Free Printable OnRamps Spring Final Review

1.

Using the given triangle, find the cos(A)

a)

$\frac{1}{\sqrt{5}}$

b)

$2$

c)

$\frac{2}{\sqrt{5}}$

d)

$6$

2.

Using the given triangle, find the cot(A)

a)

$\frac{1}{2}$

b)

$2$

c)

$\frac{2}{\sqrt{5}}$

d)

$\frac{1}{\sqrt{5}}$

3.

Using the given triangle, find the csc(A)

a)

$\frac{1}{2}$

b)

$12$

c)

$\frac{\sqrt{5}}{2}$

d)

$\sqrt{5}$

4.

Given that $\cos\left(\theta\right)=\frac{24}{25}$ , find $\sin\left(\theta\right)$

a)

$\frac{7}{25}$

b)

$\frac{24}{25}$

c)

$\frac{25}{7}$

d)

$\frac{25}{24}$

5.

Given that $\cos\left(\theta\right)=\frac{24}{25}$ , find $\tan\left(\theta\right)$

a)

$\frac{7}{25}$

b)

$\frac{24}{7}$

c)

$\frac{25}{7}$

d)

$\frac{7}{24}$

6.

Solve for a. You may use a calculator.

a)

12

b)

8.9

c)

0.06

d)

7.2

7.

Solve for B. You may use a calculator.

a)

31

b)

121

c)

59

8.

A 25-ft ladder leans against a building so that the angle between the ground and the ladder is 70°.

How high does the ladder reach up the side of the building? You may use a calculator.

a)

23.5 ft

b)

8.6 ft

c)

68.7 ft

d)

25 ft

9.

A radio tower is located 600 feet from a building. From a window in the building, a person determines that the angle of depression to the bottom of the tower is 40° and that the angle of elevation to the top of the tower is 19°. How tall is the tower? You may use a calculator.

a)

710 ft

b)

2457.6 ft

c)

206.6 ft

d)

1742.5 ft

10.

Find the length x. You may use a calculator.

a)

124.7

b)

150.1

c)

45.9

11.

Convert the angle 90° to radians.

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

$\frac{3\pi}{2}$

d)

$\frac{2\pi}{3}$

12.

Convert the angle 36° to radians.

a)

$\frac{\pi}{5}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{10}$

13.

Convert the angle $\frac{2\pi}{3}$ from radians to degrees.

a)

120°

b)

60°

c)

270°

d)

2.09°

14.

Convert the angle $\frac{5\pi}{12}$ from radians to degrees.

a)

75°

b)

0.42°

c)

150°

d)

15°

15.

Simplify to an expression containing one trig function and no fractions.
$\csc\theta\cdot\tan\theta$

a)

$\sec\theta$

b)

$\cos\theta$

c)

$\sin\theta$

d)

$\csc\theta$

16.

Simplify to an expression containing one trig function and no fractions.
$\frac{\sec\theta}{\csc\theta}$

a)

$\tan\theta$

b)

$\cot\theta$

c)

$\sin\theta$

d)

$1$

17.

Simplify to an expression containing one trig function and no fractions.
$\frac{\cot\theta}{\csc\theta}$

a)

$\tan\theta$

b)

$\cos\theta$

c)

$\sin\theta$

d)

$\sec\theta$

18.

Simplify to an expression containing one trig function and no fractions.
$\frac{\sin^2\theta+\cos^2\theta}{\cos^2\theta}$

a)

$\sec^2\theta$

b)

$\tan^2\theta$

c)

$\cos^2\theta$

d)

$\csc^2\theta$

19.

Simplify to an expression containing one trig function and no fractions.
$\sec\theta\cdot\tan\theta\cdot\cos\theta$

a)

$\sin\theta$

b)

$\tan\theta$

c)

$\cos^2\theta$

d)

$1$

20.

Simplify to an expression containing one trig function and no fractions.
$\frac{\cos^2\theta-1}{1-\sin^2\theta}$

a)

$\cot^2\theta$

b)

$\tan^2\theta$

c)

$-\tan^2\theta$

d)

$-\cot^2\theta$

21.

Which of the following angles is coterminal with $645\degree$ ?

a)

$285\degree$

b)

$465\degree$

c)

$-645\degree$

d)

$45\degree$

22.

