Add Math Mid Year Form 5 Paper 1 2015

1. Diagram 1 shows the relation between set P and Set Q in the arrow diagram form. State

a. the relation in the form of ordered pairs.b. the type of relation.c. the range of the relation.

[ 3 marks ]

Answer;

2. Diagram 2 shows the function , where m is a constant.Find the value of m.

[ 2 marks ]

Answer;

3472/1 2015 Hak Cipta SMKJ [ Lihat sebelahSULIT

4

Set Q –3 –1 0

41Set P

2

Diagram 1 1

fx

52m

3x – m

Diagram 2

3. Diagram 3 shows the function f maps set A to set B and function g maps set B to set A.Find

a. the function g in similar form.b. g(–5)

[ 3 marks ]

Answer;

4. The Diagram 4 shows a trapezium ABCD in which AB = x cm, AD = (x + 2) cm and BC = (2x + 5) cm.

a. Given that the area of the trapezium is 24 cm2 , show that 3x2 + 7x = 48.

b. Hence, find the value of x.

[ 3 marks ]Answer;


5

f

yx 3x,

x3x2

A B

BA

g

Diagram 3

B

x

x + 2

2x +5 C

A D

Diagram 4

5. Find the range of values of m such that the roots of the equation mx2 – x(x + 4) + 2 = 0 are not real.

[ 3 marks ]

Answer;

6. Diagram 5 shows the graph of a quadratic function f(x) = –2(x – p)2 + 18, where p

is constant, intersects the x-axis at –1 and 5. The curve y = f(x) has the maximum point (2, 3k). State

a. the value of p, b. the value of k,

c. the values of x when f(x) = 0[ 3 marks ]

Answer;


6

y = f(x)

(2, 3k)

–1 50

y

x

Diagram 5

7. Diagram 6 shows the graph of quadratic function y = f(x).

i. Express the quadratic function in the form of f(x) = ax2 + bx + c, where a, b and c are constants

ii. Find the range of values of x when f(x) ≤ 0

[ 3 marks ]Answer;

8. a. Simplify the expression 3p + 3p + 1 + 3p + 2 + 3p + 3.

b. Hence, show that 3p + 3p + 1 + 3p + 2 + 3p + 3 is divisible by 5 for all positive integers

of p.[ 3 marks ]

Answer;


7

–5 20

f(x)

x

Diagram 6

9. Given that p = 2m and q = 2n, express the following in term of m and n

a.

b. log16 p – log4 q[ 4 marks ]

Answer;

10. a. Given log9 n = , find the value of n

b. Solve the equation . [ 3 marks]

Answer;


8

11. A graduate is required to service his interest-free education loan in 36 monthly

instalments, with the first instalment being RM 100. Subsequent instalments are increased by RM 20 each month. Find

a. the amount of the 10th instalment.b. the total sum of his education loan instalment.

[ 3 marks ]

Answer;

12. It is given the sum of the first n terms of a geometric progression is .Find

a. the first term of the progressionb. the common ratio of the progression.

[ 4 marks ]Answer;


9

13. The Diagram 7 shows the graph xy against x is a straight line passing though the point P(5, 3) and Q(0, –3).

a. Find the gradient of the straight line PQ.

b. Show that

[3 marks]

Answer;

14. Diagram 8 shows the straight line PQ with equation intersects the

straight line AB at point P.

a. State the y-intercept of PQb. Find the coordinate of B if 2BP = 3PA

[3 marks]Answer;


10

0 xP(5, 0)

y

Q

A(3, –4)

B

0

P

xy

x

Q

Diagram 7

Diagram 8

15. Given and . Find

a. in term of h and k.b. the numerical value of h and of k if is zero vector.

