CST Algebra 1

Is the equation 3(2x – 4) = (-18) equivalent to 6x – 12 = (-18)?

A. Yes, the equations are equivalent by the Associative Property of Multiplication.

B. Yes, the equations are equivalent by the Commutative Property of Multiplication.

C. Yes, the equations are equivalent by the distributive property of Multiplication over Addition.

D. No, the equations are not equivalent.

1 A1.1

CST Algebra 2

A1.1

CST Algebra 3

A. 4B. 6C. 9D. 10

3

316 8

A2.0

CST Algebra 4

Which expression is equivalent to

A. C.

B. D.

4

6 2x x

4 3x x

5 3x x

7 3x x9 3x x

A2.0

CST Algebra 5

Which number does not have a reciprocal?

A. -1

B. 0

C.

D. 3

5

1

1000

A2.0

CST Algebra 6

What is the multiplicative inverse of ?

A. -2

B.

C.

D. 2

6

1

2

1

2

1

2

A2.0

CST Algebra 7

What is the solution for this equation?

A. x = -4 or x = 4

B. x = -4 or x = 3

C. x = -1 or x = 4

D. x = -1 or x = 3

7

2 3 5x

A3.0

CST Algebra 8

What is the solution set of the inequality

A. -2 ≤ x ≤ 6

B. x ≤ -2 or x ≥ 6

C. -12 ≤ x ≤ 4

D. x ≤ -12 or x ≥ 4

8

5 4 3?x

A3.0

CST Algebra 9

Which equation is equivalent to 5x – 2(7x + 1) = 14x ?

A. -9x – 2 = 14x

B. -9x + 1 = 14x

C. -9x + 2 = 14x

D. 12x – 1 = 14x

9 A4.0

CST Algebra 10

Which equation is equivalent to 4(2 – 5x) = 6 – 3( 1 – 3x)?

A. 8x = 5

B. 8x = 17

C. 29x = 5

D. 29x = 17

10 A4.0

CST Algebra 11

A4.0

CST Algebra 12

The total cost (c) in dollars of renting a sailboat for n days is given by the equation

c = 120 + 60n.If the total cost was $360, for how many days was the sailboat rented?

A. 2B. 4C. 6D. 8

12

A5.0

CST Algebra 13

Solve: 3(x + 5) = 2x + 35

Step 1: 3x + 15 = 2x + 35Step 2: 5x + 15 = 35Step 3: 5x = 20Step 4: x = 4

Which is the first incorrect step in the solution shown above?

A. Step 1B. Step 2C. Step 3D. Step 413 A5.0

CST Algebra 14

A 120-foot-long rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope?

A. 20 feetB. 40 feetC. 60 feetD. 80 feet

14 A5.0

CST Algebra 15

The cost to rent a construction crane is $750 per day plus $250 per hour of use. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed $2500 per day?

A. 2.5 hoursB. 3.7 hoursC. 7.0 hoursD. 13.0 hours

15

A5.0

CST Algebra 16

What is the solution to the inequality x – 5 > 14 ?

A. x > 9B. x > 19C. x < 9D. x < 19

16

A5.0

CST Algebra 17

The lengths of the sides of a triangle are y, y + 1, and 7 centimeters. If the perimeter is 56 centimeters, what is the value of y?

A. 24B. 25C. 31D. 32

17

A5.0

CST Algebra 18

A5.0

CST Algebra 19

Which number serves as a counterexample to the statement below?

All positive integers are divisible by 2 or 3.

A. 100B. 57C. 30D. 25

19

A24.1

CST Algebra 20

What is the conclusion of the statement in the box below?

If = 4, then x = -2 or x = 2

A. = 4B. x = -2C. x = 2D. x = -2 or x = 2

20

2x

2x

A24.2

CST Algebra 21

Which of the following is a valid conclusion to the statement “If a student is a high school band member, then the student is a good musician”?

A. All good musicians are high school band members.

B. A student is a high school band member.

C. All students are good musicians.

D. All high school band members are good musicians.

21

A24.2

CST Algebra 22

The chart below shows an expression evaluated for fourdifferent values of x.