Which of the following angles is NOT coterminal with $43\degree$ ?

a)

$137\degree$

b)

$403\degree$

c)

$1123\degree$

d)

$-317\degree$

23.

Which of the following angles is NOT coterminal with $-\frac{7\pi}{2}$ ?

a)

$\frac{7\pi}{2}$

b)

$-\frac{3\pi}{2}$

c)

$\frac{\pi}{2}$

d)

$\frac{41\pi}{2}$

24.

Which of the following angles is coterminal with $\frac{3\pi}{4}$ ?

a)

$\frac{11\pi}{4}$

b)

$\frac{\pi}{4}$

c)

$-\frac{3\pi}{4}$

d)

$\frac{7\pi}{4}$

25.

Using your unit circle, evaluate the following expression:

\cos\left(\frac{\pi}{3}\right)

a)

$\frac{1}{2}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

$\frac{\pi}{3}$

26.

Using your unit circle, evaluate the following expression:
$\sin\left(\frac{\pi}{4}\right)$

a)

$\frac{\sqrt{2}}{2}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

27.

Using your unit circle, evaluate the following expression:
$\sin\left(\pi\right)$

a)

$1$

b)

$0$

c)

$-1$

d)

$\frac{1}{2}$

28.

Using your unit circle, evaluate the following expression:
$\tan\left(\frac{4\pi}{3}\right)$

a)

$\sqrt{3}$

b)

$\frac{\sqrt{3}}{3}$

c)

$-\sqrt{3}$

d)

$-\frac{\sqrt{3}}{3}$

29.

Using your unit circle, evaluate the following expression:
$\cos\left(\frac{4\pi}{3}\right)$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

$-\frac{\sqrt{3}}{2}$

d)

$-\frac{\sqrt{2}}{2}$

30.

Using your unit circle, evaluate the following expression:
$\cot\left(0\right)$

a)

$0$

b)

undefined

c)

$1$

d)

$-1$

31.

Using your unit circle, evaluate the following expression:
$\csc\left(\frac{7\pi}{6}\right)$

a)

$-2$

b)

$-\frac{1}{2}$

c)

$-\frac{2\sqrt{3}}{3}$

d)

$-\frac{\sqrt{3}}{2}$

32.

Using your unit circle, evaluate the following expression:
$\sec\left(\frac{\pi}{6}\right)$

a)

$\frac{2\sqrt{3}}{3}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

$2$

33.

Using your unit circle, evaluate the following expression:
$\cos\left(\pi\right)$

a)

$-1$

b)

$1$

c)

$0$

d)

$\frac{1}{2}$

34.

Using your unit circle, evaluate the following expression:
$\csc\left(\frac{5\pi}{4}\right)$

a)

$-\sqrt{2}$

b)

$-\frac{\sqrt{2}}{2}$

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

35.

Using your unit circle, evaluate the following expression:
$\tan\left(\frac{\pi}{4}\right)$

a)

$1$

b)

$-1$

c)

$2$

d)

$0$

36.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\sin\theta=\frac{\sqrt{2}}{2}$

a)

$\frac{\pi}{4}$

b)

$\frac{3\pi}{4}$

c)

$\frac{5\pi}{4}$

d)

$\frac{7\pi}{4}$

37.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\tan\theta=-1$

a)

$\frac{\pi}{4}$

b)

$\frac{3\pi}{4}$

c)

$\frac{5\pi}{4}$

d)

$\frac{7\pi}{4}$

38.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\cos\theta=0$

a)

$0$

b)

$\frac{\pi}{2}$

c)

$\frac{3\pi}{2}$

d)

$\pi$

39.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\tan\theta=undefined$

a)

$0$

b)

$\frac{\pi}{2}$

c)

$\frac{3\pi}{2}$

d)

$\pi$

40.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\cot\theta=-\sqrt{3}$

a)

$\frac{2\pi}{3}$

b)

$\frac{5\pi}{6}$

c)

$\frac{5\pi}{3}$

d)

$\frac{11\pi}{6}$

41.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\sec\theta=-1$

a)

$0$

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

$\frac{3\pi}{2}$

42.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$2\sin\theta=-1$

a)

$\frac{2\pi}{3}$

b)

$\frac{7\pi}{6}$

c)

$\frac{11\pi}{6}$

d)

$\frac{4\pi}{3}$

43.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\sin^2\theta=\frac{1}{4}$

a)

$\frac{5\pi}{6}$

b)

$\frac{7\pi}{6}$

c)

$\frac{11\pi}{6}$

d)

$\frac{\pi}{6}$

44.

