Free Printable Final Exam Review 2021

1.

side opposite of 30 degrees on a unit circle (sin 30)=

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

2.

side opposite 45 on a unit circle (sin 45) =

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

3.

side opposite 60 in a unit circle (sin 60) =

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

4.

cos 30 =

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

5.

side adjacent to 60 in a unit circle (cos 60) =

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

6.

side adjacent to 45 in a unit circle (cos 45) =

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

7.

a)

A

b)

B

c)

C

d)

D

8.

a)

A

b)

B

c)

C

d)

D

9.

What is the radius of a unit circle?

a)

1

b)

2

c)

1/2

d)

0

10.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

11.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

12.

Based on the unit circle, what is the value of sin?

a)

y

b)

x

c)

x/y

d)

y/x

13.

Based on the unit circle, what is the value of cos?

a)

y

b)

x

c)

x/y

d)

y/x

14.

Please select the correct solution
cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

15.

If $\sin\theta=-\frac{3}{5}$ and $\theta$ terminates in the 4th quadrant, what is $\cos\theta$ ?

a)

$4$

b)

$\frac{4}{5}$

c)

$-\frac{4}{5}$

d)

$-4$

16.

What is the amplitude of the graph?

a)

3

b)

2

c)

-3

d)

-2

17.

What is the period of y = 2cos(4x)-5

a)

π/3

b)

6π

c)

2π/3

d)

π/2

18.

A complete cycle of the function $y=A\cos\left(Bx\right)+C$ is shown. What is the value of B?

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{8}$

c)

8

d)

$\frac{8\pi}{3}$

19.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

20.

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

21.

The horizontal line in between the maximum and minimum points is called the ______________.

a)

midline

b)

horizontal line

c)

axis of symmetry

d)

middle

22.

How do we find the period of a sinusoidal function?

a)

average of the min and max

b)

B = $\frac{2\pi}{P}$

c)

P = $\frac{2\pi}{B}$

d)

$\frac{P}{4}$

23.

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

a)

1/3

b)

-2

c)

2

d)

4

24.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

25.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

26.

Factor completely: 2x²+22x+60

a)

(2x+10)(x+6)

b)

(x+5)(x+6)

c)

2(x+1)(x+30)

d)

2(x+5)(x+6)

27.

Factor completely: x²-13x+40

a)

(x-5)(x-8)

b)

(x+5)(x+8)

c)

(x-4)(x-10)

d)

(x-2)(x-20)

28.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

29.

Factor Completely.
8x³ - 18x

a)

2x(4x²-9)

b)

(4x²+3)(2x-3)

c)

2x(2x+3)(2x-3)

d)

PRIME

30.

What type of pattern will you see in the output values of exponential functions?

a)

Adds by the same number for every unit change in x

b)

Multiplies by the same number every unit change in x

c)

Square roots all of the inputs

d)

Squares all of the inputs

31.

In an exponential function, what does the 'a' represent?

a)

Slope

b)

Rate of change

c)

Y-intercept

d)

Growth factor

32.

In an exponential function, what does the 'b' represent?

a)

Slope

b)

Rate of change

c)

Y-intercept

d)

Growth factor

33.

Is the table linear, exponential, or neither?

a)

Linear

b)

Exponential

c)

Neither

34.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

35.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

36.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

37.

What is 30° in radians?

a)

1/6

b)

π/6

c)

1/7

d)

π/7

38.

What is 2π/3 in degrees?

a)

180

b)

120

c)

150

d)

181

39.

What is 3π/5 in degrees?

a)

135

b)

108

c)

122

d)

136

40.

What is the measure of the angle shown, in radians?

a)

2π/3

b)

π/2

c)

4π/5

d)

3π/5

41.

Expand the following logarithm:
log₂ 5x.

a)

log₂ 5 - log₂ x

b)

log₂ 5 + log₂ x

c)

2log 5 + 2log x

d)

log5 2 + log_x 2

42.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

43.

a)

5log₆(a) + 6log₆(c) − 30log₆(b)

b)

log₆(a) + 6log₆(c) − 5log₆(b)

c)

6log₆(a) − 6log₆(c) − 30log₆(b)

d)

6log₆(a) + 6log₆(c) − 30log₆(b)

44.

a)

A

b)

B

c)

C

d)

D

45.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

46.

