Mathacle PSet ---- Algebra, (PARCC) Pre-Algebra Test Pre...

Mathacle

PSet ---- Algebra, (PARCC) Pre-Algebra Test Level ---- 2 Number ----- 1 Name: Date:

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Pre-Algebra Topics: P1 - Integers, Fractions, Rational Numbers, and Expressions P2 - Factors, Fractions, and Exponents P3 - Equations and Inequalities P4 - Ratio, Proportion and Percent P5 - Function and Graphing P6 - Statistics and Probability P7 - Polynomials and Nonlinear Functions

Task Types:

Type I – Tasks assessing concepts, skills and procedures Type II – Tasks assessing expressing mathematical reasoning Type III – Tasks assessing modeling / applications PART 1 – INTEGERS, FRACTIONS, RATIONAL NUMBERS, AND EXPRESSIONS 1.) [Type I, P1] Simplify the expression 4610 +− (A) 0 (B) 2 (C) 4 (D) 6 (E) 8 2.) [Type I, P1] Simplify the expression 1)4(8)4(2)3(6 +−÷+−−−+− (A) 18− (B) 20 (C) 1 (D) 2− (E) 16−

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3.) [Type I, P1] Simplify the expression |119||106| −+−− (A) | ( 2) |− − − (B) 0 (C) 4 (D) ( 2)− − (E) | 6 |− 4.) [Type I, P1] Write 000,450 in scientific notation. (A) 310450× (B) 5105.4 × (C) 51045× (D) 4105.4 × (E) 41045× 5.) [Type I, P1] Write 000215.0 in scientific notation. (A) 310215 −× (B) 410215 −× (C) 5105.21 −× (D) 41015.2 −× (E) 510215.0 −×

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6.) [Type I, P1] Write )103()106( 33 −××× in scientific notation. (A) 180 (B) 110180 −× (C) 18 (D) 2108.1 × (E) 1108.1 × 7.) [Type I, P1]

Order the set of numbers 3

12,

3

2,4.2,3.2,666.0 −−− from least to greatest.

(A) 3

2,666.0,3.2,

3

12,4.2 −−−

(B) 4.2,3

12,3.2,

3

2,666.0 −−−

(C) 3

2,666.0,

3

12,3.2,4.2 −−−

(D) 666.0,3

2,

3

12,3.2,4.2 −−−

(E) 4.2,3.2,3

12,666.0,

3

2 −−−

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8.) [Type I, P1]

Order the set of numbers 2103,3.0%,300,3

1 −× from least to greatest.

(A) 3.0,3

1%,300,103 2−×

(B) %300,3

1,3.0,103 2−×

(C) 2103%,300,3.0,3

1 −×

(D) 2103%,300,3

1,3.0 −×

(E) %300,3

1,103,3.0 2−×

9.) [Type I, P1]

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10.) [Type I, P1] Ten less than a third of a number.

(A) 3

110 −n

(B) n3

110−

(C) 3

1−n

(D) )10(3

1 −n

(E) 103

1 −n

11.) [Type I, P1] One more than twice a number. (A) 12 +n (B) )1(2 +n (C) 12 −n (D) 2−n (E) )1(2 −n 12.) [Type I, P1] The quotient of a number and a different number.

(A) y

x

(B) yx − (C) yx ⋅ (D) yx + (E) None of the above

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13.) [Type II, P1] A number has the following properties: I.) The sum of my digits is 9 II.) I am odd and less than 100. III.) I am a power of 3. What number am I? (A) 18 (B) 45 (C) 54 (D) 81 (E) 99 14.) [Type II, P1] Find the length of one side of a square if its perimeter is 36 ft. (A) 4 ft (B) 12ft (C) 6 ft (D) 18ft (E) 9ft 15.) [Type II, P1] The first four terms of a sequence are 1, 8, 27, 64. Find the next two terms, and create an expression to find the thn term. (A) 2)4(,100,81 +n

(B) 3,216,125 n

(C) 1)1(,215,106 2 −+n

(D) 1,215,124 3 −n

(E) 23,180,100 nn −

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16.) [Type II, P1] The difference of an irrational number and a rational number is (A) a rational number (B) an irrational number (C) an integer (D) a fraction (E) a whole number 17.) [Type II, P1]