Which of the following is NOT a solution to the trig equation?
$2\sin\theta\cos\theta=\cos\theta$

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{6}$

c)

$\frac{5\pi}{6}$

d)

$\pi$

45.

Which of the following is NOT a solution to the trig equation?
$\tan\theta\sin\theta-\sin\theta=0$

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

$\frac{5\pi}{4}$

d)

$\frac{\pi}{4}$

46.

Which of the following is NOT a solution to the trig equation?
$2\cos^2\theta+3\cos\theta+1=0$

a)

$0$

b)

$\pi$

c)

$\frac{2\pi}{3}$

d)

$\frac{4\pi}{3}$

47.

Which of the following is the correct domain, range, and y-intercept for $y=\sin x$

a)

D: {x|x ∈ ℝ}, R: {y|-1 ≤ y ≤ 1}, (0,1)

b)

D: {x|x ∈ ℝ}, R: {y|-1 ≤ y ≤ 1}, (0,0)

c)

D: {x|0 ≤ x ≤ 2π}, R: {y|-1 ≤ y ≤ 1}, (0,0)

d)

D: {x|0 ≤ x ≤ 2π}, R: {y|-1 ≤ y ≤ 1}, (0,1)

48.

Which of the following is the correct domain, range, and y-intercept for $y=\cos x$

a)

D: {x|x ∈ ℝ}, R: {y|-1 ≤ y ≤ 1}, (0,1)

b)

D: {x|x ∈ ℝ}, R: {y|-1 ≤ y ≤ 1}, (0,0)

c)

D: {x|0 ≤ x ≤ 2π}, R: {y|-1 ≤ y ≤ 1}, (0,0)

d)

D: {x|0 ≤ x ≤ 2π}, R: {y|-1 ≤ y ≤ 1}, (0,1)

49.

Which of the following is the correct domain, range for $y=\tan x$

a)

D: {x|x ≠ (2n+1)π/2}, R: {y|-1 ≤ y ≤ 1}

b)

D: {x|x ≠ (2n+1)π/2}, R: {y|y ∈ ℝ}

c)

D: {x|x ∈ ℝ}, R: {y|y ∈ ℝ}

d)

D: {x|x ∈ ℝ}, R: {y|-1 ≤ y ≤ 1}

50.

What is the period (wavelength) of the function

y=2-3\sin\left(\frac{2}{5}\left(x-1\right)\right)

a)

$2\pi$

b)

$5\pi$

c)

$\frac{2\pi}{5}$

d)

$\frac{2}{5}$

51.

What is the period (wavelength) of the function

y=\cos x

a)

$2\pi$

b)

$\pi$

c)

$1$

d)

$\infty$

52.

What is the period (wavelength) of the function

y=\tan x

a)

$2\pi$

b)

$\pi$

c)

$1$

d)

$\infty$

53.

What are the maximum and minimum values of the function

y=2-4\cos\left(x+1\right)

a)

Max: 6, Min: -2

b)

Max: 2, Min: -2

c)

Max: 4, Min: -4

d)

Max: 4, Min: -2

54.

Which of the following is the correct function for this graph.

a)

$y=2\sin\left(\frac{\pi}{3}\left(x+1\right)\right)$

b)

$y=2\sin\left(\frac{\pi}{3}\left(x-2\right)\right)$

c)

$y=2\sin\left(3\left(x+1\right)\right)$

d)

$y=2\sin\left(3\left(x-2\right)\right)$

55.

Which function best describes this image.

a)

$y=\sin^{-1}x$

b)

$y=\cos^{-1}x$

c)

$y=\tan^{-1}x$

56.

Which function best describes this image.

a)

$y=\sin^{-1}x$

b)

$y=\cos^{-1}x$

c)

$y=\tan^{-1}x$

57.

Which function best describes this image.

a)

$y=\sin^{-1}x$

b)

$y=\cos^{-1}x$

c)

$y=\tan^{-1}x$

58.

Evaluate: $\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{3}$

c)

$\frac{2\pi}{3}$

d)

$\frac{11\pi}{6}$

59.

Evaluate: $\tan^{-1}\left(-1\right)$

a)

$\frac{-\pi}{4}$

b)

$\frac{\pi}{4}$

c)

$\frac{3\pi}{4}$

d)

$\frac{7\pi}{4}$

60.

