SparkNotes: Review of Precalculus: Review Test

1. f (x) = 2x, g(x) =

, and h(x) = x - 1. What is fo(goh)?

(A)

(B) x -

(C) 2

(D)

- 1

2. What is the end behavior of the function 3x⁷ +2x⁶ -3x⁴ - x² + x - 46?

(A) As x→ - ∞, f→ - ∞, and as x→∞, f→ - ∞.

(B) As x→ - ∞, f→∞, and as x→∞, f→ - ∞.

(C) As x→ - ∞, f→∞, and as x→∞, f→∞.

(D) As x→ - ∞, f→ - ∞, and as x→∞, f→infty.

3. What is

?

(A) x³ - x² + 5x - 13

(B) x² + 13x - 7

(C) x² + 7x - 13

(D) x² - 3x + 13

4. Which of the following polynomials have exactly three real roots, x = 1, -1, and 3?

(A) x⁴ -3x² + 2x - 8

(B) x⁴ - x³ -7x² + x + 6

(C) x⁵ -3x⁴ - x + 3

(D) x⁴ +3x² - 4

5. What is the remainder of

?

(A) 18

(B) 38

(C) 0

(D) 28

6. How many possible positive and negative real roots does the function x³ -4x² + 3x - 2 have?

(A) 1 or 3 positive, 0 negative

(B) 0or2 positive, and 1 negative

(C) 0 positive and 1 negative

(D) 1 positive and 0 or 2 negative

7. The function

has what asymptotes, if any?

(A) A vertical asymptote at x = 2

(B) A horizontal asymptote at x = 3

(C) A vertical asymptote at x = 0 and an oblique asymptote at y = x

(D) A vertical asymptote at x = 2 and an oblique asymptote at y = x - 2

8. Which of the following expressions is not equal to the others?

(A) log_ax

(B)

(C)

(D)

9. The exponential rate of decay of a substance is .08 per year. What is the half-life of this substance in years?

(A) 12.5 years

(B)

56.5 years

(C)

8.66 years

(D)

10.035 years

10. Which of the following bank accounts will be worth the most in 10 years?

(A) $11,000 at 10% simple interest

(B) $9,450 at 9.0% compounded daily

(C) $9,800 at 8.5% compounded continuously

(D) $9,500 at 9.0% compounded quarterly

11. In which quadrants do sine and cosine have the same sign?

(A) I and II

(B) I and IV

(C) II and III

(D) I and III

12. Which of the following is a formula for all of the quadrantal angles?

(A) 0≤θ < 2Π

(B) θ =

, where n is an integer

(C) θ = 2nΠ, where n is an integer

(D) θ = (

+1)

, where n is an integer

13. Which of the following is not equal to the others?

(A) sin(Π/2)

(B) cos(2Π)

(C) tan(

(D) csc

14. Which expression is unequal to the others?

(A) sin²(x)csc²(x)

(B) cos²(x) - sin²(x)

(C) sec²(x) - tan²(x)

(D) csc²(x) - cot²(x)

15. Which of the following does not solve the equation sin(x)cos(x) = 0?

(A) x =

(B) x =

(C) x =

(D) x =

16. What is the amplitude and period of the function f (x) = 2 cos(2x)?

(A) Amplitude: 1; Period: 2Π

(B) Amplitude:

; Period: Π

(C) Amplitude: 4; Period:

(D) Amplitude: 2; Period: Π

17. Which value is defined?

(A) arcsin(2)

(B) arctan(0)

(C) tan(

)

(D) sec(

)

18. Which polar coordinates correspond to the rectangular coordinates (2, 2)?

(A) (

,

)

(B) -

,

(C) (2, Π)

(D) (

,

)

19. Convert the polar equation 4 = r sin(θ) to rectangular form.

(A) x = 4

(B) y = 4x

(C) y = 4

(D) y = - 4

20. What are the x-intercepts, if there are any, for the function defined by x = 3t - 2, y = t² - 4, -3≤t≤3.

(A) (

,

)

(B) (- 8, 0) and (4, 0)

(C) (- 8, 0) and (0, 0)

(D) (- 2, 0) and (2, 0)

21. The graph of r = 1 + 2 sin(θ) is symmetric with respect to what?

(A) The pole

(B) The polar axis

(C) The line θ =

(D) It is not symmetrical at all

22. The graph of r = 2 cos(4θ) is an example of what?

(A) A limacon

(B) A spiral

(C) A circle

(D) A rose curve

23. What is ı⁷7?

(A) 1

(B) -1

(C) ı

(D) - ı

24. What is the polar form of z = 1 +

ı?

