, 4 blue and 5 red balls. If a

ball is drawn from the box, which of the following

outcomes is impossible?

Drawing a white

ball

Drawing a green

ball

Drawing a red ball Drawing a blue

ball

A

7 52 K In rolling a die once, which event is an impossible

outcome?

{1} {4} {6} {7} D

8 52 K Given an expirement with sample space (s)={2, 4,

6} which event is certain?

Odd number Even number Multiple of 3 Factor of 6 B

9 52 K Twelve pieces of paper are labeled by numbers 1

to 12 and put in a box. Which of the following is

an impossible event when a piece of paper is

drawn from the box at random?

The number is less

than 13

The number is

labeled 3

The number is

greater than 12

The number is

even

C

1


S.N. Com-

peten-

cy No.

Level

(K or

A)


10 52 K A box contains cards labeled with numbers as

shown below. Which event is an impossible

outcome?

A number whose __________________.

ones digit equals 2 tens digit equals 5 ones digit equals 5 tens digit equals 2 B

11 52 K In a box there are five cards labelled with letters.

Which event is an impossible outcome?

{A} {B} {D} {H} C

12 52 K Which of the following is true? An outcome with

a probability of 0

is possible

An outcome with

a probability of 1

is impossible

An outcome with

a probability of 0

is impossible

An outcome with

a probability of 0

is certain

C

13 52 K Which statement describes probability of an

outcome correctly?

An outcome with

probability of 1 is

impossible

An outcome with

probability of 0 is

certain

There is a

probability higher

than 1 for some

outcomes

The probability of

an outcome is

between 0 and 1

D

14 52 K Four students label their experiment in the scale as

shown. Whose probability is certain?

Abebe Ahmed Almaz Hayat B

15 53 K A student tossed two coins and obtained {HT}

where H means "heads" and T means "tails." What

is this outcome, {HT}, called?

An event An experiment A probability set A sample space A

2


S.N. Com-

peten-

cy No.

Level

(K or

A)


16 53 K When we roll a die with six sides once, what is the

sample space?

{1, 2, 3} {1, 2, 3, 4} {1, 2, 3, 4, 5} {1, 2, 3, 4, 5, 6} D

17 53 K Hana has ten identical cards numbered one to ten.

She draws a card at random and records the

number on it. What are the possible outcomes for

this event?

{1, 2, 3} {1, 2, 3, 4} {1, 2, 3, 4, 5, 6, 7} {1, 2, 3, 4, 5, 6, 7,

8, 9, 10}

D

18 53 K Which one is the sample space of tossing a coin

twice?

(H, T) (HH, TT) (HT, HT) (HH, HT, TH, TT) D

19 53 K If we toss three coins, then the possibility set is

__________.

{HHH, HHT,

HTH, HTT, THH,

THT, TTH, TTT)

{HHH, TTT,

THT, HTT, HTH,

TTH}

{HHH, TTT,

THT, HTH}

{HHH, THH,

TTH, TTT}

A

20 53 K If a coin is tossed three times, the possible

outcomes will be __________.

2 4 6 8 D

21 53 K If the sample space is {HH, HT, TH, TT} then

what is the experiment?

Tossing a coin Tossing two coins Tossing three

coins

Tossing four coins B

22 53 K Toss a coin and a die once. How many possible

outcomes are there?

2 6 8 12 D

23 53 K A bag contains 3 red, 5 black and 2 yellow balls.

You draw one ball from the bag. How many

possible outcomes are there?

2 3 5 10 D

24 54 K If a six-sided fair die is rolled, what is the

probability of showing 3 up?

1 1/2 1/3 1/6 D

3


S.N. Com-

peten-

cy No.

Level

(K or

A)


25 54 K If you roll a die once, what is the probability of

getting number four?

1/6 2/6 3/6 4/6 A

26 54 K If a single die is thrown once, what is the

probability of getting an even number?

1/6 1/3 1/2 5/6 C

27 54 K In rolling a fair die once, what is the probability of

getting an even number?

0 1/3 1/2 1 C

28 54 K A fair six-sided die is rolled. What is the

probability of getting an even number?

1/6 1/3 1/2 2/3 C

29 54 K If a fair six-sided die is rolled once, what is the

probability of getting a number less than 4?

1/6 1/4 1/3 1/2 D

30 54 K A mathematics teacher rolls a 6-sided die once.

What is the probability of getting a number less

than 4?

1/6 1/4 1/3 1/2 D

31 54 K In rolling a die once, what is the probablity of

getting a number less than 5?

1/6 1/3 2/3 5/6 C

32 54 K A die is rolled. What is the probability of getting

a multiple of 2?

1/6 1/4 1/3 1/2 D

33 54 K Two dice are rolled. What is the probability that

the sum of the events is 6?

1/12 1/9 5/36 5/18 C

34 54 K Two dice are thrown at the same time. What is the

probability of getting 7 as their sum?

1/6 1/9 1/12 1/18 A

4


S.N. Com-

peten-

cy No.

Level

(K or

A)


35 54 K A pair of dice is rolled. What is the probability

that the sum of the numbers observed is "8"?

5/36 6/36 7/36 8/36 A

36 54 K What is the probablity of getting a sum 9 from the

two throws of a die?