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18.) [Type II, P1]

19.) [Type III, P1]

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20.) [Type III, P1]

PART 2 – FACTORS, FRACTIONS AND EXPONENTS 21.) [Type I, P2] Find all common factors of 18and 24 (A) None (B) 2,1 (C) 6,3 (D) 6,3,2,1 (E) 9,6,3,2,1 22.) [Type I, P2] What is the Greatest Common Factors (GCF) of 28and 42? (A) None (B) 14 (C) 2 (D) 4 (E) 84

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23.) [Type I, P2] What is the Least Common Multiple of 4, 6 and 9 ? (A) 4 (B) 18 (C) 36 (D) 54 (E) 96 24.) [Type I, P2]

Evaluate 3

33 3−

(A) 0 (B) 8 (C) 9− (D) 8− (E) 1 25.) [Type I, P2] Which number is smaller, 52 or 25 ? (A) They are the same (B) 52 (C) 25 (D) It can not determined (E) None of the above

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26.) [Type I, P2] The square root of 123 is between what two whole numbers? (A) 11,10 (B) 12,11 (C) 13,12 (D) 14,13 (E) 15,14 27.) [Type I, P2] The number 65 means ______ is a factor _____ times. (A) 6,5 (B) 6,6 (C) 5,5 (D) 10,5 (E) 5,6 28.) [Type I, P2]

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29.) [Type I, P2]

What is the square root of 400

25?

(A) 2 (B) 4

(C) 10 (D) 8 (E) 16 30.) [Type II, P2] If m is the greatest prime factor of 38and n is the greatest prime factor of 100, what is the value of nm + ? (A) 7 (B) 12 (C) 24 (D) 29 (E) 44 31.) [Type II, P2] If 42 =a , then =6a (A) 12 (B) 16 (C) 24 (D) 32 (E) 64

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32.) [Type II, P2] Find the width of rectangle if its length is 12 ft and area is 156 square ft. (A) 14ft (B) 13ft (C) 66ft (D) 33ft (E) 168ft PART 3 – EQUATIONS AND INEQUALITIES 33.) [Type I, P3] If 3, 5, 1a b c= − = = − , then what is cba −+ 22 ? (A) 21 (B) 20 (C) 19 (D) 18 (E) 17 34.) [Type I, P3] How many different like terms are in the expression5 4 10 7u y x u+ − − ? (A) 3 (B) 4 (C) 5 (D) 7 (E) 10

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35.) [Type I, P3] What is the solution to 2273 −=−x ? (A) 10 (B) 1 (C) 5− (D) 10− (E) 5 36.) [Type I, P3] What is the solution to 10 4 2 44x x− < − ? (A) 9≥x (B) 9<x (C) 9−>x (D) 9>x (E) 27−<x 37.) [Type II, P3] A 17-foot ladder is leaning against a building. If the base of the ladder is 8 feet from the building, about how far up the building is the ladder? (A) 9ft (B) 11ft (C) 15ft (D) 17 ft (E) 20ft

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38.) [Type II, P3] Find the length of a rectangle if the width is 3 ft and the perimeter is 20 ft. (A) 17 ft

(B) 3

20ft

(C) 3ft

(D) 3

10ft

(E) 7 ft 39.) [Type II, P3] One square is 3 cm in a side and the second square is 9 cm on a side. Find the perimeter of each square. The perimeter of the larger square is how many times larger than that of the smaller square? (A) 2 (B) 3 (C) 9 (D) 12 (E) 24 40.) [Type II, P3] Find the sum of all possible values ofx that satisfy the equation:

0)5)(1)(6( =−+− xxx if }9,8,7,6,5,4,3,2,1,0{∈x . (A) 10− (B) 2− (C) 10 (D) 11 (E) 12

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41.) [Type II, P3] Antonio has $18 to ride the go-carts and play some games at the State Fair. If the go-carts cost $5.50 per ride and each game ticket is $1, what are the most game tickets he can buy? (A) 1 (B) 7 (C) 12 (D) 18 (E) 23 42.) [Type II, P3] If k and m are positive integers and 53 =+ mk , what is the possible value of k ? (A) 4 (B) 3 (C) 2 (D) 1 (E) 0 43.) [Type III, P3] Each term of a sequence, after the first, is three more than the term preceding it. The first term is12and the last term is102:

102,,18,15,12 ••• How many terms are there? (A) 30 (B) 31 (C) 32 (D) 90 (E) 91

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44.) [Type III, P3]

PART 4 – RATIO, PROPORTION, AND PERCENT 45.) [Type I, P4] Write the number 25.0 as a percent. (A) %25.0 (B) %5.2 (C) %25 (D) %250 (E) %2500 46.) [Type I, P4] Write the number 100as a percent. (A) %1 (B) %10 (C) %100 (D) %1000 (E) %10000

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47.) [Type I, P4]

Write the number 10

13 as a percent.

(A) %310 (B) %1.3 (C) %31 (D) %301 (E) %3100 48.) [Type II, P4] Rick scored about 84% on a 50-item test. How many did he answer correctly? (A) 16 (B) 32 (C) 42 (D) 50 (E) 84

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49.) [Type II, P4]

50.) [Type II, P4] A grizzly bear can run 30 miles in one hour. How many feet is this per second? There are 5280 feet in 1 mile and 3600 seconds in one hour. (A) 2 ft/s (B) 30ft/s (C) 600,633 ft/s (D) 45.20 ft/s (E) 44ft/s

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51.) [Type II, P4]

Which of the following ratios are NOT in proportions?

(A) 20

24and

18

15

(B) 24

50and

125

60

(C) 35

9and

18

70

(D) 15

4and

42

150

(E) None of the above 52.) [Type II, P4] Find the ratio of x to y determined by each equation 50 40x y= (A) 5: 4 (B) 4:5 (C) 40:5 (D) 5: 40 (E) 40:50 53.) [Type III, P4] In 2011, THS had an average class size of 18. There were 112 faculty members and each of them taught 5 classes. If each student took 8 classes, how many students were at THS in 2011?

(A) 1220 (B) 1230 (C) 1240 (D) 1250 (E) 1260

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PART 5 – FUNCTIONS AND GRAPHS 54.) [Type I, P5]

What is the solution of the equation 1

13

y x= − + ?

(A) (3,1) (B) (-3,0) (C) (6,-1) (D) (0,-1) (E) No solution. 55.) [Type I, P5] Where is the graph of (0,3) in the coordinate plane? (A) in Quadrant II (B) in Quadrant III (C) on the x-axis (D) on the y-axis (E) None of the above

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56.) [Type I, P5] The tuition rates for in-state residents to attend a state college are shown in the graph below.

In which year, the tuition is $6,000? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

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57.) [Type I, P5]

58.) [Type II, P5]

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59.) [Type II, P5]

60.) [Type II, P5]

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61.) [Type II, P5]

62.) [Type III, P5]

x ( )f x ( )g x

-1 5 -2

0 3 3

1 -3 -5

2 2 0

3 0 3

Several values of the functions ( )f x and ( )g x are shown in the above

table. For what x is ( ) (2)f x g= ?

(A) 3− (B) 1− (C) 0 (D) 1 (E) 3

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PART 6 – STATISTICS AND PROBABILITY 63.) [Type I, P6] What is the difference between the median and mode for the following set of numbers: {2, 6, 1, 8, 10, 3, 10, 1, 10}? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 64.) [Type I, P6] The graph below shows the number of hours different employees worked in a day. What is the median of hours worked?

(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

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65.) [Type I, P6] You are rolling a pair of dice. What is the probability of not rolling multiples of 2 on both dice? (A) 0 (B) 1

(C) 2

1

(D) 3

1

(E) 4

1

66.) [Type II, P6] Francisca needs an average score of 92 on five quizzes to earn an A. The mean of her first four scores was 91. What is the lowest score that she can receive on the fifth quiz to earn an A? (A) 91 (B) 94 (C) 96 (D) 99 (E) 100 67.) [Type II, P6] Suppose a number cube is rolled, what is the probability of rolling a prime number? (A) 0

(B) 6

1

(C) 2

1

(D) 3

2

(E) 1

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68.) [Type II, P6]

