Free Printable Pre-Calc Final Review

1.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

2.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

3.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

4.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

5.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

6.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

7.

If f(x) = 3x² -9x -20, find the value of f(5) using synthetic substitution.

a)

0

b)

10

c)

15

d)

-7

8.

if f(x) = x³+8x+24, then find f(-2) using synthetic substitution.

a)

12

b)

8

c)

0

d)

-6

9.

List all the possible rational zeros
h(x) = x³- 5x²+2x+12

a)

1,2,3,4,6,12

b)

1,2,6,12

c)

1,2,3,4,6,12,-1,-2,-3,-4,-6,-12

10.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3,±9

c)

±1,±3±9,±1/2,±3/2,±9/2

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

11.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

12.

Write a polynomial function of least degree with integer coefficients that has the given zeros.

a)

b)

c)

d)

13.

Write the simplest polynomial in standard form given the following zeros. x = -2, 1, 4

a)

$f(x)=(x+2)(x-1)(x-4)$

b)

$f(x)=x^3-3x^2-6x+8$

c)

$f(x)=x^3+8$

d)

$f(x)=x^3-3x^2+8$

14.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

15.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

16.

What is the Vertical Asymptote?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

17.

Which equation best represents the graph?

a)

y=(x-2)/(x-4)

b)

y=(x+2)/(x+4)

c)

y=(x+4)/(x-2)

d)

y=(x+2)/(x-4)

18.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

19.

Factor
9x²-6x-8

a)

(3x+2)(3x-4)

b)

(3x+2)(3x+4)

c)

(3x-2)(3x-4)

d)

(x-1)(9x+8)

20.

Factor
4x²-25x+25

a)

4(x-5)(x+5)

b)

(x+5)(4x+5)

c)

(x-5)(4x-5)

d)

(x+2)(9x+1)

21.

Factor:
2x² - 3x - 2

a)

(2x - 2)(x + 1)

b)

(2x + 1)(x - 2)

c)

(2x - 1)(x - 2)

d)

(2x - 1) (x - 1)

22.

Factor completely.
3x² + 10x - 8

a)

(3x + 2)(x + 4)

b)

(7x + 5)(x + 2)

c)

(3x - 2)(x + 4)

d)

(7x - 3)(x - 4)

23.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

24.

FInd all zeros for the polynomial
f(x) = x⁴+8x²-9

a)

-1, ⅓, ±3i

b)

½, -1, ±3i

c)

1, -1, ±i√11

d)

1, -1, ±3i

25.

Factor p³- 3p² - 16p + 48

a)

p² ( p - 3) (p - 3)

b)

(p² - 16) (p - 3)

c)

(p + 4) (p - 4) (p - 3)

26.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

27.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

28.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

29.

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

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

30.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

31.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal shift left one unit

b)

Horizontal shift right one unit

c)

Vertical shift up one unit

d)

Vertical shift down one unit

32.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal Shift to the right 1 unit

b)

Horizontal shift to the left one unit

c)

Vertical shift one unit up

d)

Vertical shift one unit down

33.

Is this graph an example of exponential growth or decay?

a)

growth

b)

decay

34.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

35.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

36.

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

37.

Use multiple log properties to write as a sum or difference of two logs: log(4x³)

a)

log 4 + 3log x

b)

3log 4 + 3log x

c)

3log 4 + log x

d)

log 12 + log x

38.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

39.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

40.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

41.

a)

24log(u) - log(v)

b)

24log(u) + 6log(v)

c)

4log(u) + 6log(v)

d)

4log(u) - 6log(v)

42.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

43.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

44.

Select the best answer

a)

A

b)

B

c)

C

d)

D

45.

Select the best answer

a)

A

b)

B

c)

C

d)

D

46.

a)

1

b)

0

c)

√2 / 2

d)

Undefined

47.

a)

0

b)

1

c)

Undefined

d)

-1

48.

a)

1

b)

-1

c)

0

d)

Undefined

49.

Evaluate tan (3π / 4)

a)

√3 / 2

b)

1 / 2

c)

1

d)

0

50.

sin ( π / 4)

a)

√2 / 3

b)

2

c)

1

d)

√2 / 2

51.

a)

-√3 / 2

b)

-1 / 2

c)

1 / 2

d)

2√3 / 3

52.

cos(5π/3)

a)

-√2/2

b)

-1/2

c)

1/2

d)

√3/2

53.

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

a)

y

b)

x

c)

x/y

d)

y/x

54.

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

a)

y

b)

x

c)

x/y

d)

y/x

55.

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

a)

y/r

b)

x/r

c)

r/y

d)

y/x

56.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

57.

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

58.

6. What is the vertical shift for y = 4cos(¹/₂x +π) - 2?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

59.

8. What is the period for y = 4cos(¹/₂x +π) - 2?

a)

pi/2

b)

pi

c)

3pi

d)

4pi

60.

9. What is the amplitude for y = 4cos(¹/₂x +π) - 2?

a)

2

b)

pi/2

c)

pi

d)

4

61.

14. What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

62.

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

63.

Solve for x.
$\log_8\left(x+4\right)=2$

a)

12

b)

60

c)

64

d)

No solution

64.

Solve for x.
$\log_3\left(2x-6\right)=\log_3\left(3x-7\right)$

a)

-3

b)

14

c)

-8

d)

No solution

65.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

66.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

67.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

68.

log₅25 = ?

a)

2

b)

5

c)

125

69.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

70.

The terminal side of a 330° angle is in what Quadrant?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

71.

The terminal side of a -45° angle is in what Quadrant?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

72.

What is the reference angle of 210°?

a)

30°

b)

60°

c)

150°

d)

-870°

73.

Identify the angle outlined in red

a)

π/2

b)

π/3

c)

π/4

d)

π/6

74.

Identify the angle outlined in red

a)

7π/6

b)

π/6

c)

5π/6

d)

11π/6

75.

What radian measure corresponds to the given point?

a)

π/4

b)

3π/2

c)

5π/4

d)

7π/3

76.

Positive angles in a Unit Circle start at the initial side and rotate

a)

Clockwise

b)

Counter Clockwise

c)

Anti-Counter Clockwise

d)

Super Clockwise

77.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

78.

Solve for x.

a)

24.20

b)

4.92

c)

290.4

d)

29.75

79.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

80.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

81.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

82.

Choose the correct ratio.

a)

A

b)

B

c)

C

d)

D

83.

a)

27/36

b)

27/45

c)

45/36

d)

45/27

84.

a)

24/32

b)

32/24

c)

32/40

d)

24/40

85.

a)

18/30

b)

24/30

c)

18/24

d)

24/18

86.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

87.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

88.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

89.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

Pre-Calc Final Review

Total questions: 89

Worksheet time: 6hrs 13mins

Similar Resources on Wayground