1/6 1/8 1/9 1/12 C

37 54 K Two dice are rolled. What is the probability of

their sum being 9?

1/18 1/9 1/6 1/3 B

38 54 K Two dice are rolled. What is the probability of

their sum being 13?

0 1/6 1/3 1/2 A

39 54 K If two dice are thrown at the same time, what is

the probability that the sum of dots on the top

faces will be less than 10?

11/12 5/6 1/6 1/12 B

40 54 K Roll a six-sided die once. What is the probability

of getting 1 or 6 on the upper face?

1/6 1/3 1/2 2/3 B

41 54 K A fair die numbered 1, 2, 3, 4, 5, 6 is rolled. What

is the probability of getting number 1 or 6?

2/3 1/2 1/3 1/6 C

42 54 K A pair of fair dice tossed once. What is the

probability of getting the same number on both

dice?

1/3 1/6 4/6 5/6 B

43 54 K If you toss two coins, what is the probability of

getting two heads?

1/4 1/2 3/4 1 A

44 54 K A coin is tossed once. What is the probability of

getting head and tail?

0 1/3 1/2 1 A

5


S.N. Com-

peten-

cy No.

Level

(K or

A)


45 54 K A bag contains 3 white balls and 6 black balls. If a

ball is drawn at random, what is the probability

that the drawn ball is white?

0 1/3 2/3 1 B

46 54 K A bag contains 6 black and 8 white balls. In a

single draw, what is the probability that the ball is

white?

3/4 4/7 3/7 1/8 B

47 54 K A jar contains 2 orange, 5 blue and 3 red marbles.

If a marble is drawn at random from the jar, what

is the probability of getting a blue marble?

4/5 1/2 3/10 1/5 B

48 54 K A bag contain 3 yellow, 5 blue and 2 red balls. A

ball is drawn at random. What is the probability of

obtaining a red ball?

1/2 1/3 1/4 1/5 D

49 54 K A bag contains 3 orange, 4 blue, 5 red amd 8

yellow marbles. What is the probability of getting

a red marble when a marble is drawn from the

bag?

3/20 1/5 1/4 2/5 C

50 54 K What is the probability of choosing a green ball

from a box containing 5 red, 6 green and 4 blue

balls?

4/15 1/3 2/5 2/3 C

51 54 K A basket contains 5 lemons, 3 organges and 8

bananas. If you take a fruit from the basket

without looking, what is the probability that you

get a lemon?

3/16 5/16 1/2 1 B

52 54 K A bag contains 6 black and 8 white balls. One ball

is drawn at random. What is the probablity that

the ball is white?

3/4 4/7 1/8 3/7 B

6


S.N. Com-

peten-

cy No.

Level

(K or

A)


53 54 K A bag contains 4 red balls and 5 black balls. If a

ball is drawn from the bag at random, what is the

probability of getting a black ball?

1/3 4/9 5/9 4/5 C

54 54 K There are 25 pens in a box. 12 of the pens are

blue. 8 of the pens are black. The rest of the pens

are red. If one pen is chosen at random, wht is the

probablity of getting a red pen?

1/5 8/25 12/25 4/5 A

55 54 K A bag contains 40 balls. 15 are green balls and 9

are yellow. The rest of the balls are red. A ball is

chosen at random. What is the probability of this

ball being red?

9/4 3/8 2/5 6/10 C

56 54 K The probablity of drawing a black ball in an

experiment is 2/5. What is the probablity of not

drawing a black ball?

0 2/5 3/5 1 C

57 54 K If you select one ball without looking from 1 red,

2 green and 2 yellow balls, which outcome has

lowest probability?

Green Red Yellow All have equal

chances

B

58 54 K What is the probability of drawing a vowel from a

total of 26 English alphabet?

1/26 4/26 5/26 21/26 C

59 54 K Six slips of paper labelled with letter

"B","A","N","A","N","A" are reshuffled in a hat.

What is the probability of drawing a slip with

letter N?

2/3 1/2 1/3 1/6 C

60 54 K You select one letter from the word "LAMS"

randomly. What is the probability of selecting a

vowel?

0.25 0.5 0.75 1 A

7


S.N. Com-

peten-

cy No.

Level

(K or

A)


61 54 K What is the probability of choosing letter 'A' from

the word MATHEMATICS at random?

1/11 2/11 1/10 2/10 B

62 54 K One letter is chosen randomly from the word

"experiment". What is the probability of choosing

a vowel?

1/5 2/5 3/5 4/5 B

63 54 K What is the probability of getting a letter of vowel

or consonant from the word "probability" ?

4/11 7/11 0 1 D

64 54 K What is the probability that even prime numbers

are chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10?

2/3 3/5 1/2 1/10 D

65 54 K If you draw a card from 16 cards numbered from 1

to 16, what is the probability of drawing a card

with an even number?

1/4 1/3 1/2 1 C

66 54 K If a deck of cards are labeled 1 to 25, what is the

probability of drawing a card with an even

number?

1/25 2/25 12/25 13/25 C

67 54 K A number from 1 to 30 is chosen at random. What

is the probability of choosing a number less than

10?

3/10 2/9 2/10 1/3 A

68 54 K There are nine cards in a box. Each card is

labelled with a natural number from 1 to 9. If you

take a card once at randam, what is the probability

of getting an even number?