Josiah concluded that for all positive values of x,produces a prime number. Which value of x serves as acounterexample to prove Josiah’s conclusion false? A. 5B. 11C. 16D. 2122

X

1 7

2 11

6 47

7 61

2 5x x

2 5x x

A24.3

CST Algebra 23

John’s solution to an equation is shown below,Given:Step 1: (x + 2)(x + 3) = 0Step 2: x + 2 = 0 or x + 3 = 0Step 3: x = -2 or x = -3

Which property of real numbers did John use for Step 2?

A. Multiplication property of equalityB. Zero product property of multiplicationC. Commutative property of multiplicationD. Distributive property of multiplication over addition

23

2 5 6 0x x

A25.1

CST Algebra 24

Stan’s solution to an equation is shown below,Given: n + 8(n + 20) = 110Step 1: n + 8n + 20 = 110Step 2: 9n + 20 = 110Step 3: 9n = 110 – 20Step 4: 9n = 90Step 5:

Step 6: n = 10Which statement about Stan’s solution is true?

A. Stan’s solution is correct.B. Stan made a mistake in Step 1.C. Stan made a mistake in Step 3.D. Stan made a mistake in Step 5.24

9 90

9 9

n

A25.2

CST Algebra 25

When is this statement true?

A. This statement is never true.B. This statement is always true.C. This statement is true for positive numbers.D. This statement is true for negative numbers.

25

The opposite of a number is less than the original number.

A25.3

CST Algebra 26

What is the y-intercept of the graph of 4x + 2y = 12

A. -4B. -2C. 6D. 12

26 A6.0

CST Algebra 27

Which inequality is shown on the graph below?

A.

B.

C.

D.

27

11

2y x

11

2y x

11

2y x

11

2y x

A6.0

CST Algebra 28

A6.0

CST Algebra 29

A6.0

CST Algebra 30

A6.0

CST Algebra 31

A6.0

CST Algebra 32

A6.0

CST Algebra 33

What point lies on the line defined by 3x + 6y = 2 ?

A. ( 0, 2 )B. ( 0, 6)C. ( 1, -1/6)D. ( 1, -1/3)

33

A7.0

CST Algebra 34

What is the equation of the line that has a slope of 4 and passes through the point (3, -10) ?

A. y = 4x - 22B. y = 4x + 22C. y = 4x - 43D. y = 4x + 43

34 A7.0

CST Algebra 35

The data in the table shows the cost of renting a bicycle by the hour, including a deposit.

If hours, h, were graphed on the horizontal axis and cost, c, were graphed on the vertical axis, what would be the equation of a line that fits the data?

A. c = 5hB. c = (1/5)h + 5C. c = 5h + 5D. c = 5h – 535

Hours (h) Cost in dollars ( c )

2 15

5 30

8 45

A7.0

CST Algebra 36

Some ordered pairs for a linear function of x are given in the table below.

Which of the following equations was used to generate the table above?

A. y = 2x + 1B. y = 2x - 1C. y = 3x - 2D. y = 4x - 336

X Y

1 1

3 7

5 13

7 19

A7.0

CST Algebra 37

A7.0

CST Algebra 38

The equation of line l is 6x + 5y = 3, and the equation of line q is 5x – 6y = 0. Which statement about the two lines is true?

A. Lines l and q have the same y-intercept.B. Lines l and q are parallel.C. Lines l and q have the same x-intercept.D. Lines l and q are perpendicular.

38 A8.0

CST Algebra 39

Which equation represents a line that is parallel to

?

A.

B.

C.

D.

39

52

4y x

51

4y x

42

5y x

43

5y x

54

4y x

A8.0

CST Algebra 40

A9.0

CST Algebra 41

What is the solution to this system of equations?

A. ( 6, 2 )

B. ( 1, -5 )

C. no solution

D. infinitely many solutions

41

3 2

6 2 4

y x

x y

A9.0

CST Algebra 42

Which ordered pair is the solution to the system of equations below?

x + 3y = 7x + 2y = 10

A.

