Free Printable Midterm Pre-Calculus

1.

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

a)

x = -4, x = 3, x = -2

b)

x = -4, x = 3, x = 2

c)

x = -4, x = -3, x = 2

d)

x = 4, x = 3, x = 2

2.

Which of the following is a solution to the function? (x - 8)(x - 9) = 0

a)

8

b)

-9

c)

-17

d)

0

3.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

4.

Give the y-interecept
3x + y = 5

a)

-3

b)

(0,5)

c)

-5

d)

(0, -3)

5.

Factor completely:

3x² + 18x +15

Hint: Assign x a value and check answers

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

6.

Five times Mike's age, increased by nine

a)

5(x+9)

b)

9(5+x)

c)

9x+5

d)

5x+9

7.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

8.

Find the zeros: y = x(x - 1)(x + 3)

a)

0, 1, -3

b)

-3, 1

c)

-1, 3, 0

d)

-1, 3

9.

What would be the term for the degree of the polynomial x³+ 5

a)

quadratic

b)

linear

c)

cubic

d)

constant

10.

How many terms are there is 2x³ +x² + 4x + 6

a)

4

b)

2

c)

1

d)

6

11.

Find the solutions to the equation:
2x² + 11x = -12.

a)

-4, -1.5

b)

4, 1.5

c)

-4, 1.5

d)

4, -1.5

12.

Factor: x² - 6x + 9

a)

(x - 3)(x - 3)

b)

(x + 3)(x + 3)

c)

(x - 6)(x +3)

d)

(x - 9)(x - 1)

13.

Find the zeroes for:
f(x) = x² - 6x - 27

a)

x = 9, x = -3

b)

x = 9, x = 3

c)

x = -9, x = 3

d)

x = -9, x = -3

14.

How many zeros should the polynomial function
P(x) = 3x⁴+4x-8 have?

a)

1

b)

2

c)

3

d)

4

15.

What is the factored form of a function if it has zeros of 2, 3 and -1?

a)

(x-2)(x-3)(x+1)

b)

(x-1)(x-2)(x-3)

c)

(x-1)(x+2)(x+3)

d)

(x+1)(x+2)(x+3)

16.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

17.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

18.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

19.

Use the quadratic formula to solve 2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

20.

Simplify:
-6x² - 4x + 10 - 9 + 2x + 10x²

a)

-4x² + 2x + 1

b)

4x² + 2x - 1

c)

-4x² - 2x + 1

d)

4x² - 2x + 1

21.

Name the x-intercept(s)?

a)

(0, 0)

b)

(2, 4)

c)

(0, 0) and (0, 4)

d)

(0, 0) and (4, 0)

22.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

23.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

24.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

25.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

26.

Does the equation open up, down, left, or right?
Y = -3x² +7x - 2

a)

up

b)

down

c)

right

d)

left

27.

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

a)

$480\degree$

b)

$240\degree$

c)

$800\degree$

d)

$24\degree$

28.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

29.

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

a)

150

b)

120

c)

60

d)

30

30.

Solve sinθ = -1 on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

31.

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

32.

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

33.

a)

No solution

b)

π/3 +2πn, 5π/3 +2πn

c)

π/6 +2πn, 11π/6 +2πn

d)

2π/3 +2πn, 4π/3 +2πn

34.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

35.

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

36.

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

37.

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

38.

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

a)

-1

b)

sin θ

c)

csc θ

d)

1

39.

Simplify

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

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

40.

Simplify

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

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

41.

Simplify

$\tan x\csc x\cos x$

a)

1/cos x

b)

1

c)

cot x

d)

-1

42.

Simplify

$\cot\theta\sin\theta$

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

43.

Please select the correct solution cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

44.

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

a)

$0.80$

b)

$0.63$

c)

$1.25$

d)

$1.58$

45.

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

a)

$\frac{9}{5}$

b)

$\frac{5}{4}$

c)

$\frac{1}{5}$

d)

$\frac{1}{4}$

46.

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

Hint: you will need to FOIL first

a)

tan²x

b)

sinx

c)

cot²x

d)

cosx

47.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

48.

If the equation of a graph is y = x² + 4, what kind of graph does it create?

a)

Straight Line

b)

Circle

c)

Parabola

d)

Point

49.

What is the slope of 4x + 6y = 36?

a)

m = 4

b)

m = -3/2

c)

m = -2/3

d)

m = -4

50.