Evaluate: $\cos^{-1}\left(-\frac{1}{2}\right)$

a)

$\frac{2\pi}{3}$

b)

$\frac{4\pi}{3}$

c)

$\frac{-\pi}{6}$

d)

$\frac{-\pi}{3}$

61.

Evaluate: $\sin\left(\cos^{-1}\left(-\frac{1}{2}\right)\right)$

a)

$\frac{\sqrt{3}}{2}$

b)

$\frac{1}{2}$

c)

$-\frac{\sqrt{3}}{2}$

d)

$-\frac{1}{2}$

62.

Evaluate: $\sin\left(\tan^{-1}\left(-\frac{3}{4}\right)\right)$

a)

$-\frac{3}{5}$

b)

$-\frac{4}{5}$

c)

$\frac{3}{5}$

d)

$\frac{4}{5}$

63.

Evaluate: $\sin^{-1}\left(\cos\left(\frac{\pi}{4}\right)\right)$

a)

$\frac{\pi}{4}$

b)

$\frac{\sqrt{2}}{2}$

c)

$-\frac{\pi}{4}$

d)

$\frac{\sqrt{3}}{2}$

64.

Evaluate: $\cos^{-1}\left(\sin\left(\frac{3\pi}{2}\right)\right)$

a)

$\pi$

b)

$-1$

c)

$\frac{3\pi}{2}$

d)

$0$

65.

Evaluate: $\cos\left(\frac{5\pi}{12}\right)$

a)

$\frac{-\sqrt{2}-\sqrt{6}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

66.

Evaluate: $\sin\left(\frac{19\pi}{12}\right)$

a)

$\frac{-\sqrt{2}-\sqrt{6}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

67.

Rewrite: $\sin\left(x-\frac{\pi}{3}\right)$

a)

$\frac{\sqrt{3}}{2}\sin x-\frac{1}{2}\cos x$

b)

$\frac{1}{2}\sin x-\frac{\sqrt{3}}{2}\cos x$

c)

$\frac{\sqrt{3}}{2}\sin x+\frac{1}{2}\cos x$

d)

$\frac{1}{2}\sin x+\frac{\sqrt{3}}{2}\cos x$

68.

Evaluate: $\cos^2\left(67.5\degree\right)-\sin^2\left(67.5\degree\right)$

a)

$1$

b)

$-1$

c)

$-\frac{\sqrt{2}}{2}$

d)

$-\frac{1}{2}$

e)

$-\frac{\sqrt{3}}{2}$

69.

Select the solutions, 0 ≤ x < 2π.

\sin x-\cos\left(2x\right)=0

a)

$\frac{\pi}{6}$

b)

$\frac{5\pi}{6}$

c)

$\frac{3\pi}{2}$

d)

$\frac{\pi}{3}$

e)

$\frac{\pi}{2}$

70.

Select the solutions, 0 ≤ x < 2π.

\sin\left(2x\right)=\sqrt{3}\sin x

a)

$0$

b)

$\pi$

c)

$\frac{\pi}{6}$

d)

$\frac{11\pi}{6}$

71.

Solve for x.

a)

$\frac{12}{\sqrt{2}}$

b)

$\frac{12\sqrt{3}}{\sqrt{2}}$

c)

$4\sqrt{3}$

d)

$12$

72.

A jogger ran 3 miles due east of his house. Then he ran 5 miles at a heading of 30° East of North (or 30° NE). How far is he from his house after running 8 miles?

a)

$\frac{15\sqrt{3}}{2}$

b)

$\sqrt{34-15\sqrt{3}}$

c)

$7$

d)

$\sqrt{34}$

73.

What is the question of the missing piece of the roller coaster?

a)

$y=3.5-1.5\cos\left(\frac{\pi}{2}\left(x-4\right)\right)$

b)

$y=3.5+1.5\cos\left(\frac{\pi}{2}\left(x+4\right)\right)$

c)

$y=2+5\cos\left(2\left(x-4\right)\right)$

d)

$y=2+5\cos\left(2\left(x+4\right)\right)$

e)

$y=3.5+1.5\cos\left(\frac{\pi}{2}\left(x-4\right)\right)$

74.

(5.1) Can you have multiple holes in a rational function?

a)

yes

b)

no

75.