4/9 5/9 6/9 1 A

69 54 K A box contains small balls numbered from 1 to

100. If you pick a ball from the box randomly,

what is the probability of the ball being 50 or less?

50/100 49/100 25/100 5/100 A

8


S.N. Com-

peten-

cy No.

Level

(K or

A)


70 54 K Almaz has five cards numbered 1 to 5. She draws

one card and records the number. What is the

probability that the result will be a multiple of 2?

1/5 2/5 4/5 4/5 B

71 54 K Hailu has four cards numbered 1 to 4. He draws

one card and records the number. What is the

probability of getting a multiple of 2?

1/4 1/3 1/2 3/4 C

72 54 K A number is selected at random from 1 to 20.

What is the probability to get a number divisible

by 3?

1/4 6/10 3/10 3/20 C

73 54 K Seven cards numbered 2 to 8 are in a bag. Pick

one card from the bag once. What is the

probability of the card being an even number?

1/7 3/7 4/7 6/7 C

74 54 K There are five cups of coffee on a table. Two of

them contain sugar. What are your chances of

choosing a cup with sugar in it?

1/5 2/5 3/5 4/5 B

75 54 K In a class there are 12 boys and 14 girls. The

teacher calls on a student at random to read a

passage. What is the probability that the first

person called is a girl?

1/7 6/13 7/13 6/7 C

76 54 K If you spin the spinner once, what is the

probablity of getting number 8?

1/8 1/4 1/2 1 A

9


S.N. Com-

peten-

cy No.

Level

(K or

A)


77 54 K The spinnes is rotated and the pointer points either

black or white color. What is the probability that a

spinner points black?

1/8 1/4 1/3 1/2 D

78 54 A A fair die is rolled once. What is the probability

that the number is greater than 2 and even?

1/2 1/3 2/3 8/6 B

79 54 A In a rolling of a die, the event(s) that a multiple of

2 and 3 will appear on the upper face of the die is

___________.

2 and 3 4 and 6 2, 4 and 6 6 D

80 54 A If three coins are thrown, what is the probability

of obtaining at least one head?

7/8 1/2 3/8 1/4 A

81 54 A A fair die is rolled three times and the number was

written down each time. What is the probability

that a prime number will be written down three

times?

3/2 8/27 1/8 1/9 C

82 54 A If three coins are thrown, what is the probability

of obtaining at least two tails?

1/8 3/8 4/8 5/8 C

83 54 A If three coins are tossed, what is the probability of

obtaining at least one head?

1/8 4/8 7/8 1 C

84 54 A A bag contains 10 red, 8 green and 2 white balls.

Each ball has an equal chance of being chosen.

What is the probability of choosing a ball that is

not red?

3/5 1/2 2/5 1/10 B

10


S.N. Com-

peten-

cy No.

Level

(K or

A)


85 54 A A box contains 20 balls. 4 of them are blue, and

the rest are yellow or red. If the number of yellow

balls is three times that of red, the probability of

picking a red ball at random is ________.

1/5 2/5 3/5 4/5 A

86 54 A The probability that Abebe wins a game when he

plays against his friend Tolossa is 0.3. What is the

probability that Abebe does not win the game?

3/10 5/10 7/10 9/10 C

87 54 A A school has forty classrooms numbered from 1 to

40. What is the probability that a classroom

number has the numeral '1' in it?

0 1/40 1/10 13/40 D

88 55 K The probability that I win a game of tennis when I

play against my friend is 0.75. What is the

probability that I do not win?

0 0.25 0.75 1 B

89 55 K The probability that Bikilla rides a bicycle to go to

school is 0.35. What is the probability that Bikilla

does not ride a bicycle to go to school?

0.75 0.65 0.55 0.45 B

90 55 K The table shows the number of boys and girls in

Year 7 and 8 at a local school. If you randomly

select one student from Year 8, what is the

probability that the student is a boy?

0.4 0.55 0.6 0.9 C

91 55 K Toss two coins at the same time. What is the

probability of getting two heads?

0.25 0.5 0.75 1 A

92 55 K Mesfin tosses two coins at the same time. What is

the probability of getting a head on both coins?

0.25 0.5 0.75 1 A

11


S.N. Com-

peten-

cy No.

Level

(K or

A)


93 55 K A bag contains 10 red and 10 blue balls. One ball

is selected at random. What is the probability of

black ball?

0 0.5 0.75 1 A

94 55 K A bowl of fruit contians 4 apples, 2 banabas, 3

lemons and 1 orange. Kebede takes a piece of fruit

without looking. What is the probability that he

takes an apple?

0.4 0.3 0.2 0.1 A

95 55 K A letter is selected randomly from the word

"GALIMATIUS." what is the probability of

selecting a consonant?

0.4 0.5 0.6 0.8 B

96 55 K What is the percentage of choosing a vowel in the

word "equilateral"?

0.545 0.455 0.5 0.4 A

97 55 K What is the probability that a number chosen from

the numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a

prime number?

0.222 0.4 0.6 0.8 B

12


S.N. Com-

peten-

cy No.

Level

(K or

A)


1 56 K In the figure below, ∆ABC is a right-angled

triangle. Which of the following is true?a

2=(AD)x(DC) b

2=(AC)x(DC) a

2=(AC)x(AB) b

2=a

2+b

2 B

2 56 K In ∆ABC, angle C is a right angle with CD⊥AB.