Solve for x

e^{2x}=3

a)

1.099

b)

0.549

c)

0.405

d)

2.197

47.

Solve for x

2e^x=15

a)

1.354

b)

1808

c)

4.029

d)

2.015

48.

$\log_9\left(r-8\right)\ =\ 2$

a)

55

b)

$\frac{11}{6}$

c)

89

d)

6

49.

a)

(-2.55, 0), (2.55, 0)

b)

(-3, 0), (-2, 0), (2, 0), (3, 0)

c)

(0, 36)

d)

(0, -3), (0, -2), (0, 2), (0, 3)

50.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

51.

Write a 4th degree polynomial function with:

*right tail going up

*zeros: 9, 3, -2, 0

a)

y = x(x - 9)(x - 3)(x + 2)

b)

y = x(x + 9)(x + 3)(x - 2)

c)

y = -x(x - 9)(x - 3)(x + 2)

d)

y = -x(x + 9)(x + 3)(x - 2)

52.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

53.

What is the degree of the function graphed here?

a)

6

b)

4

c)

3

d)

5

54.

Simplify

a)

$\frac{x\ -\ 9}{x\ +\ 9}$

b)

$\frac{1}{x\ -\ 9}$

c)

(x+9)

d)

$\frac{1}{x\ \ +9}$

55.

Simplify.

a)

$\frac{x\ +\ 6}{x\ -\ 3}$

b)

$\frac{7}{m\ -\ 3}$

c)

7(m+6)

d)

(m-3)

56.

a)

A

b)

B

c)

C

d)

D

57.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

58.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

59.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

60.

Determine the center and radius: x²+ y²+ 14x - 2y = -1

a)

center= (-7,2) radius= 3

b)

center= (-7,1) radius= 7

c)

center= (-4,1) radius= 5

61.

Determine the center and radius:
x²+ y²- 10x + 8y -8 = 0

a)

C = (5,-4) r = 7

b)

C = (-5,4) r = 7

c)

C = (-4,5) r = 49

d)

C = (5,-4) r = 49

62.

Solve: 2^x = 4^x+1

a)

-2

b)

2

c)

-3

d)

3

63.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

64.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

65.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

66.

Simplify:

a)

2

b)

8

c)

16

d)

32

67.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

68.

Simplify . Your answer should contain only positive exponents. $\left(a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{-1}$

a)

$\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}$

b)

$a^{\frac{1}{2}}b^{\frac{1}{2}}$

c)

$-\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}$

d)

$-a^{\frac{1}{2}}b^{\frac{1}{2}}$

69.

Simplify . Your answer should contain only positive exponents. $\left(x^{\frac{5}{3}}y^{-2}\right)^0$

a)

$1$

b)

$\frac{x^{\frac{5}{3}}}{y^2}$

c)

$x^{\frac{5}{3}}y^2$

d)

$\frac{y^2}{x^{\frac{5}{3}}}$

70.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

71.

In which quadrant would you find an angle measuring -740°

a)

1

b)

2

c)

3

d)

4

72.

Solve

a)

20

b)

-4

c)

4

d)

-10

73.

Solve by graphing.

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

74.

$x^2+5x\ +8\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-5\pm\sqrt{57}}{2}$

b)

$\frac{5\pm\sqrt{57}}{2}$

c)

$\frac{-5\pm i\sqrt{7}}{2}$

d)

$\frac{5\pm i\sqrt{7}}{2}$

75.

$-x^2+13x\ -10\ =7x$

Put the following quadratic into standard form.

a)

$-x^2+13x\ -17\ =0$

b)

$-x^2+20x\ -10\ =0$

c)

$-x^2+13x\ -3\ =0$

d)

$-x^2+6x\ -10\ =0$

76.

$3x^2-8x\ +2\ =-5x\ -\ 11$

Put the following quadratic into standard form.

a)

$3x^2-13x\ -9\ =0$

b)

$3x^2+6x\ -9\ =0$

c)

$3x^2-3x\ +13\ =0$

d)

$6x^2+13\ =0$

Final Exam Review 2021

Total questions: 76

Worksheet time: 4hrs 43mins

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