(5.1) Can a function have more than one vertical asymptote?

a)

yes

b)

no

76.

(5.1) Determine the veritcal asymptote:
$f\left(x\right)=\frac{3x^2+5x+2}{2x-6}$

a)

$x=3$

b)

$x=6$

c)

$x=\frac{3}{2}$

d)

$x=-\frac{1}{3}$

77.

(5.1) Determine the x-intercepts of the function $f\left(x\right)=\frac{15x^2-8x-7}{x+2}$

a)

$\left(-\frac{7}{15},0\right),\ \left(1,0\right)$

b)

$\left(-2,0\right)$

c)

$\left(-\frac{7}{2},0\right)$

d)

$\left(-\frac{1}{5},0\right),\ \ \left(\frac{7}{3},0\right)$

78.

(5.1) Find the x and y intercepts of $f\left(x\right)=\frac{3x-8}{9x-4}$

a)

$\left(\frac{8}{3},0\right),\ \left(0,2\right)$

b)

$\left(0,\frac{8}{3}\right),\ \ \left(2,0\right)$

c)

$\left(\frac{8}{3},0\right),\ \left(\frac{4}{9},\ 0\right),\ \left(0,2\right)$

d)

$\left(\frac{1}{3},0\right),\ \left(0,2\right)$

79.

(5.1) Find the x-intercepts and y-intercepts for the function below.
$f\left(x\right)=\frac{3x-5}{x+6}$

a)

$\left(\frac{5}{3},0\right),\ \left(0,\ -\frac{5}{6}\right)$

b)

$\left(3,0\right),\ \left(0,-\frac{5}{6}\right)$

c)

$\left(\frac{5}{3},0\right),\ \left(0,-6\right)$

d)

$\left(3,0\right),\ \left(0,-6\right)$

80.

(5.1) Find the vertical and horizontal asymptotes for the function below.
$f\left(x\right)=\frac{3x-5}{x+6}$

a)

$x=-6,\ y=3$

b)

$x=\frac{5}{3},\ y=-\frac{5}{6}$

c)

$x=\frac{5}{3},\ y=3$

d)

$x=-6,\ y=-\frac{5}{6}$

81.

(5.1) Find the vertical and horizontal asymptotes for the function below.
$f\left(x\right)=\frac{5x}{\left(x-3\right)\left(x+6\right)}$

a)

$x=3,\ x=-6,\ y=0$

b)

$x=3,\ x=-6,\ y=5$

c)

$x=-3,\ x=6,\ y=0$

d)

$x=-3,\ x=6,\ y=5$

82.

(5.1) Graph: $f\left(x\right)=\frac{3x^2-12x}{x^2-2x-3}$

a)

b)

c)

d)

83.

(5.1) Find the correct function for this graph.

a)

$f\left(x\right)=\frac{4}{\left(x-2\right)^2}$

b)

$f\left(x\right)=\frac{-2}{x-2}$

c)

$f\left(x\right)=\frac{1}{\left(x-2\right)^2}$

d)

$f\left(x\right)=\frac{-x}{x-2}$

84.

(5.1) Write an equation for a rational function with the given characteristics: Vertical asymptotes at x=0 and x=5; x-intercepts at (6,0) and (3,0); horizontal asymptote at y=1.

a)

$f\left(x\right)=\frac{\left(x-6\right)\left(x-3\right)}{x\left(x-5\right)}$

b)

$f\left(x\right)=\frac{\left(x-6\right)\left(x-3\right)}{\left(x-1\right)\left(x-5\right)}$

c)

$f\left(x\right)=\frac{\left(x+6\right)\left(x+3\right)}{\left(x-5\right)}$

d)

$f\left(x\right)=\frac{\left(x-6\right)\left(x-3\right)}{\left(x-5\right)^2}$

85.

(5.2) Evaluate: $\lim_{x\rightarrow3}\ \frac{2x^2-x-3}{x+1}$

(a)

86.

(5.2) Evaluate: $\lim_{x\rightarrow2}\ \frac{x^2+2x+1}{x+1}$

(a)

87.

(5.2) Evaluate: $\lim_{x\rightarrow0}\ \frac{x^2+2x}{x}$

(a)

88.

(5.2) Evaluate: $\lim_{x\rightarrow1}\ \frac{x^2+2x+1}{x+1}$

(a)

89.