Then which relation is correct?

AD=BD (AB)(AD)=(AC)2

(AB)(AD)=(BC)2 (AB)(BC)=(AB)(

BD)

B


triangle where AD is the altitude of the

hypotenuse, BD=12cm and DC=4cm. Then what

is the value of AB?

2√3cm 4√3cm 6√3cm 8√3cm D

4 56 K In the figure below, if BD=9cm and AD=3cm,

then what is the length of BC?

3√3 6√3 3√6 2√3 B

1


S.N. Com-

peten-

cy No.

Level

(K or

A)


5 56 K In the figure below, ∆ACB is a right-angled

triangle with the right angle at C and CD⊥AB,

where D is on AB. Then what is the value of AC

if AD=6cm and DB=12cm?

6√2cm 6√3cm 6√5cm 6√6cm B

6 56 A In the ∆ABC below, what is the value of x if ∆

ABC is a right-angled triangle where

m(<ABC)=90o and BD is altitude of AC?

48cm 32cm 12cm 4√3cm D

7 56 A In the figure below, AC⊥BC and CD⊥AB. If

AD=9cm and BD=16cm, what is the length of

CD?


8 56 A In the figure below, ABC is a semicircle with

center at O. If BD⊥AC such that AB=5cm and

BD=4cm, what is the lenght of the radius (OC)?

3 25/3 25/6 25 C

2


S.N. Com-

peten-

cy No.

Level

(K or

A)


9 56 A In the figure given below is a semicircle with

center at O. If AD⊥CB, AC=10cm and CD=5cm,

then which of the following is true?

BC=15cm DB=20cm AD=5√2 cm AB=10√3 cm D

10 56 A In a right angled triangle ABC given below, if BD

is the altitude to the hypotenuse and AD=12cm,

AB=13cm, then what is the measure of DC?

25/12cm 5cm 144/13cm 25cm A

11 56 A In the figure below, ∆ABC is a right angled

triangle. If m(<ABC)=90o and BD is the altitude

to the hypotenuse AC, then what is the perimeter

of ∆ABC?

15+ 2√15 9+ 2√15 15+ 3√5 6+ 3√5 C

12 57 K Which statement is true about a right-angled

triangle ABC?c

2=a

2+ b

2b

2=a

2+c

2a

2=b

2+c

2a

2=c

2-b

2 C

A

B

CD 5cm4cm

3


S.N. Com-

peten-

cy No.

Level

(K or

A)


13 57 K Given the right-angled triangle as follows, which

one of the following states pythagoras' theorem?b

2=ADxAB a

2=BDxAB h

2=ADxBD a

2 + b

2 = c

2 D

14 57 K Which of the following figures represents a right-

angled triangle?

D

15 57 K If AB=BC=AC are sides of a triangle and AD is

the altitude, which of the following is true?

∆ABC is a right-

angled triangle

∆ADB is a right-

angled trianglem(<BAC)=90

o(BC)

2=(AB)

2+(A

C)2

B

16 57 K If a right-angled triangle ∆ABC has legs AB=4cm

and BC=3cm, what is the length of its

hypotenuse?

1cm 5cm 6cm 7cm B

4


S.N. Com-

peten-

cy No.

Level

(K or

A)


17 57 K PQR is a right-angled triangle at Q with PQ=4cm

and QR=3cm. Find the length of PR.

5cm 6cm 7cm 8cm A

18 57 K In the given figure below, find the value of X. 25cm 12cm 7cm 5cm D

19 57 K ∆ABC has base length 3cm and hypotenuse 5cm.

Find the height of the triangle.

2cm 4cm 6cm 8cm B

20 57 K In the figure below, find the value of x. 3cm 4cm 5cm 6cm C

5


S.N. Com-

peten-

cy No.

Level

(K or

A)


21 57 K Find the length of AB in the given figure. 6 8 10 14 C

22 57 K In the figure below, ∆ABC is right-angled at B,

then what is the value of X?



triangle and its legs AB=6cm and BC=8cm. What

is the length of the hypotenuse?

2cm 4cm 10cm 14cm C

24 57 K If a right-angled triangle has a leg of length 6cm

and its hypotenuse is 10cm, then what is the

second leg's length?

4cm 6cm 8cm 16cm C

25 57 K The length of two legs of a right-angled triangle

are 12cm and 16cm. Find the length of its

hypotenuse.


6


S.N. Com-

peten-

cy No.

Level

(K or

A)


26 57 K In the right-angled triangle below, if hypotenuse is

13cm and one leg is 12cm, then what is the length

of the other leg?

3cm 4cm 5cm 6cm C

27 57 K In the right-angled triangle shown below, what is

the value of x?

12cm 25cm 144cm 169cm A

28 57 K In the figure below, find the length of AC, if

AB=13cm and BC=12cm. Hint <C=90o

12cm 9cm 6cm 5cm D

29 57 K What is the perimeter of a right-angled triangle in

the given figure?


7


S.N. Com-

peten-

cy No.

Level

(K or

A)


30 57 K In the figure below, find the value of 'b'. 9cm 10cm 11cm 13cm A

31 57 K In the figure below, ∆DEF is right-angled at F.

Find the value of X.


