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Practice Exam MAT/002

MAT/002 Practice Exam

1. Select the difference of (6x2 – 7x3) – (2x2 – x3)

A. 6x6 B. 6x5 C. 4x2 + 2x3 D. – 6x3+4x2

2. Simplify the following expression. 6(4x + 1)

A. 24x + 6 B. 24x + 1 C. 30x D. 10x + 7

3. Select the product of (9x – 2)(7x + 9)

A. 63x2 – 67x – 18 B. 130x – 18 C. 63x2 + 67x – 18 D. 16x + 7

4. Simplify the following expression (x + 3)3

A. 27x3 B. x3 + 27 C. x3 + 9x2 + 27x + 27 D. x2 + 6x + 9

5. Select the product of (9x + 6) (9x – 6)

A. 81x2 – 36 B. 81x2 – 108x – 36 C. 18x2 D. 18x

6. Select the product of (6x + 7)(x2 – 2x + 1)

A. 6x3 – 5x2 – 8x + 7 B. 13x2 – 26x + 13 C. 6x3 – 19x2 – 20x + 7 D. x2 + 4x + 8

7. Select the product of (-4x3y)(x7y5)

A. 4x10y6 B. -4x10y6 C. -4x21y2 D. 4x21y5

8. Select the product of (7x – 5)(7x – 5)

A. 49x2 + 25 B. 49x2 + 70x + 25 C. 49x2 – 25 D. 49x2 – 70x + 25

Practice Exam MAT/002

9. Select the product of (2x + 3)*(4x – 5)

A. 8x2 + 22x – 15 B. 8x2 + 2x – 15 C. -5x3 D. 8x2 – 15

10. Select the difference of (4x2 – 14x + 7) – (3 – 8x)

A. 4x2 – 22x + 4 B. 4x2 – 22x + 10 C. 4x2 – 6x + 4 D. 4x2 + 6

11. Which of the following best illustrates a geometric representation of (x + 1)(x + 2)

A. B.

C. D.

Practice Exam MAT/002

12. Factor the expression. x2 + 13x + 22

A. (x + 1) (x + 22) B. (x + 2)(x + 11) C. (x – 3)(x – 9) D. prime polynomial (can’t factor)

13. Factor the expression. x2 – 12x + 35

A. (x – 5) (x – 7) B. (x + 7)(x + 5) C. (x – 1)(x + 35) D. prime polynomial (can’t factor)

14. Factor the expression. x2 – 16x + 39

A. (x – 6)2 B. (x – 13)(x + 3) C. (x – 3)(x – 13) D. prime polynomial (can’t factor)

15. Factor the expression. 15x2 + 26x + 8

A. (5x – 2) (3x – 4) B. (5x + 2)(3x + 4) C. (15x + 4)(x +2) D. prime polynomial (can’t factor)

16. Factor the expression. 75x2 + 80x + 20

A. 5(5x – 2) (3x – 2) B. 5(5x + 2)(3x + 2) C. (75x + 1)(x +20) D. prime polynomial (can’t factor)

17. Factor the expression. -10x2 - 43x – 28

A. -(2x – 7) (5x + 4) B. -(2x + 7)(5x + 4) C. (-2x + 7)(5x +4) D. prime polynomial (can’t factor)

18. Factor the expression. x2 + 3x + 36

A. (x + 3) (x + 13) B. (x + 7)2 C. (x – 3)(x + 13) D. prime polynomial (can’t factor)

19. Factor the expression. 49x2 – 1

A. (7x + 1) (7x – 1) B. (7x + 1)2 C. (49x – 1) (x + 1) D. prime polynomial (can’t factor)

20. Factor the expression. y2 + 8xy + 16x2

A. (y – 4x)2 B. (y + 4x)2 C. (y + 4x) (y – 4x) D. prime polynomial (can’t factor)

Practice Exam MAT/002

21. Factor the expression. -125x3 + 1

A. (-5x + 1)(25x2 + 5x + 1) B. (5x + 1)3

C. (-5x – 1)(25x2 – 5x + 1) D. prime polynomial (can’t factor)

22. Simplify the following rational expression. 𝑥2−36

𝑥2−3𝑥−18

A. 𝑥+6

𝑥+3 B.