(5.2) Evaluate: $\lim_{x\rightarrow5}\ \frac{\left(\frac{-1}{x}+\frac{1}{5}\right)}{5-x}$

(a)

90.

(5.3.1) Find the average rate of $f\left(x\right)=2\sqrt{x}$ on the interval [7,13].

a)

$\frac{\sqrt{13}-\sqrt{7}}{3}$

b)

$\frac{\sqrt{6}}{3}$

c)

$\sqrt{2}$

d)

$2\sqrt{6}$

91.

(5.3.1) Find the average rate of change of $f\left(x\right)=2x^2$ on the interval $\left[3,a\right]$

a)

$2a+6$

b)

$2a-6$

c)

$2a+3$

d)

$2a-3$

92.

(5.3.1) Find the average rate of change of $f\left(x\right)=\frac{1}{x+4}$ on the interval $\left[x,x+h\right]$

a)

$\frac{-1}{\left(x+4\right)\left(x+h+4\right)}$

b)

$\frac{-1}{2x+h+8}$

c)

$\frac{1}{h^2}$

d)

$\frac{1-h}{h\left(x+h+4\right)}$

93.

(5.3.3) Which of the following is the correct derivative graph for the given graph?

a)

b)

c)

d)

94.

(5.4.1) What is the power rule for the derivative of a polynomial function of the form $f\left(x\right)=ax^n$ ?

a)

$f'\left(x\right)=anx^{\left(n-1\right)}$

b)

$f'\left(x\right)=ax^{\left(n-1\right)}$

c)

$f'\left(x\right)=anx^n$

d)

$f'\left(x\right)=ax^n$

95.

(5.4.1) Find the derivative of $f\left(x\right)=4x^3+7x-23$

a)

$f'\left(x\right)=12x^2+7$

b)

$f'\left(x\right)=12x^2-16$

c)

$f'\left(x\right)=12x^3+7x$

d)

$f'\left(x\right)=12x^2+7-\frac{23}{x}$

96.

(5.4.1) Find the derivative of $f\left(x\right)=\frac{3}{x^3}+\frac{12}{x^2}+10$

a)

$f'\left(x\right)=-\frac{9}{x^4}-\frac{24}{x^3}$

b)

$f'\left(x\right)=-\frac{9}{x^4}-\frac{24}{x^3}+10$

c)

$f'\left(x\right)=\frac{3}{x^2}+\frac{12}{x}$

d)

$f'\left(x\right)=-\frac{9}{x^2}-\frac{24}{x}$

97.

(5.4.1) Find the derivative of $f\left(x\right)=\frac{7}{3}x^2+\frac{x}{2}+11$

a)

$f'\left(x\right)=\frac{14}{3}x+\frac{1}{2}$

b)

$f'\left(x\right)=\frac{14}{3}x+\frac{23}{2}$

c)

$f'\left(x\right)=\frac{7}{6}x-\frac{2}{x^2}$

d)

$f'\left(x\right)=\frac{7}{6}x+\frac{1}{2}$

98.

(5.4.1) What is the derivative of $f\left(x\right)=\sqrt{x}$ ?

a)

$f'\left(x\right)=\frac{1}{2\sqrt{x}}$

b)

$f'\left(x\right)=\frac{\sqrt{x}}{2}$

c)

$f'\left(x\right)=2\sqrt{x}$

d)

$f'\left(x\right)=\frac{2}{\sqrt{x}}$

99.

(5.4.2) Given $f\left(x\right)=x^3-6x^2+9x+1$ , how is the function behaving at $x=2$ ?

a)

Increasing

b)

Decreasing

c)

Stationary (slope is zero)

d)

Undefined

100.

(5.4.2) At what values does $f\left(x\right)=x^3-6x^2+9x+1$ have a relative maximum or minimum?

a)

$x=1,\ x=3$

b)

$x=-0.104$

c)

$x=-3,\ x=-1,\ x=3$

d)

$x=-1,\ x=4$

101.

(5.4.2) On what interval is the graph of $f\left(x\right)=3x^2-12x+7$ increasing?

a)

$\left(2,\infty\right)$

b)

$\left[2,\infty\right)$

c)

$\left(-\infty,2\right)$

d)

$\left(-\infty,2\right]$

102.

$x\left(s\right)=1.5$

Given that s is the distance along the path from the origin, solve for s.

a)

$\frac{5}{2}$

b)

$\frac{25}{4}$

c)

$5$

d)

$2$

103.

