Free Printable 2nd Quarter Pre-Calculus Review

1.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

2.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

3.

Where does the graph of y=sin(x) begin its first cycle?

a)

(0,0)

b)

(1,0)

c)

(0,Pi)

d)

(1, Pi)

4.

Where does the graph of cosine begin?

a)

(0,0)

b)

(0,1)

c)

(0, Pi)

d)

(1, Pi)

5.

What is the period of either graph?

y = sin(x) & y = cos (x)

a)

$\pi$

b)

$2\pi$

c)

$\frac{\pi}{2}$

d)

$\frac{\pi}{4}$

6.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

7.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

8.

What does a negative A value cause?

a)

A negative amplitude

b)

A reflection across the Y axis

c)

No effect

d)

A reflection across X axis

9.

The vertical stretch of the graph; distance between the midline and the max/min.

a)

Period

b)

Cycle

c)

Axis of Oscillation

d)

Amplitude

10.

Describe the transformation of the parent function y = sin θ to y = 3 sin θ − 2 (Hint: Identify the values of A & D) Remember : y = A sin B(θ − C) + D

a)

stretches vertically by a factor of 3, and up 2 units

b)

stretches horizontally by a factor of 3 and down 2 units

c)

stretches vertically by a factor of 3 and down 2 units

d)

stretches horizontally by a factor of 3 and up 2 units

11.

5. Write an equation for the cosine function with amplitude 3, period 2pi, phase shift of $\pi$ , and vertical shift of 5.

a)

y = 5cos(x - $\pi$ ) + 3

b)

y = 3cos(x - $\pi$ ) + 5

c)

y = 3cos(2x - $\pi$ ) + 5

d)

y = 5cos(2x - $\pi$ ) + 3

12.

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

13.

How many DEGREES are in a circle?

a)

180^o

b)

360^o

c)

π rad

d)

2π rad

14.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

15.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

16.

$\frac{8\pi}{3}$ is equivalent to what degree measure?

a)

$480\degree$

b)

$240\degree$

c)

$800\degree$

d)

$24\degree$

17.

What is sin^-1(1/2)?

a)

150

b)

120

c)

60

d)

30

18.

What is cos^-1(0)?

a)

-180

b)

90

c)

0

d)

-90

19.

Solve sinθ = -1 on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

20.

Solve
cosθ = - √(3)/2
on θ∈[0, 2π)

a)

θ = π /3, 2π /3

b)

θ = 2π /3, 4π /3

c)

θ = π /6, 5π /6

d)

θ = 5π /6, 7π /6

21.

Solve
cos²θ = ½
on θ∈[0, 2π)

a)

θ = π /4, 7π /4

b)

θ = π /4, 3π /4

c)

θ = 3π /4, 5π /4

d)

θ = π /4, 3π /4, 5π /4, 7π /4

22.

Solve on the Interval [0,2π)
tan(x)+1=2

a)

0 and π

b)

3π/4 and 7π/4

c)

π/4 and 5π/4

d)

3π/4 and 5π/4

23.

a)

No solution

b)

π/3 +2πn, 5π/3 +2πn

c)

π/6 +2πn, 11π/6 +2πn

d)

2π/3 +2πn, 4π/3 +2πn

24.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

25.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

26.

Solve on the domain [0, 2π)
cos x + 2 = 3 cos x

a)

0, 2π/3, 4π/3

b)

π

c)

0

d)

No solution

27.

Which one is the easy trick to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

28.

What is the correct ratio?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

29.

Set up the problem...

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

30.

Find the area of this triangle.

a)

240 ft²

b)

56 ft²

c)

66 ft²

d)

120 ft²

31.

Find the area of a triangle with a height of 4 mm and a base of 6 mm?

a)

5 mm squared

b)

6 mm squared

c)

12 mm squared

d)

24 mm squared

32.