−3𝑥 C.

𝑥−6

𝑥+3 D.

𝑥2−36

𝑥2−3𝑥−18

23. Select the product. 8

𝑥−2 ∙

𝑥−4

A. 40

𝑥−6 B.

8𝑥−32

5𝑥−10 C.

(𝑥−2)(𝑥−4) D.

(𝑥−2)(𝑥−4)

24. Select the quotient. 𝑥+5

𝑥−2 ÷

𝑥3+𝑥2

𝑥−2

A. 𝑥+5

𝑥2(𝑥+1) B.

𝑥+5

(𝑥+1)3 C.

𝑥 D.

𝑥2+5𝑥+5

2𝑥

25. Select the difference. 3

2𝑥−1 −

2𝑥−1

A. −15

(2𝑥−1)2 B.

−2

2𝑥−1 C. 1 D. undefined

26. Select the sum. 𝑥

2𝑥−7 +

A. 𝑥(2𝑥−7)

2(𝑥−2) B.

𝑥+1

8𝑥−28 C.

𝑥+1

2𝑥−3 D.

6𝑥−7

8𝑥−28

Practice Exam MAT/002

27. Select the value of x that is a solution for this equation: 8

𝑥 =

𝑥+3

A. -3 B. 24 C. 21 D. 9

28. An object 5.7 feet tall casts a shadow that is 17.1 feet long. How long in feet would the shadow be for

an object which is 19.2 feet tall?

A. 7.8 feet B. 6.4 feet C. 30.6 feet D. 57.6 feet

29. Simplify the expression: √ 6

A. 6

3 B.

√6 3

3 C.

√27 3 D. Is already simplified

30. Simplify the expression √6(5 − √6) + 2√6

A. 6√6 B. 7√6 − 6 C. 5√6 + 6 D. 2√6 + 5

31. Simplify the expression: 6

6+√3

A. 1

3 B.

1+√3 C.

36−6√3 33

D. 12−2√3

32. On a recent test, Jeremy wrote the equation 𝑥2−9

𝑥−3 = x + 3. Which of the following statements is

correct about the equation?

A. The equation is always true.

B. The equation is always true, except when x = 3

C. The equation is sometimes true when x = 3.

D. The equation is never true.

Practice Exam MAT/002

33. Solve for x in the equation x2 – 2x – 63 = 0

A. {-7, -9} B. {7, -9} C. {-7, 9} D. {7, 9}

34. Consider the equations: f(x) = -8x – 2 and g(x) = 5x2. Select the solution for (f + g)(x).

A. -8x – 2 + 5x2 B. -40x3 – 10x2 C. -40x2 – 2 D. -8x – 2 – 40x2

35. Consider the equations: f(x) = -8x – 2 and g(x) = 5x2. Select the solution for (fg)(x).

A. -8x – 2 + 5x2 B. -40x3 – 10x2 C. -40x2 – 2 D. -8x – 2 – 40x2

36. Select the x-coordinate of the vertex of the parabola defined by the function f(x) = -9x2 + 7x + 1

A. −9

7 B. 1 C.

18 D. 7

37. Determine the equation of g(x) that results from translating the function f(x) = x2 + 9 upward 10 units.

A. g(x) = (x + 19)2 B. g(x) = (x + 10)2 + 9 C. g(x) = x2 – 1 D. g(x) = x2 + 19

38. Determine the equation of g(x) that results from translating the function f(x) = (x+2)2 to the right 4

units.

A. g(x) = (x – 2)2 B. g(x) = (x + 6)2 C. g(x) = (x+2)2 – 4 D. g(x) = (x+2)2 + 4

39. Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -2x2 + 4x + 3.

A. {-0.67, 1.33} B. {-2, 4} C. {-2.00, -1.50} D. {-0.58, 2.58}

40. Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -2x2 + 3x + 7.