32 57 K Find the length of BC in the given right-angled

triangle below.

3√5cm 5√3cm √15cm 15cm C

33 57 K Tola ran 4km east and Chalitu ran 5km north.

How far are they from each other?

3 km √18 km 6 km √41 km D

8


S.N. Com-

peten-

cy No.

Level

(K or

A)


34 57 K What is the length of AC in the given triangle

below?


35 57 K If the length of the hypotenues and one of its side

length of a right-angled triangle are 30cm and

20cm respectively, what is the length of the other

side?

22.36 cm 23.56 cm 24.01 cm 25.45 cm A

36 57 K Find the length of the unknown side x. √5 √6 √7 √8 C

37 57 K ∆ABC is an isoceles right-angled triangle as

shown in the figure below. If BC=6cm, what is the

length of AC?

3√2 6√2 2√6 2√3 B

38 57 K One leg of an isosceles right-angled triangle is

8cm long. What is the length of the hypotenuse?

4√2 cm 6√2 cm 8 cm 8√2 cm D

9


S.N. Com-

peten-

cy No.

Level

(K or

A)


39 57 K One leg of an isoceles right-angled triangle is 3√2.

What is the length of the hypotenuse?

6cm 8cm 10cm 12cm A

40 57 K What is the altitude of an equilateral triangle

whose side is 6cm long?

3cm 3√2cm 3√3cm 6cm C

41 57 K In the figure below, ∆PQR is an equilateral

triangle. QS⊥PR and QR=10cm. What is the

length of QS?

3√5 5√3 10√3 25√3 B

42 57 K How long is the altitude of an equilateral triangle

if the length of one side of the triangle is 8cm?

4cm 4√3cm 8cm 24cm B

10


S.N. Com-

peten-

cy No.

Level

(K or

A)


43 57 K How long is an altitude of an equilateral triangle

whose side is 4cm?

12cm 8cm 2√3cm 4√3cm C

44 57 K What is the length of the altitude of an equilateral

triangle of side 8cm?

3√3cm 4√3cm 8√2cm 16√2cm B

45 57 K What is the height of an issosceles triangle where

AD=BD in the given figure below?

6cm 8cm 18cm 26cm A

46 57 K In the figure below, ∆ABD is a right-angled

triangle and D is on AC such that BD┴AC. If BD

=12cm and AD=5cm, then find AB.

21cm 13cm 9cm 7cm B

47 57 K In the figure below, D is the midpoint of AC and

BD⊥AC. What is the length of BD in cm?

15 16 18 20 D

11


S.N. Com-

peten-

cy No.

Level

(K or

A)


48 57 K What is the diagonal of a square with side 10cm? 12.12 cm 14.14 cm 13.13 cm 15.15 cm B

49 57 K What is the diagonal of a rectangle whose sides

are 8cm and 6cm long?

4cm 6cm 8cm 10cm D

50 57 K Let PQRS be a rectangle. If PS=6cm and PR=10

cm, then what is the value of SR?

16 14 8 6 C

51 57 K What is the perimeter of the rhombus if the

diagonals are 8cm and 6cm long?


52 57 K If ABCD is a rhombus where the lengths of its

diagonals AC and BD are 10cm and 24cm,

rspectively, what is the length of the side of the

rhombus?


53 57 K The figure shown below is a trapezium. If

AD=BC=5cm, DC=7cm and DE=4cm, what is the

length of AB?

3cm 6cm 13cm 17cm C

12


S.N. Com-

peten-

cy No.

Level

(K or

A)


54 57 K What is the perimeter of an isosceles trapezium

with height 3cm and parallel sides are 6cm and

14cm?


55 57 K In the figure to the right, what is the perimeter of

trapezium ABCD?


56 57 K The figure below is a right cube of side 4cm long.

Find the length of DE.

4cm 4√2cm 4√3cm 5cm B

57 57 K In the figure below, the lateral surface area of the

triangullar prism is _________.

24 sq. unts 42 sq. units 64 sq. units 72 sq. units D

13


S.N. Com-

peten-

cy No.

Level

(K or

A)


58 57 K The total surface area of the triangullar prism

given below is _________.

24 sq. units 42 sq. units 72 sq. units 84 sq. units D

59 57 K ∆ABC is a right-angled triangle in the figure

shown below. Find the length of CD.

2√5cm 4cm 5√2cm 20cm A

60 57 K From the following given below, which one is the

pythagorean triple?

1, 2, 3 2, 3, 4 3, 4, 5 4, 5, 6 C

61 57 K Which of the following set of numbers could be

the lengths of sides of a right-angled triangle?

2, 3, 4 4, 5, 6 6, 8, 10 4, 6, 8 C

62 57 K From the given alternatives, which shows the three

sides of a right-angled triangle?

3, 4, 5 4, 6, 8 6, 12, 13 8, 9, 10 A

63 57 K Which of the following is pythagoras triple? 5, 12, 13 21, 22, 29 5, 7, 9 1 , 2, 3 A

14


S.N. Com-

peten-

cy No.

Level

(K or

A)


64 57 K If three sides form a right-angled triangle as

shown, then which one of the following is a

correct pythagorean triple?

5, 12, 13 9, 12, 13 6, 9, 10 4, 6, 10 A

65 57 K Which of the following lengths can be the sides of

a right-angled triangle?