69.) [Type III , P6] Each of the marbles in a bag is either red, black, or green. The number of green marbles is 1 more than the number of red marbles, and the number of black marbles is 3 times the number of green marbles. Which of the following could be the total number of marbles in the bag? (A) 8 (B) 12 (C) 14 (D) 17 (E) 21

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70.) [Type III, P6] How many positive integers less than 1,000 do not have 7 as any digit? (A) 700 (B) 728 (C) 736 (D) 770 (E) 819 PART 7 – POLYNOMIALS AND NONLINEAR FUNCTIONS 71.) [Type I, P7] What is monomial? (A) A variable used in an equation (B) An algebraic expression with multiple terms (C) An algebraic expression with one term (D) An equation with only one variable (E) None of the above 72.) [Type I, P7]

The number of diagonals of an n-sided polygon is ( )nn 32

1 2 − . How many diagonals

would a 10-sided polygon have? (A) 20 (B) 35 (C) 50 (D) 65 (E) 70

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73.) [Type I, P7] Which expression is equivalent to 2 23 ( 4 1)x x x+ − ? (A) 4 3 23 12 3x x x+ − (B) 4 2 23 12 3x x x+ + (C) 4 2 23 12 3x x x+ − (D) 4 3 23 12 3x x x− + (E) xxx 3123 24 −− 74.) [Type I, P7] If 2( ) 2f x x x= − , then =− )3(f (A) 15 (B) 14 (C) 13 (D) 12 (E) 11 75.) [Type II, P7] Rita’s dog weighed 5pounds when she bought it. Over the next several years, the dog’s weights increased by 10percent per year. Which of the following functions gives the weight, w in pounds, of the dog after n years of the weight grain at this rate? (A) n1.05 + (B) n)1.0(5

(C) n)9.0(5

(D) n)1.1(5

(E) 1.1)(5 n

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Answer Sheet

1.) _________ 2.) _________ 3.) _________ 4.) _________ 5.) _________ 6.) _________ 7.) _________ 8.) _________ 9.) _________ 10.) _________ 11.) _________ 12.) _________ 13.) _________ 14.) _________ 15.) _________ 16.) _________ 17.) _________ 18.) _________ 19.) _________

20.) _________ 21.) _________ 22.) _________ 23.) _________ 24.) _________ 25.) _________ 26.) _________ 27.) _________ 28.) _________ 29.) _________ 30.) _________ 31.) _________ 32.) _________ 33.) _________ 34.) _________ 35.) _________ 36.) _________ 37.) _________ 38.) _________

39.) _________ 40.) _________ 41.) _________ 42.) _________ 43.) _________ 44.) _________ 45.) _________ 46.) _________ 47.) _________ 48.) _________ 49.) _________ 50.) _________ 51.) _________ 52.) _________ 53.) _________ 54.) _________ 55.) _________ 56.) _________ 57.) _________

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58.) _________ 59.) _________ 60.) _________ 61.) _________ 62.) _________ 63.) _________

64.) _________ 65.) _________ 66.) _________ 67.) _________ 68.) _________ 69.) _________

70.) _________ 71.) _________ 72.) _________ 73.) _________ 74.) _________ 75.) _________

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Answers: PART 1 1.) E 2.) D 3.) A 4.) B 5.) D 6.) E 7.) A 8.) B 9.) D 10.) E 11.) A 12.) A 13.) D 14.) E 15.) B 16.) B 17.) B 18.) A 19.) D 20.) E PART 2 21.) D 22.) B 23.) C 24.) D 25.) C 26.) B 27.) A 28.) D 29.) B 30.) C 31.) E 32.) B PART 3

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33.) B 34.) A 35.) C 36.) D 37.) C 38.) E 39.) B 40.) D 41.) C 42.) D 43.) B 44.) B PART 4 45.) C 46.) E 47.) A 48.) C 49.) D 50.) E 51.) D 52.) B 53.) E PART 5 54.) C 55.) D 56.) A 57.) B 58.) C 59.) D 60.) E 61.) E 62.) E PART 6

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63.) B 64.) C 65.) E 66.) C 67.) C 68.) A 69.) C 70.) B PART 7 71.) C 72.) B 73.) A 74.) A 75.) D

Mathacle PSet ---- Algebra, (PARCC) Pre-Algebra Test Pre...

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