(A) (4,

)

(B)

,

)

(C) (1,

)

(D) (2,

)

25. Which of the following complex numbers has a different modulus than the rest?

(A) 3 - 4ı

(B) 5 - ı

(C)

+

ı

(D)

-2ı

26. What are the imaginary roots of the polynomial x⁴ +3x³ +5x² + 27x - 36, if there are any?

(A) ı, - imath

(B)

ı, -

ı

(C) 2ı, -2ı

(D) None of these options is correct

27. What is (

+

ı)⁴?

(A) -16

(B) 4ı

(C)

ı - ı

(D) 2

28. Which of the following options is not a 4th root of 1?

(A) 1

(B) - ı

(C) 1 - ı

(D) ı

29. 3x² + 6x - 5y - 7 = 0 is what kind of conic?

(A) An ellipse

(B) A parabola

(C) A hyperbola

(D) A circle

30. x² +2xy - 5y² + 4x - 4y + 7 is what kind of conic?

(A) An ellipse

(B) A parabola

(C) A Hyperbola

(D) A circle

31. Given 25x² +4y² - 100 = 0, solve for a, b, and c.

(A) a = 25, b = 4, and c = 21

(B) a = 5, b =

, c = 2

(C) a = 2, b = 5, c =

(D) a = 5, b = 2, c =

32. Given -4x² +2xy - 5y² + 6x - 2y - 1 = 0, about how many degrees must the axes be rotated in order to eliminate the xy-term?

(A)

31.7^o

(B)

41.3^o

(C)

43.7^o

(D)

27.1^o

33. Given the polar equation for a conic is

, what kind of conic is it?

(A) An ellipse

(B) A parabola

(C) A hyperbola

(D) A circle

34. Given

is the polar form of a conic, where is the directrix in relation to the pole?

(A) The directrix is to the left of the pole.

(B) The directrix is above the pole.

(C) The directrix is to the right of the pole.

(D) The directrix is below the pole.

35. What is the next apparent term in the sequence 1, 2, 4, 5, 7, 8, 10,…

(A) 11

(B) 12

(C) 13

(D) Impossible to tell

36. Define the sequence a_n = 3n + 6 recursively.

(A) a₁ = 9; a_n+1 = 3a_n + 6

(B) a₁ = 6; a_n+1 = 2a_n + 6

(C) a₁ = 9; a_n+1 = a_n + 3

(D) a₁ = 9; a_n+1 = a_n - 9

37. Define the sequence a_n =

recursively.

(A) a₁ =

; a_n+1 =

(B) a₁ =

; a_n+1 =

(C) a₁ = 3; a_n+1 =

(D) This sequence cannot be defined recursively.

38. Find an explicit formula for the following sequence: 1,

, 2,

, 3,

, 4,….

(A) a_n =

(B) a_n = 2n - 1

(C) a_n = n +

(D) a_n =

39. What is

7(4n - 2)?

(A) 476

(B) 500

(C) 578

(D) 1238

40. What is

(3ⁱ)?

(A) 32400

(B) 3240

(C) 456

(D) 128

41. Calculate the sum of the first 200 terms of a_n = n + 1.

(A) 20300

(B) 23000

(D) 203203

42. What is the sum of the first five terms in the sequence a_n = 2×3ⁿ?

(A) 240

(B) 726

(C) 126

(D) 1452

43. What is the limit of the infinite geometric series a_n = 3×

ⁿ

(A)

(B)

(C) 3

(D) ∞

44. Evaluate

5x.

(A) 10

(B)

(C)

(D) The limit does not exist.

45. Evaluate

.

(A) The limit doesn't exist.

(B) Impossible to Calculate

(C) 1

(D) -1

46. Calculate

x² - 4x - 2

(A) 5

(B) 3

(C) 0

(D) - ∞

47. Let f (x) = 1 for all x≠ 0, f (x) = 4 for x = 0. Calculate

f (x).

(A) 2

(B) 4

(C) 1

(D) The limit doesn't exist

48. Over which of the following intervals is f (x) =

discontinuous?

(A) [1, 3]

(B) [0, 1]

(C) (2,∞]

(D) The function is continuous on all of these intervals.

49. Over which of the following intervals is the function f (x) =

discontinuous?

(A) (0, 1]

(B) All x > 0

(C) Any interval including 0

(D) The function is continuous everywhere

50. Which type of discontinuity happens to the function f (x) =

at the vale x = 5?

(A) Infinite discontinuity

(B) Jump Discontinuity

(C) Point Discontinuity

(D) It is continuous at this point.

Review of Prealgebra

Review Test