3cm, 4cm, 6cm 6cm, 8cm, 9cm 6cm, 7cm, 9cm 6cm, 8cm, 10cm D

66 57 K If a2+b

2=c

2 then a, b and c are a pythagorean

triple. Which one of the following is a

pythagorean triple?

6, 10, 12 12, 16, 20 15, 19, 25 17, 19, 20 B

67 57 K What are the values of a, b and c for ∆ABC to be

right-angled at B?

a=3, b=4, c=5 a=5, b=13, c=12 a=6, b=8, c=10 a=9, b=12, c=15 B

68 57 A A rectangular floor has a 5m diagonal and 3m

width. To cover this floor with carpet, what

length should it be?

9m 8m 6m 4m D

69 57 A The length of the side of a rhombus whose

diagonals are of length 6 units and 8 units is

________.

3 units 4 units 5 units 6 units C

15


S.N. Com-

peten-

cy No.

Level

(K or

A)


70 57 A A square has a diagonal of 6√2cm. What is the

area of the square?6cm

212cm

224cm

236cm

2 D

71 57 A If the two sides of a triangle are perpendicular to

each other and its legs are equal and the

hypotenuse of the triangle is 8cm, then what is the

value of one leg?

4√2cm 8√2cm 16cm 12cm A

72 57 A ∆ABC is an equilateral triangle with each side "a"

units long as shown in the figure below. What is

the value of "h" in units?

√2/3 a √2/4 a √3/2 a √3/4 a C

73 57 A In the figure below, ABCD is an isosceles

trapezium with leg 5cm long, altitude 4cm and one

of the bases 10cm long. What is the area of the

trapezium?

24cm2

28cm2

48cm2

56cm2 B

74 57 A In the figure below, what is the value of AC? 3cm 5cm 3√2cm 2√3cm C

16


S.N. Com-

peten-

cy No.

Level

(K or

A)


75 57 A What is the length of ED in the figure below? 1cm 2cm 3cm 4cm D

76 57 A In ∆ABC given below, find the area of the shaded

region.13cm

215cm

226cm

230cm

2 A

77 57 A In the figure given below, calculate the length

marked "x".

25cm 16cm 7cm 5cm D

17


S.N. Com-

peten-

cy No.

Level

(K or

A)


78 57 A In the figure shown below, find the area of

rectangle PQRY.16cm

224cm

236cm

250cm

2 B

79 57 A If ABCD shown below is a parallelogram, find its

area.16cm

220cm

228cm

235cm

2 C

80 57 A Yohannes runs 4km to west and then 3km to

south. How far is he from the starting point?

1km 3km 5km 7km C

81 57 A If a man goes 12m to east and 16m to south, then

the distance from the beginning to the end is

_____.

28m 20m 16m 12m B

82 57 A From the same point A, Tesfu runs 6km to east

and Daniel runs 4km to south. What is the shortest

distance between Tesfu and Daniel?

2√13km 4√13km 10√13km 12√2km A

83 57 A A tree casts a shadow of 24 meters long. If the tip

of the shadow is 25 meters far from the top of the

tree, how high is the tree from the ground?

10 meters 9 meters 7 meters 5 meters C

18


S.N. Com-

peten-

cy No.

Level

(K or

A)


84 57 A A ladder of length 5m leans against a vertical wall.

If the top of the ladder reaches 4m up the wall,

find the distance of the foot of the ladder from the

wall.

5m 4m 3m 2m C

85 57 A A ladder of length 10m leans against a vertical

wall of 6m. What is the distance between the base

of the wall and the foot of the ladder?

16m 10m 8m 6m C

86 58 K Sin 30o is the same as _______. tan30

osin60

otan60

ocos60

o D

87 58 K In the figure given below, <A=45o and right angle

at <E. Then which of the following is correct

about sin 45o?

EB/AB AD/DC AC/CD CD/DE A

88 58 K If ∆ABC is right-angled at A and the lables d, e

and f show the length of the sides, find the ratio of

sin α.

sinα=e/d sinα=d/e sinα=e/f sinα=f/e B

19


S.N. Com-

peten-

cy No.

Level

(K or

A)


89 58 K In the figure below, if ∆ABC is right-angled, then

which of the following is correct?

tanƟ=12/13 tanƟ=5/12 tanƟ=13/5 tanƟ=13/12 B

90 58 K In the figure below, ∆ABC is right-angled at C. If

BC=5cm, AB=13cm and AC=12cm, what is the

ratio of tanα?

5/13 5/12 12/13 12/5 B

91 58 K Given a right-angled triangle ABC below, find tan

Ɵ.

b/a a/b a/c b/c A

92 58 K In a triangle shown at the right, m(<ABC)=90o.

Which one is true about trignometric ratio?

sinƟ=adj/opp cosƟ=opp/adj tanƟ=opp/adj sinƟ=adj/hyp C

20


S.N. Com-

peten-

cy No.

