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Review of Precalculus

Review Test

1.

3

+ x

= ?

(A)

(B)

(C)

(D)

2.

= ?

(A)

(B)

(C)

(D)

3. The reduced row echelon form of

is

(A)

(B)

(C)

(D)

4. Which of the following is the multiplicative inverse of

?

(A)

(B)

(C)

(D)

5. Which of the following is a solution to

(A) (-3, 1, 2)

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

(C) (6, -2, -4)

(D) (7, -5, -2)

6. Which of the following is equal to x, if

(A)

(B)

(C)

(D)

det

7. How many different values of (x, y, z) satisfy the following system of equations?

(A) 0

(B) 1

(C) 2

(D) Infinitely many.

8. Which of the following is a graph of 3x - y≥3?

Figure A.1: 3x - y≥3

(A) A

(B) B

(C) C

(D) D

9. Which of the following graphs represents the solution to the system of inequalities

Figure A.2: System of inequalities

(A) A

(B) B

(C) C

(D) D

10. Factor 15x² - x - 6.

(A) 15(x - 3)(x + 2)

(B) (3x + 2)(5x - 3)

(C) (3x - 2)(5x + 3)

(D) (5x - 6)(3x + 1)

11. Factor 8x³ - y³.

(A) (2x - y)(2x² + xy + y²)

(B) (2x - y)(4x² +2xy + y²)

(C) (2x + y)(4x² -2xy + y²)

(D) (2x + y)(4x² -2xy - y²)

12. Factor 2x³ +5x² - 18x - 45.

(A) (x + 3)(x - 3)(2x + 5)

(B) (x - 9)(2x² + 5)

(C) (x² + 9)(2x - 5)

(D) (x + 3)(x - 3)(2x - 5)

13. How many real roots does f (x) = 4x² - 8x - 16 have?

(A) 0

(B) 1

(C) 2

(D) Infinitely many.

14.

+

-

= ?

(A)

(B)

(C)

(D)

15.

×

= ?

(A)

(B)

(C)

(D) (2x + 3)²(x + 1)²

16.

÷

= ?

(A)

(B)

(C)

(D) 1

17. What is the solution set of

+

=

?

(A)

(B)

(C)

(D)

18. y is a function of x in all the following relations EXCEPT:

(A) (x, y) = {(2, 1),(3, -1),(- 2, -1),(6, 5)}

(B) (x, y) = {(2, 7),(1, 7),(- 1, 7)}

(C) (x, y) = {(4, 2),(2, 4),(0, 0),(- 4, -2),(- 2, -4)}

(D) (x, y) = {(1, 6),(0, 4),(- 2, 5),(1, 3)}

19. What is the domain of f (x) =

?

(A) x:x≠-1, 0

(B) x:x≠-3, 2

(C) x:x≠0, 2,-3

(D) x:x≠-3,-1, 0, 2

20. What is the range of f (x) = x² - 4 ?

(A) f (x):f (x)≥4

(B) f (x):f (x)≥-4

(C) f (x):f (x)≥2

(D) f (x):-2≤f (x)≤2

21. If f (x) = 2x + 1 and g(x) = x² - 6x, what is 3f (x) + 2g(x) ?

(A) x² + 3

(B) 2x² + 3

(C) 2x² - 6x + 3

(D) 2x² + 6x + 3

22. If f (x) = 2x - 4 and g(x) = 5x + 3, what is fg(x) ?

(A) 10x² - 26x - 12

(B) 10x² - 14x - 12

(C) 10x + 2

(D) 10x - 17

23. If f (x) = 3x - 7 and g(x) = x² - 1, what is gof (x) ?

(A) 3x² - 10

(B) 3x² - 7x - 1

(C) 9x² - 42x + 48

(D) 3x³ -7x² - 3x + 7

24. What is the inverse of f (x) =

+ 5 ?

(A) f^-1 =

- 5

(B) f^-1 =

+ 4

(C) f^-1 =

(D) f^-1 =

25. If g(x) is shifted up 3 units and right 4 units from f (x), what is g(x) ?

(A) g(x) = f (x + 4) + 3

(B) g(x) = f (x - 4) + 3

(C) g(x) = f (x - 4) - 3

(D) g(x) = f (x + 4) + 3

26. If g(x) is stretched horizontally by a factor of 2 and shifted down 3 units from f (x), what is g(x)?

(A) g(x) = 2f (x) - 3

(B) g(x) = f (2x) - 3

(C) g(x) = f (2x - 3)

(D) g(x) = f (

x) - 3

27. If g(x) is a reflection of f (x) = x³ + x² - 4 over the y-axis, what is g(x)?

(A) g(x) = - x³ - x² + 4

(B) g(x) = x³ - x² + 4

(C) g(x) = - x³ + x² - 4

(D) g(x) = - x³ - x² - 4

28. Which of the following graph is symmetric with respect to the origin?

Figure A.3: Graphs

(A) A

(B) B

(C) C

(D) D

29. Name all the vertical asymptotes and holes in the graph of f (x) =

?