A. {2.77, -1.27} B. {-2, -3} C. {-1.50, -3.50} D. {-0.29, 0.43}

41. Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -2x2 + 2x + 6.

A. {-1.30, 2.30} B. {-2, 2} C. {-1.30, -2.30} D. {-0.33, 0.33}

Practice Exam MAT/002

42. Select the values of x that are solution to the inequality 0 > x2 + 5x – 2

A. 𝑥 ∈ ( −5+√33

2 ,

−5−√33

2 ) B. 𝑥 ∈ [

−5+√33

2 ,

−5−√33

2 ]

C. 𝑥 ∈ (−∞, −5+√33

2 ) ∪ (

−5−√33

2 , ∞) D. 𝑥 ∈ (

−5+√17

2 ,

−5−√17

2 )

43. If f(𝑥) = √𝑥2 − 1 and g(𝑥) = √𝑥 + 1, which expression represents f(𝑥)

g(𝑥) for 𝑥 > −1?

A. √𝑥 + 1 B. √𝑥 C. √𝑥 − 1 D. 1

√𝑥−1

44. Which of the following conclusions is true about the statement below? 𝑥3 = √𝑥

A. the statement is true when x = 1 B. the statement is never true

C. the statement is true when x is negative D. the statement is always true.

45. Consider the diagram below.

The function h(x) = 1

98 x2 describes h(x), the height of part of a roller coaster track, where x is the

horizontal distance in feet from the center of this section of the track. The towers that support part of

the track are the same height and are 200 feet apart. Which is the best estimate of the height of the

towers?

A. 57.4 feet B. 102.0 feet C. 1.0 feet D. 408.2 feet

Practice Exam MAT/002

46. The profit (P), in dollars, for a company is modeled by the functions P(x) = -250x2+ 1,250x, where x is

the number of items produced. For which values of x will the company lose money?

A. x < 0 B. 0 < x < 5 C. x > -250 D. x > 5

47. Which of the following sentences is true about the graphs of y = 4(x – 6)2 + 1 and y = 4(x + 5)2 + 4?

A. Their vertices are maximums.

B. The graphs have the same shape with different vertices.

C. The graphs have different shapes with different vertices.

D. One graph has a vertex that is a maximum, while the other have a vertex that is a minimum.

48. Find the inverse of 𝑓(𝑥) if 𝑓(𝑥) = 𝑥−3

A. 𝑓−1(𝑥) = 5𝑥 − 3

B. 𝑓−1(𝑥) = 𝑥 + 5

C. 𝑓−1(𝑥) = 5𝑥 + 3

D. 𝑓−1(𝑥) = 3𝑥 − 5

49. Select the approximate solution to log3(48).

A. 3.5 B. 1.7 C. 0.5 D. 16

50. Select the first five terms in the arithmetic sequence an = 7n, starting with n = 1.

A. { 1

7 ,

14 ,

21 ,

28 ,

35 } B. {1, 2, 3, 4, 5}

C. {8, 9, 10, 11, 12} D. {7, 14, 21, 28, 35}

51. Select the first five terms in the geometric sequence an = (3)n-2, starting with n = 1.

A. { 1 3 , 1, 3, 9, 27} B. {-3, 1, 3, 9, 27} C. {-3, 0, 1, 3, 9} D. {− 1

3 , 0, 1, 3, 9}

52. Select the sum of the series ∑ 𝑘34𝑘=1

A. 64 B. 100 C. 27 D. 200

Practice Exam MAT/002

Answer Key

1. D

2. A

3. C

4. C

5. A

6. A

7. B

8. D

9. B

10. C

11. D

12. B

13. A

14. C

15. B

16. B

17. B

18. D

19. A

20. B

21. A

22. A

23. C

24. A

25. B

26. D

27. B

28. D

29. B

30. B

31. D

32. B

33. C

34. A

35. B

36. C

37. D

38. A

39. D

40. A

41. A

42. A

43. C

44. A

45. B

46. D

47. B

48. C

49. A

50. D

51. A

52. B