Level

(K or

A)


93 58 K In the diagram below, ∆ABC is right-angled at C

as shown. If BC=3cm and AB=5cm, then which


sinα= 4/3 tanα= 4/3 cosα= 3/4 cosα= 5/3 B

94 58 K Express the length of BC in terms of sinβ. BC=AC sinβ BC=sinβ/AC BC=AB sin β BC=sinβ/AB A

95 58 K Which one of the following is true about

trigonometric ratio?

sinƟ=Hypotenues/

Opposite Side

sinƟ=Adjacent/Hy

potenues

sinƟ=Opposite

Side/Adjacent

sinƟ=Opposite

Side/Hypotenues

D

96 58 K Which of the following is true about a right-

angled triangle ABC as shown below?

The opposite side

to angle α is AC

The opposite side

to angle β is AB

The adjecent side

to angle α is BC

The adjecent side

to angle β is AC

B

21


S.N. Com-

peten-

cy No.

Level

(K or

A)


97 58 K In the figure below, ∆ABC is right-angled at C,

where BC=a, AC=b and AB=c units long. Which


sinα=b/c sinα=cosβ cosβ=b/c tanβ=a/b B

98 58 K Which of the following is true about the right-

angled triangle ABC below?

sinƟ=x/z cosƟ=z/y sinβ=x/z cosβ=y/x C

99 58 A In the figure to the right, AB=6cm, AC=4cm and

BC=x. Then the value of cos<B is _______.

x/4cm 6/xcm √5/3cm √5/6cm C

100 58 A In the figure given below, the value of tan <Y =

_________.

q/r p/r p/q q/p C

22


S.N. Com-

peten-

cy No.

Level

(K or

A)


101 59 K Refering to the figure below, if sinƟ=3/5, then

what is the value of cosƟ?

5/3 3/4 4/5 4/3 C

102 59 K If sin30o=1/2 and cos30

o=√3/2, then what is the

value of tan 30o?

1/3 1/2 √3/3 2√3 C

103 59 K Which of the following is true? tan30o=√3/3 sin30

o=√3/2 cos30

o=1/2 tan30

o=√2/2 A

104 59 K Which of the following has the same value as tan

45o?

sin30o/cos30

osin60

o/cos30

osin45

o/cos60

osin60

o/cos45

o B

105 59 K Which one of the following values of

trigonometric ratio is true?sin30

o=cos60

osin45

o=tan45

osin60

o=cos60

otan30

o=tan60

o A

106 59 K In the right-angled triangle below, what is the

value of sin 60o?

1/2 √3/3 √3/2 √3 C

107 59 K In the right-angled triangle shown below, what is

the value of cos 60o?

√3 √3/2 √3/3 1/2 D

23


S.N. Com-

peten-

cy No.

Level

(K or

A)


108 59 K If m(<ACB)=45o and BC=4cm as shown in the

figure below, then what is the value of x? (sin

45o=cos 45

o=√2/2 and tan 45

o=1)

2 2√2 4 4√2 C

109 59 A Using the figure of a right-angled triangle below,

which of the following is true?

sin(<C)=2 cos(<C)=√3/2 sin(<B)=√3 tan(<B)=4√3 B

110 59 A In the figure below, what are the values of x and

y?

x=3 and y=3√3 x=√3 and y=1/2 x=√3 and y=2 x=3√3 and y=3 D


triangle. What is the value of a?

3 6 3√3 3√5 B

24


S.N. Com-

peten-

cy No.

Level

(K or

A)


112 60 K A triangle ∆ABC is given below. Which of the

following is true?

The length of AD

is 3cm

The length of DC

is √3/2cm

The length of AC

is √3/3 cm

The length of BC

is 3√3cm

B

113 60 K If an equilateral triangle's side is 6cm, then what is

the altitude of the triangle?


114 60 K In a right-angled triangle ABC given below, if

m(<B)=60o and BC=6cm, what is the length of

AC? (Take tan 60o=√3)

8cm 3√3cm 6cm 6√3cm D

115 60 K For the given figure below, find the value of x. 50√3 45√3 28√3 10√3 D

25


S.N. Com-

peten-

cy No.

Level

(K or

A)


116 60 K If the figure given below is a right-angled triangle

at C, find the length of AB.

20√3/3 10√3 60√3 30√3 A

117 60 K Find the length of AB in the right-angled triangle

shown below. (sin 60o=√3/2, cos 60

o=1/2)

2√3 units 3√2 units 4 units 6 units D

118 60 K What is the value of "Y" in the given figure? 1/2cm 3cm 5cm 20cm C

119 60 K The diagonal of a rectangle ABCD is 10cm and

make an angle of 60o with one side. Find the

length of BC.

√3cm 3√3cm 5√3cm 10√3cm C

26


S.N. Com-

peten-

cy No.

Level

(K or

A)


120 60 A The diagonal of a rectangle is 10cm long and

makes an angle 60o with one side of the rectangle

as shown in the figure below. How long is side

AB?

5√3cm 5√10cm 10cm 10√3cm A

121 60 A A park in the form of right-angled triangle has the

hypotenuse 5km. The angle between the

hypotenuse and one side is 60o. Then find the

length x of the other side of the park.

6km 5km 5√3/2km 5√3/4km C

122 60 A Find the value of x in the figure given below.

(sin30o=1/2)

8cm 9cm 10cm 12cm D

123 60 A In the figure given below, which one of the

following is true?

x=√3y y=2z z=(√3/3) x y=3x A

27


S.N. Com-

peten-

cy No.

