Free Printable Quarter 3 Exam Review for PreCalc

1.

What is the period of the equation shown?

a)

3π

b)

2π

c)

3π / 2

d)

2π / 3

2.

What is the period of the equation shown?

a)

8π

b)

4π

c)

π / 4

d)

π / 2

3.

Describe the horizontal shift.

a)

left π / 2

b)

left 2π

c)

right 2π

d)

right π / 2

4.

Describe the horizontal and vertical shifts.

a)

right 3π/2 , down 5

b)

left 2π/3 , up 5

c)

right 2π/3 , up 5

d)

left 2π , down 5

5.

What is the equation of the graph shown?

a)

y = 2sin(θ + π/2) + 3

b)

y = 3cos(θ - π/2) + 2

c)

y = 3sin(θ - π/2) + 2

d)

y = 2cos(θ + π/2) + 3

6.

What is the equation of the graph shown?

a)

y = 2sin(θ + π/2) + 2

b)

y = 2cos(θ - π/2) + 2

c)

y = 2sin(θ - π/2) + 2

d)

y = 2cos(θ + π/2) + 2

7.

What is the equation of the graph shown?

a)

y = 3sin(θ + π/4) - 1

b)

y = 3cos(θ - π/4) -1

c)

y = 3sin(θ - π/4) + 1

d)

y = 3cos(θ + π/4) + 1

8.

What is the equation of the graph shown?

a)

y = -sinθ -1

b)

y = -sinθ/2 -1

c)

y = -2sin2θ + 1

d)

y = sinθ/2 + 1

9.

What is the equation of the graph shown?

a)

y = tan θ

b)

y = sin θ

c)

y = cos θ

d)

y = -5tan θ

10.

What is the equation for the graph shown.

a)

y = 4sinθ - 2

b)

y = 3tcosθ - 1

c)

y = 2tanθ - 4

d)

y = 2-4tanθ + 2

11.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

12.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

13.

Which equation?

a)

y= cos2x

b)

y= (1/2)cosx

c)

y= cos(1/2)x

d)

y= 2cosx

14.

What is the amplitude of y = 3 cos 2x?

a)

3

b)

2

c)

90
90⁰

d)

350⁰

15.

The __________ represents half the distance between the max and min of a sine or cosine graph.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

16.

What is the period of
y= -3sin(x)

a)

π

b)

2π

c)

3π

d)

4π

17.

What is the midline for
y=2cos(1/3x +π/6) +2

a)

1/3

b)

-2

c)

+2

d)

4

18.

Which trig function does this graph represent?

a)

sin

b)

sec

c)

tan

d)

cot

19.

Which function below matches this graph?

a)

sec2(x)

b)

sec(x)

c)

csc2(x)

d)

2-sec(x)

20.

Which function below matches this graph?

a)

tan(x-π/4)

b)

tan(x+π/4)

c)

cot(x)

d)

π/4cot(x)

21.

What is the period of
y=cos(3x - π) - 5?

a)

π/3

b)

π/6

c)

2π/3

d)

2π/6

22.

Which point represents (3, 3π/4)?

a)

F

b)

E

c)

B

d)

A

23.

In the coordinate points (2,7⁰) the 2 represents the...

a)

theta

b)

radius

c)

x

d)

angle

24.

Which point represents (5, π)

a)

F

b)

E

c)

B

d)

A

25.

Convert the rectangular coordinates to polar form

a)

(√2 , 7π/4)

b)

(2 , 3π/4)

c)

(4 , π/4)

d)

(4 , 5π/4)

26.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

27.

Find the polar coordinates of the rectangular point. (0,3)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

28.

When converting between rectangular and polar coordinates:

y = ?

a)

rcosθ

b)

rsinθ

c)

x² + y²

d)

y/x, x ≠ 0

29.

10.1-10.2 Converting between rectangular and polar coordinates:
x = ?

a)

rcosθ

b)

rsinθ

c)

x² + y²

d)

y/x, x ≠ 0

30.

Which are possible coordinates of the point graphed?

a)

(-2, 120^o)

b)

(-2, 60^o)

c)

(2, -120^o)

d)

(2, 60^o)

31.

Covert the rectangular equation to polar form

a)

r² = 81

b)

r = 3

c)

r = 4.5

d)

r sin θ = 9

32.

Covert the rectangular equation to polar form

a)

r = cot θ csc θ

b)

r = tan θ csc θ

c)

r = tan θ sec θ

d)

r = 0

33.

Convert the polar equation to rectangular form

a)

x = 2 cos θ

b)

x = 2

c)

y = 2

d)

x² + y² = 2

34.

Eliminate the parameter from x(t) = t² + 5 and y(t) = t² - 4. Which of the following sketches results?

a)

Linear

b)

Quadratic

c)

Quartic

d)

Square Root

35.

Find the polar coordinates of the rectangular point. (0,3)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

36.

The average shark has _____ row(s) of teeth.

a)

50

b)

1

c)

10

d)

15

37.

What type of animal is Abu from the Disney film Aladdin?

a)

Monkey

b)

Dog

c)

Tiger

d)

Cat

38.