Calculate the area of Triangle ABC if b=32, c=27 and angle A = 108 degrees

a)

400sq units

b)

411sq units

c)

345sq units

d)

525sq units

33.

What is the area of this triangle?

a)

14.494 meters squared

b)

108.184 meters squared

c)

54.092 meters squared

d)

54.35 meters squared

34.

Find the area of the triangle

a)

You cannot find the area of this triangle

b)

10.811 meters squared

c)

52.3 meters squared

d)

43.9 meters squared

35.

If the sides of a triangle are 8, 8, and 8, what is the area?

a)

8

b)

15.58

c)

27.71

d)

62.91

36.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

37.

Find AC

a)

12

b)

10

c)

23

d)

14

38.

Find AB

a)

10

b)

8

c)

6.1

d)

4.9

39.

4. Name the smallest angle in this triangle.

a)

∠A

b)

∠B

c)

∠C

40.

Which of the following scenarios cannot be used for the Law of Sines?

a)

AAS

b)

ASA

c)

SSA

d)

SSS

41.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

42.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

43.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

44.

Identify the Law of Sines

a)

$\sin^2x\ +\ \cos^2x\ \ =\ 1$

b)

$\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}$

c)

Sin(A)Sin(B)Sin(C) = 1

d)

y=Sin(x)

45.

What are the possible criteria for the Law of Cosines?

a)

SSA, SSS

b)

SSA, ASA

c)

SSS, SAS

d)

AAS, ASA

46.

9.Solve for a.

a)

4.28

b)

8.56

c)

3.22

d)

9.45

47.

Solve for "a" if:

A = 70^o, b = 10, and c =4.

a)

88.6

b)

9.4

c)

10.8

d)

6

48.

Solve for m < B rounded to the nearest tenth if:

a = 4, b = 5, and c = 8.

a)

47.5^o

b)

125.1^o

c)

30.8^o

d)

24.1^o

49.

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

a)

-1

b)

sin θ

c)

csc θ

d)

1

50.

Simplify

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

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

51.

Simplify

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

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

52.

Simplify

$\tan x\csc x\cos x$

a)

1/cos x

b)

1

c)

cot x

d)

-1

53.

Simplify

$\cot\theta\sin\theta$

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

54.

Please select the correct solution cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

55.

Find $\sin\theta$ if $\cos\theta=\frac{3}{5}$ .

a)

$0.80$

b)

$0.63$

c)

$1.25$

d)

$1.58$

56.

If $\sin\theta=\frac{4}{5}$ , find $\csc\theta$ .

a)

$\frac{9}{5}$

b)

$\frac{5}{4}$

c)

$\frac{1}{5}$

d)

$\frac{1}{4}$

57.

Simplify: (secx - 1)(secx + 1)

Hint: you will need to FOIL first

a)

tan²x

b)

sinx

c)

cot²x

d)

cosx

58.

Which of the following is the same as $\cos\ \left(A+B\right)$

a)

$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$

b)

$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$

c)

$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$

d)

$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$

59.

Which of the following is equivalent to $\tan\ \left(A-B\right)$

a)

$\tan\ A\ -\ \tan\ B$

b)

$\frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B}$

c)

$\frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B}$

d)

$\frac{\sin\ A}{\cos\ B}$

60.

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)

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

61.

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}\$

62.

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

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

63.

$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$ is equivalent to

a)

$\tan75^o$

b)

$\tan\ 15^o$

c)

$\frac{\sin45^o}{\cos30^o}$

d)

$\tan90^{o\ }$

64.

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)

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

65.

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)

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

66.

a)

A

b)

B

c)

C

d)

D

67.

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

68.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

69.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

70.

Using the second identity, find Cos(50)

a)

sin²(25) - cos²(25)

b)

cos²(50) - sin²(50)

c)

cos²(25) - sin²(25)

d)

sin²(50) - cos²(50)

71.