[3 marks]

Answer;

16. In Diagram 9, O is the origin and A, B and C are three points on a horizontal plane. Given the vector OA = –a + b, OB = a + 5b and OC = 4a + 11b.

a. Find AB and BC in terms of a and bb. Show that A, B and C are collinear and hence find the ratio AB : BC

[4 marks] Answer;


11

Diagram 9

A

x0

yC

B

17. Solve the equations for

a. tan (2x + 500) = 0.8b. 3sin x cos x = cos x

[4 marks]Answer

18. The Diagram 10 shows a circle PAQ with centre O, of radius 8 cm. SR is an arc of

a circle with centre O. The reflex angle POQ is radians. Given that P and Q are midpoints of OS and OR respectively, find the area of shaded region, giving your answer in terms of .

[ 3 marks ]

Answer:


12

P

QR

S

OA 1.6 rad

8 cm

Diagram 10

19. Diagram 11 shows a cylindrical jar contains water to a depth of h cm. The

volume v cm2 of water given by . If h is increasing at the rate of

0.25 cm s–1, find the rate of increase of volume when the depth of water is 2 cm.

[3 marks]

Answer;

20. Given , find

a. , if h is a constant

b. , if r is a constant

[3 marks]

Answer;


13

h cm

Diagram 11

21. A set of numbers 3, k, 2k, 10, 12 and 17 arranged in ascending order has a mean of m.

a. Find k in term of mb. If each number in the set is decreased by 2, the median of the new

set of data is m – 2. Calculate the values of m and k.[4 marks]

Answer;

22. A set of data consists of twelve positive numbers. It is given that

.

Finda. the varianceb. the mean

[4 marks}

Answer;


14

23. Of the 80 boy students, 26 students play football, 20 students play football and hockey, and 42 students play football or hockey.

a. Find the number of students who play hockey.b. Hence, calculate the probability that a students, chosen at

random, plays hockey.

(Hint: Use formula)

[3 marks]Answer;

24. a. Find the number of code words, with their consonants placed side by side that

can be formed from the letters of word RANDOM

b. Diagram 12 shows a piece of broken business-card. The last three digits of the hand phone numbers could not be made out. Find the number of ways to fill the last three digits if the number forms an odd number.

[3 marks]Answer;


15

Dr. Hjh. Balqis Binti Medical Consultant UIAM

H/Phone.: 019–5874

Diagram 12

25. Diagram 13 shows two parallel lines, L1 and L2. Three points are marked on L1 and five points are marked on the L2. A triangle will be formed by chosen any three points. Determine the number of different triangles that can be formed by connecting

a. only a point from L1.b. any points.

[ 3 marks]

Answers;

END OF QUESTION PAPER

Prepared byHj. Busrah bin Md. Seh / SMKJ 2015


16

L1

L2

Diagram 13

JADUAL SPESIFIKASI UJIAN (JSU) MATEMATIK TAMBAHAN

(KERTAS 1)

Bidang

TOPIK

Tin

gkata

n

Jum

lah

soala

n

KERTAS 1

No

Soala

n

Ara

s

KB

AT

Mark

ah

Alg

eb

raic

Functions 4 3

1 R 3

2 R 2

3 T / 3

Quadratic Equations4

24 S 3

5 S 3

Quadratic Functions4

26 S 3

7 T / 3

Indices and Logarithms 4 3

8 T / 3

9 T 4

10 S 3

Progressions5

211 T / 3

12 T 4

Linear Law 5 1 13 S 3

Geom

etr

y

Coordinate Geometry 4 1 14 S 3

Vectors5

215 R 3

16 T / 4

Sta

tisti

cs Statistics4

221 T / 4

22 T / 4

Probability 5 1 23 T / 3

Permutations/Combinations5

224 T / 3

25 T / 3

Tri

gon

om

etr

y Circular Measure 4 1 18 T 3

Trigonometric Functions 5 1 17 T / 4

Calc

ulu

s Differentiation 4 2

19 S 3

20 T /3

TOTAL 25 12 80


17

Add Math Mid Year Form 5 Paper 1 2015

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Transcript of Add Math Mid Year Form 5 Paper 1 2015