Level

(K or

A)


124 60 A In the figure below, which of the following is

true?

x=12cm y=12√2cm sinƟ=√2/2 cosƟ=√2 C

125 60 A A ladder of length 10m lean on a wall so that the

angle between the ladder and the wall is 30o. How

far is the base of the ladder from the wall?

5m 5√3m 10√2m 10√3m A

126 60 A A ladder of length 6m leans against a vertical wall

so that the base of the ladder is 3m from the wall

as shown in the figure below. What is the angle

between the ladder and the wall?

30o

40o

60o

90o C

127 60 A A building casts a 70 meter shadow and makes an

angle 60o with the ground. What is the height of

the building?

35√3meter 70√3/3meter 70meter 70√3meter D

28


S.N. Com-

peten-

cy No.

Level

(K or

A)


128 60 A A ladder of length 12m leans against a vertical

wall making an angle 60o with the horizontal

ground. How far is the foot of the ladder from the

front of the wall?

6m 6√3m 12m 12√3m A

129 60 A A ladder of 10m leans against the vertical wall.

The base of the ladder makes 60o with the ground.

Ccalculate the distance between the base of the

ladder and the wall.

10m 8m 6√3m 5m D

130 60 A The angle of elevation of the sun is 30o to the pole

shadow which is 20m long. What is the height of

the pole?

20√3m 10√3m 20√3/2m 20√3/3m D

29


S.N. Com-

peten-

cy No.

Level

(K or

A)


131 60 A In the figure below, a guide wire is used to support

a 30-meter radio antenna so that the angle of the

wire makes with the ground is 60o. How far is the

wire anchored from the base of the antenna?

5√3cm 10√3cm 10√3/3cm 5√3/3cm B

132 60 A A ladder of length 10m rests against a building.

The angle between the ladder and the ground is

45o. How far is the base of the ladder from the

building?

10√2 meter 5√2 meter 10 meter 5 meter B

133 60 A As shown in the figure below, point P is 50m from

the top of the building Q. Which of the following

is true?

x=25m tanƟ=x-h h=25√2m tanƟ=√2/2 C

134 60 A A 20m-long ladder leans against a wall and make

an angle of 600 with the ground. How high on the

wall does the ladder reach? (Use sin60o=√3/2,

cos60o = ½, tan60

o=√3)

5√3m 10m 10√3m 20√3m C

135 60 A A flag pole casts a shadow 25 meters long when

the angle of elevation of the sun is 30o. How high

is the flag pole?

12.5 m 14.5 m 21.75 m 37.5 m B

30


S.N. Com-

peten-

cy No.

Level

(K or

A)


136 60 A A pole casts 30-meter shadow and makes an angle

of 30o with the ground. Then what is the height of

the pole?

20 meter 30 meter 10√3 meter 30√3 meter C

137 60 A In the figure below to the right, what is the value

of x, if cosƟ =1/2?

1 2 3 4 B

138 60 A What is the ratio of √3 √3/2 √3/3 1/2 A

139 60 A Find (sin 45o) x (cos 45

o). 1/2 √2/4 √2/2 1 A

140 60 A √3tan60o

+ 2sin30o = _______. 2 3/2+ √3 4 3+ √3 C

31


S.N. Com-

peten-

cy No.

Level

(K or

A)


141 60 A In the figure below, if BC=9 and AC=15, then

sinβ

cosβ

3/4 4/5 4/3 5/3 C

142 61 K Which of the following is true about the given

pyramid figure below?

a is a lateral face b is a lateral edge c is the base d is the slant

height

C

143 61 K In the figure given below, which one is the lateral

edge of a pyramid?

AB DC VA AD C

144 61 K In the figure shown below, which one is the lateral

face of the pyramid?

V̅A̅ A̅B̅ ∆VAB ∆ABC C

= ______

32


S.N. Com-

peten-

cy No.

Level

(K or

A)


145 61 K Which line segement represents the height of the

pyramid below?

VF VE VA VC B

146 61 K Which one of the following is true about regular

pyramids?

The lateral faces

are isoceles

triangles

The lateral faces

are rectangular

The lateral faces

are parallel to each

other

The lateral faces

bisect each other

A

147 61 K Which of the following is NOT true about regular

pyramids?

The lateral edges

are equal

The base must be

a regular polygon

The pyramid must

be a right pyramid

Its base must be a

four-sided figure

D

148 62 A Which one of the following pyramids looks like a

flat form of the figure?

B

149 62 A Which one of the following can be the faces of a

right square pyramid?

A

33


S.N. Com-

peten-

cy No.

Level

(K or

A)


150 63 K A solid figure with one circular base and a vertex

on the other plane is called __________.

cone cube cylinder sphere A

151 63 K If the base of a pyramid is a regular polygon and if

the vertex is equidistance from each vertex of

base, this pyramid is called ________.

a triangular

pyramid

a rectangular

pyramid

a regular pyramid a circular pyramid C

152 63 K Which of the following is true about the given

figure and its name?

D

153 63 K In the figure given below, what is the name of the

pyramid?

Regular triangular

pyramid

Regular

rectangular

pyramid

Regular

pentagonal

pyramid

Regular hexagonal

pyramid

D

154 63 K The name of the pyramid shown in the figure at

the right is ___________.

triangular pyramid rectangular

pyramid

pentagonal

pyramid

hexagonal

pyramid

A

34

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