Joe's father had three sons- Snap, Crackle, and ....

a)

John

b)

Jenny

c)

Joe

d)

Pop

39.

What are they doing?

a)

They are ice skating.

b)

They are decorating a Christmas tree.

c)

They are building a snowman.

d)

They are playing ice hockey.

40.

Which weather event usually happens in winter?

a)

Tornado

b)

Hurricane

c)

Blizzard

d)

Flooding

41.

tanθ =

a)

1/cosθ

b)

1/sinθ

c)

cosθ/sinθ

d)

sinθ/cosθ

42.

cotθ =

a)

1/cosθ

b)

1/cscθ

c)

1/secθ

d)

1/tanθ

43.

cscθ=

a)

1/cosθ

b)

1/sinθ

c)

1/tanθ

d)

1/secθ

44.

secθ=

a)

1/cosθ

b)

1/sinθ

c)

1/tanθ

d)

1/cscθ

45.

$1+\tan^2x=$

a)

$\csc^2x$

b)

$\cot^2x$

c)

$\sin^2x$

d)

$\sec^2x$

46.

$1+\cot^2x\ =$

a)

$\csc^2x$

b)

$\sec^2x$

c)

$\cos^2x$

d)

$\tan^2x$

47.

Simplify

$\cot\theta\tan\theta$

a)

sin²θ/cos²θ

b)

1

c)

0

d)

cos²θ/sin²θ

48.

Simplify
$\sec\theta\cot\theta\sin\theta$

a)

-1

b)

sin θ

c)

csc θ

d)

1

49.

Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

50.

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

51.

Simplify

$\tan x\csc x\cos x$

a)

1/cos x

b)

1

c)

cot x

d)

-1

52.

Simplify

$\cot\theta\sin\theta$

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

53.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

2secθ

b)

cot²θ

c)

tan²θ

d)

sec²θ + 1

54.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

55.

Simplify $\tan x\left(\cot x\ +\ \csc x\right)$

a)

1 + sec x

b)

1 + csc x

c)

sec x - 1

d)

tan² x

56.

$\sec^2x\ -\ 1\ =$

a)

$\cot^2x$

b)

$\csc^2x$

c)

$\cos^2x$

d)

$\tan^2x$

57.

$1-\sin^2x\ =$

a)

$\sin^2x$

b)

$\cos^2x$

c)

$\sec^2x$

d)

$\csc^2x$

58.

Expand $\sin\ \left(33^{o\ }+42^o\right)$

a)

$\sin\ 75^{o\ }$

b)

$\sin\ 33^o\cos42^o+\cos33^o\sin42^o$

c)

$\sin\ 33^o\cos42^o-\cos33^o\sin42^o$

d)

$\cos33^o\cos42^o+\sin33^o\sin42^o$

59.

Expand $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$

a)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

b)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

c)

$\cos\ \frac{2\pi}{11}$

d)

$\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$

60.

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

61.

Use sum or difference angles identity to find the exact value for $\cos105^o$

a)

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

b)

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

c)

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

d)

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

62.

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

a)

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

b)

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

c)

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

d)

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

63.

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

a)

$\frac{3\sqrt{5}+8}{15}$

b)

$\frac{4\sqrt{5}+6}{15}$

c)

$\frac{2\sqrt{5}+12}{15}$

d)

$\frac{4\sqrt{5}+2}{5}$

64.

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

a)

sin(120)

b)

cos(120)

c)

cos(230)

d)

sin(230)

65.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

a)

$-\frac{2}{3}$

b)

$\frac{4\sqrt{5}-6}{15}$

c)

$\frac{4\sqrt{5}+2}{5}$

d)

$\frac{4\sqrt{5}+6}{15}$

66.

$2\sin\left(10\right)\cos\left(10\right)=$

a)

$\sin\left(5\right)\cos\left(5\right)$

b)

$\sin\left(20\right)\cos\left(20\right)$

c)

$\cos\left(20\right)$

d)

$\sin\left(20\right)$

67.

$\cos^2\left(10\right)-\sin^2\left(10\right)=$

a)

$\cos\left(20\right)$

b)

$\sin\left(20\right)$

c)

1

d)

$\cos\left(100\right)-\sin\left(100\right)$

68.

$\sin\left(40\right)\cos\left(40\right)=$

a)

$\frac{1}{2}\sin\left(80\right)$

b)

$\frac{1}{2}\cos\left(80\right)$

c)

$\sin\left(80\right)$

d)

$\cos\left(80\right)$

69.

$\frac{2\tan\left(50\right)}{1-\tan^2\left(50\right)}=$

a)

$\frac{1}{2}\tan\left(100\right)$

b)

$\frac{1}{2}\tan\left(50\right)$

c)

$\tan\left(100\right)$

d)

$\tan\left(50\right)$

70.

What is the capital of Vermont?

a)

Montpelier

b)

Richmond

c)

Olympia

d)

Madison

Quarter 3 Exam Review for PreCalc

Total questions: 70

Worksheet time: 4hrs 9mins

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