$y\left(6\right)$

Given that s is the distance along the path from the origin, and the notation above is y(s), evaluate.

a)

$3$

b)

$4$

c)

$6$

d)

undefined

104.

Given that s is the distance along the path from the origin, what value of s yields the coordinate $\left(6,3\right)$ ?

a)

$6+\sqrt{5}$

b)

$3\sqrt{5}$

c)

$1+\sqrt{7}+\sqrt{3}$

105.

Which graph more closely models the following parametric equation on the domain -2 ≤ t ≤ 2

x\left(t\right)=2t^2+t

y\left(t\right)=t^3-3

a)

b)

c)

d)

106.

Which of the following parametric functions creates this graph?

a)

$x\left(t\right)=4\sin\left(t\right)+2,\ \ y\left(t\right)=2\cos\left(t\right)$

b)

$\frac{\left(x-2\right)^2}{16}+\frac{y^2}{4}=1$

c)

$x\left(t\right)=2\sin\left(t\right)+2,\ \ \ y\left(t\right)=4\cos\left(t\right)$

d)

$x\left(t\right)=4\cos\left(t-2\right),\ \ \ y\left(t\right)=2\sin\left(t\right)$

e)

$x\left(t\right)=2\cos\left(t\right)+2,\ \ y\left(t\right)=4\sin\left(t\right)$

107.

Which of the following parametric functions describes the motion of the end of the second hand on the clock. Make sure it starts at the 12, rotates clockwise, and takes 60 seconds to complete one revolution.

a)

$x\left(t\right)=21+8\sin\left(\frac{\pi}{30}t\right),\ \ y\left(t\right)=20+8\cos\left(\frac{\pi}{30}t\right)$

b)

$x\left(t\right)=21+8\cos\left(\frac{\pi}{30}t\right),\ y\left(t\right)=20+8\sin\left(\frac{\pi}{30}t\right)$

c)

$x\left(t\right)=21-8\sin\left(\frac{\pi}{30}t\right),\ \ y\left(t\right)=20-8\cos\left(\frac{\pi}{30}t\right)$

d)

$x\left(t\right)=21-8\cos\left(\frac{\pi}{30}t\right),\ y\left(t\right)=20-8\sin\left(\frac{\pi}{30}t\right)$

108.

Convert the polar coordinate, $\left(9,\frac{5\pi}{3}\right)$ to Cartesian coordinates.

a)

$\left(\frac{9}{2},\frac{-9\sqrt{3}}{2}\right)$

b)

$\left(\frac{9}{2},\frac{9\sqrt{3}}{2}\right)$

c)

$\left(9,\frac{-\sqrt{3}}{2}\right)$

d)

$\left(-9,\frac{\sqrt{3}}{2}\right)$

109.

Convert the polar coordinate, $\left(-4,\frac{3\pi}{2}\right)$ to Cartesian coordinates.

a)

$\left(4,0\right)$

b)

$\left(-4,0\right)$

c)

$\left(0,4\right)$

d)

$\left(0,-4\right)$

110.

Convert the Cartesian coordinate, $\left(-\sqrt{2},-\sqrt{2}\right)$ to polar coordinates.

a)

$\left(2,\frac{5\pi}{4}\right)$

b)

$\left(\sqrt{2},\frac{\pi}{4}\right)$

c)

$\left(-2,\frac{5\pi}{4}\right)$

d)

$\left(2,\frac{\pi}{4}\right)$

111.

Convert the rectangular equation, $y=5$ to polar.

a)

$r=5\csc\theta$

b)

$r=5\sin\theta$

c)

$r=5\sec\theta$

d)

$r=5\cos\theta$

112.

Convert the rectangular equation, $x^2+y^2=81$ to polar.

a)

$r^2=9$

b)

$r=9$

c)

$\theta^2+r^2=81$

d)

$\cos^2\theta+\sin^2\theta=9$

113.

Which of the following is the graph for the function $\theta=\frac{2\pi}{3}$

a)

b)

c)

d)

114.

Which of the following is the polar function that creates this graph?

a)

$r=3-3\sin\theta$

b)

$r=3+3\sin\theta$

c)

$r=3+3\cos\theta$

d)

$r=3-3\cos\theta$

OnRamps Spring Final Review

Total questions: 114

Worksheet time: 19hrs 0mins

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