B.

C. ( -2, 3)

D. ( 16, -3 )

42

7 13,2 4

7 17,2 5

A9.0

CST Algebra 43

Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have?

A. 27

B. 40

C. 56

D. 73

43

A9.0

CST Algebra 44

Which of the following best describes the graph of this system of equations?

y = -2x + 35y = -10x + 15

A. two identical lines

B. two parallel lines

C. two lines intersecting in only one point

D. two lines intersecting in only two points44 A9.0

CST Algebra 45

A9.0

CST Algebra 46

A9.0

CST Algebra 47

A.

B.

C.

D.

47

3

7

5

10

x

x

42x

4

1

2x

4

1

5x4

5

x

A10.0

CST Algebra 48

A.

B.

C.

D.

48

2 24 2 8 3 2x x x x

23 6x x

23 10x x

23 5 10x x

23 5 6x x

A10.0

CST Algebra 49

The sum of two binomials is . If one of the binomials is , what is the other binomial?

A.

B.

C.

D.

49

25 6x x23 2x x

22 4x x

22 8x x

28 4x x

28 8x x

A10.0

CST Algebra 50

Which of the following expressions is equal to (x + 2) + (x – 2)(2x + 1)?

A.

B.

C.

D.

50

22 2x x

22 4x x

22x x

24 2x x

A10.0

CST Algebra 51

A volleyball court 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 court in square meters?

A. 3x

B.

C.

D.

51

22x

23x

32xA10.0

CST Algebra 52

A10.0

CST Algebra 53

Which is the factored form of

A. (3a – 8b)(a – 6b)

B. (3a – 16b)(a – 3b)

C. 3(a – 4b)(a – 4b)

D. 3(a – 8b)(a – 8b)

53

2 23 24 48a ab b

A11.0

CST Algebra 54

Which is a factor of ?

A. x + 3

B. x - 3

C. x + 4

D. x - 4

54

2 11 24x x

A11.0

CST Algebra 55

Which of the following shows factored completely?

A.

B. (3t + 4)(3t + 1)

C. (9t + 4)( t + 1)

D.

55

29 12 4t t

23 2t

29 12 4t t

A11.0

CST Algebra 56

What is the complete factorization of ?

A. -8(2 + z)(2 – z)

B. 8(2 + z)( 2 – z)

C.

D.

56

232 8z

28(2 )z

28(2 )z

A11.0

CST Algebra 57

If is added to x, the sum is 42. Which of the following could be the value of x?

A. -7

B. -6

C. 14

D. 42

57

2x

A14.0

CST Algebra 58

A14.0

CST Algebra 59

A14.0

CST Algebra 60

A14.0

CST Algebra 61

A14.0

CST Algebra 62

A14.0

CST Algebra 63

A19.0

CST Algebra 64

A19.0

CST Algebra 65

A20.0

CST Algebra 66

A20.0

CST Algebra 67

A20.0

CST Algebra 68

A20.0

CST Algebra 69

A21.0

CST Algebra 70

A21.0

CST Algebra 71

A21.0

CST Algebra 72

A21.0

CST Algebra 73

A22.0

CST Algebra 74

A23.0

CST Algebra 75

A23.0

CST Algebra 76

A23.0

CST Algebra 77

A12.0

CST Algebra 78

A12.0

CST Algebra 79

A12.0

CST Algebra 80

A12.0

CST Algebra 81

A12.0

CST Algebra 82

A13.0

CST Algebra 83

A13.0

CST Algebra 84

A13.0

CST Algebra 85

A13.0

CST Algebra 86

A15.0

CST Algebra 87

A15.0

CST Algebra 88

A15.0

CST Algebra 89

A15.0

CST Algebra 90

A15.0

CST Algebra 91

A15.0

CST Algebra 92

A16.0

CST Algebra 93

A16.0

CST Algebra 94

A17.0

CST Algebra 95

A17.0

CST Algebra 96

A18.0