Use the Half-angle formulas to find the exact value of each expression
sin 22.5º

a)

√(2 + √3)/2

b)

√(2 - √2)/2

c)

√(2 + √2)/2

d)

√(2 - √3)/2

72.

Use a half-angle identity to find the exact value of $\sin165\degree$

a)

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

b)

$-2-\sqrt{3}$

c)

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

d)

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

73.

Use the half-angle formula to find the exact value of $\cos\left(\frac{5\pi}{12}\right)$

a)

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

b)

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

c)

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

d)

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

74.

Anthony Davis wants to make a matrix of his basketball statistics using 3 rows and 3 columns. How many elements will he have in his matrix?

a)

9

b)

none

c)

33

d)

12

75.

Identify the dimensions of the given matrix.

a)

4 rows by 5 columns

b)

5 rows by 4 columns

c)

6 rows by 4 columns

d)

3 row by 2 columns

76.

Find B-A

a)

-3 1
7 -1

b)

1 0
1 -4

c)

4 0
-6 0

d)

not possible because rows do not match columns

77.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

78.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

79.

Find the values of x, y and z.

a)

w = 13, x = 4, y = 7, z = 23

b)

w = 13, x = -4, y = 11, z = 23

c)

w = 13, x = 4, y = 11, z = 23

d)

w = 13, x = 4, y = 11, z = 17

80.

What are the dimensions of this matrix?

a)

3x1

b)

1x3

c)

3x3

d)

1x1

81.

a)

A

b)

B

c)

C

d)

D

82.

a)

A

b)

B

c)

C

d)

D

83.

When you multiply a matrix by the inverse matrix, you obtain the

a)

inverse matrix

b)

identity matrix

c)

transpose matrix

d)

determinant

84.

Matrices can be multiplied only...

a)

if the row of the first matrix is equal to the column of the second matrix.

b)

if the column of the first matrix is equal to the column of the second matrix.

c)

if the column of the first matrix is equal to the row of the second matrix.

d)

if the row of the first matrix is equal to the row of the second matrix.

85.

Matrices can be used to

a)

store information

b)

solve sets of simultaneous equations

c)

analyse networks

d)

encode information

e)

all of the above

86.

iWhat type of matrix is this?

a)

Column Matrix

b)

Row Matrix

c)

Square Matrix

d)

Identity Matrix

87.

What type of matrix is this?

a)

Column Matrix

b)

Row Matrix

c)

Square Matrix

d)

Zero Matrix

88.

What type of matrix is this?

a)

Column Matrix

b)

Row Matrix

c)

Square Matrix

d)

Zero Matrix

89.

What type of matrix is this?

a)

Column Matrix

b)

Row Matrix

c)

Square Matrix

d)

Zero Matrix

90.

Element A₂₃ is

a)

-4

b)

3

c)

5

d)

-2

91.

How many jeans were sold in total?

a)

9

b)

15

c)

5

d)

8

92.

Element G₂₂ is

a)

1

b)

2

c)

3

d)

4

93.

The order of the matrix is

a)

3 x 6

b)

6 x 3

94.

a)

The matrices can be multiplied.

b)

The matrices cannot be multiplied.

95.

a)

The matrices can be multiplied.

b)

The matrices cannot be multiplied.

96.

$9m-3n=-8$
$-3m\ -\ 9n=7$

a)

b)

97.

mark the correct statement

a)

This is an identity matrix

b)

this is a 4 x 5 matrix

c)

This is NOT a square matrix

d)

matrices are scary (don't pick this one!)

98.

a)

b)

c)

d)

99.

If matrix A is a 2 x 5, and is transposed, what are the new dimensions?

a)

2 x 2

b)

5 x 2

c)

5 x 5

d)

2 x 5

100.

Matrices obtained by changing rows and columns is called

a)

rectangular

b)

symmetric

c)

transpose

d)

none of the above

2nd Quarter Pre-Calculus Review

Total questions: 100

Worksheet time: 4hrs 2mins

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