Free Printable HPC 2nd Sem Final Exam Review

1.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

2.

a)

√3/3

b)

√3

c)

1

d)

undefined

3.

What is csc(x) equivalent to?

a)

1/sin(x)

b)

1/tan(x)

c)

sin(x)

d)

1/cos(x)

4.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

5.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

6.

Simplify

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

7.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

8.

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

a)

π

b)

2π

c)

3π

d)

4π

9.

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

a)

3

b)

2

c)

90
90⁰

d)

350⁰

10.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

11.

Write the equation for a sine function with an amplitude of 6 and a period of π/4.

a)

y=6sin(8x)

b)

y=6sin8(x-1)

c)

y=6sin1/4x

d)

y=6sinx

12.

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)

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

13.

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

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

14.

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)

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

15.

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)

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

16.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

17.

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

18.

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

19.

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

a)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

20.

Solve equation for $0\le\theta<2\pi$ .
$0=-\sqrt{3}\sin\theta-2\sin^2\theta$

a)

$\theta=0,\frac{2\pi}{3},\pi,\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

c)

$\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$

d)

$\theta=0,\pi,\frac{5\pi}{3}$

21.

sin^-1(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

22.

tan(sin^-1(-1/2))

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

23.

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

24.

Identify the Law of Sines

a)

Sin²x + Cos²x =1

b)

Sin(A)/a = Sin(B)/b = Sin(C)/c

c)

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

d)

y=Sin(x)

25.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees. How far away, to 2 decimal places, is the bird from Amanda?

a)

25.23 ft

b)

23.19 ft

c)

22.15 ft

d)

20.85 ft

26.

a)

A

b)

B

c)

C

d)

D

27.

What is the area of this triangle to three decimal places?

a)

14.494 meters squared

b)

108.184 meters squared

c)

54.092 meters squared

d)

54.350 meters squared

28.

Solve for x for the given triangle:

a)

8.7

b)

14

c)

6.8

d)

12.2

29.

Two stakes are holding a small blimp in place. Stake A measures an angle of elevation of 49^o and Stake B measures an angle of elevation of 58^o. If the string attached to Stake A has a length of 148 feet, what is the length of the string attached to Stake B?

a)

152.7 feet

b)

166.3 feet

c)

157.3 feet

d)

131.7 feet

30.

Convert to polar coordinates

a)

A

b)

B

c)

C

d)

D

31.

Convert to rectangular coordinates

a)

A

b)

B

c)

C

d)

D

32.

Calculate the value for the given vector

a)

A

b)

B

c)

C

d)

D

33.

Calculate the value for the given vector

a)

A

b)

B

c)

C

d)

D

34.

Find the magnitude for the vector whose initial and terminal points are given

a)

A

b)

B

c)

C

d)

D

35.

Find the dot product: u ⋅ v

a)

A

b)

B

c)

C

d)

D

36.

Which vector has an initial point at (-3,-5) and a terminal point at (7,-2)?

a)

<10, 3>

b)

<-10, -7>

c)

<10, -7>

d)

-10, -3>

37.

Which equation represents the polar graph?

a)

r = sin θ

b)

r = sin 4θ

c)

r = 4 sin θ

d)

r = 4 cos θ

38.

Which point represents the polar coordinate
(-4, -2π/3)

a)

B

b)

F

c)

D

d)

A

39.

Find the partial fraction decomposition...

a)

b)

c)

d)

HPC 2nd Sem Final Exam Review

Total questions: 39

Worksheet time: 2hrs 25mins

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