(A) Asymptotes: x = 2
Holes: x = -

, - 1

(B) Asymptotes: x = -

, - 1
Holes: x = 2

(C) Asymptotes: x = -

, - 1, 2
Holes: x = 3

(D) Asymptotes: x = -

, - 1
Holes: x = 3

30. Which equation could describe the following graph?

Figure A.4: Graph

(A) f (x) =

(B) f (x) =

(C) f (x) =

(D) (x) =

31. If 7 athletes are running a race, in how many different ways can they finish in first place, second place, and third place?

(A) 7!

(B) P(7, 3)

(C) C(7, 3)

(D) 7^3

32. Which of the following is equivalent to C(15, 10) ?

(A) C(15, 5)

(B) P(15, 10)

(C) C(10, 15)

(D) P(15, 5)

33. A function is defined recursively by

What is f (4) ?

(A) 5

(B) 7

(C) 33

(D) 47

34. What are the next two number in the sequence 1, 1, 2, 3, 5, 8, 13, __, __ ?

(A) 18, 23

(B) 18, 31

(C) 21, 29

(D) 21, 34

35. What is (

)^- ?

(A) -

(B) -

(C) 16

(D) 512

36. If

= 1 - 2x, what are all the possible values of x?

(A) x = - 3

(B) x = - 1

(C) x = - 1, 3

(D) x = 3

37. Which equation could describe the following graph?

Figure A.5: Graph

(A) f (x) = 2^x-2

(B) f (x) = 2^x - 4

(C) f (x) = 2^x - 3

(D) f (x) = log₂x - 4

38. log₃

= ?

(A) -2

(B) -

(C)

(D) 2

39. Simplify 3 log₂x + 2 log₂(x - 2) - log₂(x - 3).

(A) log₂(x³ + x² - 5x + 7)

(B) log₂

(C) log₂

(D) log₂

40. Solve for x: log₂(x² -1) - log₂(x + 1) = 3.

(A) x = - 1, 2

(B) x = 7

(C) x = 9

(D) x = 10

41. Solve for x: 6^x36^x-1 = 216.

(A) x =

(B) x =

(C) x = 2

(D) x = 3

42. If $700 is put into a bank account with an interest rate of 5%, compounded yearly, how much money is in the account after 6 years?

(A) $944.90

(B) $1349.86

(C) $3995.16

(D) $14059.88

43. Simplify

.

(A) 4

i

(B) -4

i

(C) 2

i

(D) -2

i

44. (2 - 3i)(5 + 7i) = ?

(A) -11 + i

(B) -11 - i

(C) 31 - i

(D) 31 + i

45. (4 + 3i)÷(5 + 3i) = ?

(A)

(B)

(C)

(D)

46. Which of the following is a factor of x⁴ -22x² + 31x - 28 ?

(A) x + 4

(B) x + 3

(C) x - 3

(D) x - 4

47. What is the remainder when P(x) = 2x⁵ -2x⁴ -6x³ +12x² + 4x + 16 is divided by x + 2 ?

(A) -2

(B) 8

(C) 16

(D) 56

48. Factor completely: 2x⁴ +11x³ +10x² - 11x - 12.

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

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

(C) (2x + 3)(x + 4)(x² + 1)

(D) (x +

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

49. If 2 - i is a zero of P(x) = x³ -3x² + x + 5, factor P(x) completely.

(A) (x + 2 + i)(x + 2 - i)(x + 1)

(B) (x - 2 + i)(x + 2 - i)(x + 1)

(C) (x - 2 + i)(x - 2 - i)(x + 1)

(D) (x - 2 + i)(x - 2 - i)(x - 1)

50. (x - 5y)⁴ = ?

(A) x⁴ -20x³y - 30x²y² -20xy³ -5y⁴

(B) x⁴ -20x³y + 30x²y² -20xy³ +5y⁴

(C) x⁴ +20x³y + 150x²y² +500xy³ + 625y

(D) x⁴ -20x³y + 150x²y² -500xy³ + 625y

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