Determine if the lines are parallel, perpendicular, or neither.
y = -2x + 4
y = 2x - 3

a)

Parallel

b)

Perpendicular

c)

Neither

51.

Factor completely:
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

52.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

53.

Evaluate f(x)=-2x+13 for f(10)

a)

-7

b)

1

c)

-8

d)

7

54.

What is the value of f(0)?

a)

-2

b)

2

c)

4

d)

0

55.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

56.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

57.

Factor completely: 3x² - 7x + 2

a)

(x - 1) (3x + 2)

b)

(x - 2) (3x -1)

c)

(x - 1) (3x - 2)

d)

(x + 2) (3x + 1)

58.

Factorly Completely: 2x² - 7x + 6

a)

(x -1)(2x - 6)

b)

(x - 3) (2x - 2)

c)

(x - 2) (2x - 3)

d)

(x - 6) (2x - 1)

59.

Factor Completely: 4x² - 20x + 25

a)

(4x - 25) (x -1)

b)

(2x + 5) (2x - 5)

c)

(2x - 5)²

d)

(4x - 5) (x - 5)

60.

Factor x³ + 2x² - 49x - 98

a)

(x² - 49) (x + 2)

b)

(x² - 49) (x + 2) (x + 2)

c)

(x + 7) (x - 7) (x + 2)

61.

If h(a) = 3 - 2a²
Find h(-3).

a)

33

b)

21

c)

39

d)

-15

62.

Find x if f(x) = 0.

a)

5

b)

-1

c)

-5

d)

-1 and -5

63.

Solve the equation sin(76°) = 29.72 / x

a)

29.72

b)

30.63

c)

0.97

d)

31.57

e)

28.84

64.

Solve the equation cos(25°) = 6.961 / x

a)

6.961

b)

7.681

c)

0.906

d)

8.475

e)

6.309

65.

Solve the equation sin(24°) = x / 8.046

a)

3.273

b)

8.046

c)

0.407

d)

19.782

e)

1.331

66.

What is sin(44°) to the nearest thousandth?

a)

0.695

b)

0.719

c)

0.966

d)

0.018

67.

What is tan^-1(1.15) to the nearest degree?

a)

49°

b)

41°

c)

28°

d)

44°

68.

What is sin^-1(0.961) to the nearest degree?

a)

74°

b)

16°

c)

36°

d)

56°

69.

*

a)

cos x

b)

csc x

c)

sec x

d)

cot x

70.

*

a)

sin x

b)

cos x

c)

tan x

d)

csc x

71.

*

a)

sin x

b)

cos x

c)

csc x

d)

cot x

72.

sec²x −1

a)

sin²x

b)

cos²x

c)

tan²x

d)

cot²x

73.

1 + tan²x

a)

sin²x

b)

cos²x

c)

csc²x

d)

sec²x

74.

sin²x + cos²x + 1

a)

0

b)

1

c)

2

d)

3

75.

-(sin²x + cos²x)

a)

-1

b)

1

c)

-2

d)

2

76.

cotθ=

a)

cosθ/sinθ

b)

sinθ/cosθ

c)

tanθ

d)

1/cosθ

77.

secθ=

a)

1/cosθ

b)

1/sinθ

c)

1/tanθ

d)

1/cscθ

78.

What is the ratio for Sine?

a)

Hyp/Opp

b)

Opp/Hyp

c)

Opp/Adj

d)

Adj/Opp

79.

What is the ratio for Tangent

a)

Opp/Adj

b)

Adj/Opp

c)

Opp/Hyp

d)

Hyp/Opp

80.

What is the ratio for Cosine?

a)

Opp/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Adj/Hyp

81.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

82.

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

83.

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

84.

What is sin 45°?

a)

1

b)

^√3/₂

c)

½

d)

^√2/₂

85.

What is cos 90°?

a)

½

b)

undefined

c)

1

d)

0

86.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

87.

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

a)

y

b)

x

c)

x/y

d)

y/x

88.

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

a)

y

b)

x

c)

x/y

d)

y/x

89.

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

a)

y/r

b)

x/r

c)

r/y

d)

y/x

90.

What is a complete circle in radians?

a)

π

b)

2π

c)

1/2 π

d)

1

Midterm Pre-Calculus

Total questions: 90

Worksheet time: 23hrs 30mins

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