Free Printable Pre-Calc Final Review

1.

Find the partial fraction decomposition.

a)

b)

c)

d)

2.

Find the partial fraction decomposition...

a)

b)

c)

d)

3.

Set up the partial fractions...

a)

b)

c)

d)

4.

Which one should be used in the partial fraction decomposition of $\frac{4x}{\left(x+1\right)\left(3+x^2\right)}?$

a)

$\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x\right)}+\frac{C}{\left(3+x\right)^2}$

b)

$\frac{A}{\left(x+1\right)}+\frac{Bx+C}{\left(3+x^2\right)}$

c)

$\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x^2\right)}$

d)

$\frac{A}{\left(3+x^2\right)}+\frac{Bx}{\left(1+x\right)}$

5.

What is a Matrix?

a)

An equation of over 5 numbers or symbols

b)

A set of numbers in rows and columns

c)

A method of finding the n^th value of a series

d)

A complicated number system

6.

Name the order of this matrix.

a)

6x2

b)

2x6

c)

12

d)

36

7.

How many columns are in a 5 x 4 matrix?

a)

5

b)

4

c)

20

d)

9

8.

In Matrix R (pictured) what element is r₂₃?

a)

8

b)

9.01

c)

6

d)

1

9.

If the matrices can be multiplied, what dimension is the product? If not, write undefined.

a)

( 2 x 2 )

b)

( 6 x 2)

c)

( 2 x 6 ) )

d)

( 3 x 2 )

10.

If the matrices can be multiplied, what dimension is the product? If not, write undefined.

a)

undefined

b)

( 3 x 1 )

c)

( 1 x 2 )

d)

( 3 x 2 )

11.

Perform the operation if possible.

a)

A

b)

B

c)

C

d)

D

12.

Solve by graphing. Show all work on a graph paper.

a)

(2, 7)

b)

(7,6)

c)

(-6,1)

d)

No Solution

13.

What does it mean to substitute?

a)

to remember

b)

to replace or to plug in

c)

to get rid of or to take away

d)

to connect the dots

14.

Solve by using substitution method.

a)

(2, 7)

b)

(0, 1)

c)

(2/5, 9/5)

d)

(2, 5)

15.

Solve by using elimination method.

a)

(3, 1)

b)

( 5, -5)

c)

(2, 5)

d)

(15, 1)

16.

Solve by elimination
-2x + 6y = 16
-4x - 3y = 2

a)

(2,2)

b)

(-2, -2)

c)

(-2,2)

d)

(2,1)

17.

Kristin spent $202 on tops. Tank Tops cost $12, Graphic T- shirts cost $28 and Hoodies cost $35. She bought twice as many tank tops as hoodies. If she bought a total of 9 then how many of each kind did she buy?

a)

4 tank tops, 3 graphic tees, and 2 hoodies

b)

6 tank tops, 3 graphic tees, and 3 hoodies

c)

2 tank tops, 6 graphic tees, and 1 hoodies

18.

Use elimination or substitution to solve the systems.

a)

(4, 0, 2)

b)

(-4, 0, -2)

c)

(4, 0, -2)

19.

Use elimination or substitution to solve the systems.

a)

(4, 2, 0)

b)

(4, -2, 0)

c)

(-4, -2, 0)

20.

What if you are solving a system and your variables cancel out and you end up with a statement such as: 1=12? What conclusion can you make about the system?

a)

the solution is 1

b)

there is no solution

c)

the solution is 12

d)

infinite solutions

21.

-4x-2y=-12
4x+8y=-24

a)

(5,6)

b)

(6,-6)

c)

(6,-2)

d)

(4,-3)

22.

Is the sequence arithmetic: -3, 3, -3, 3, ...

a)

Yes

b)

No

23.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

24.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

25.

Evaluate the arithmetic series described:
28 + 38 + 48 + 58..., S₇

a)

1644

b)

812

c)

406

d)

3290

26.

Evaluate the arithmetic series described:
11 + 18 + 25 + 32..., S₇

a)

225

b)

450

c)

384

d)

224

27.

Find the sum of the 1st 20 terms: 2+5+8+......

a)

1220

b)

610

c)

600

d)

612

28.

Find the sum of the 1st 100 terms: 100+98+96+......

a)

100

b)

1000

c)

50

d)

-98

29.

Find the sum: 11 + 15 + 19 + .......+ 83

a)

19

b)

83

c)

893

d)

624

30.

Find S_n for the given series:
a₁=22
d=-8
n=21

a)

1911

b)

-1449

c)

-2436

d)

-1218

31.

Find the sum of first 20 even numbers.

a)

400

b)

410

c)

420

d)

430

32.

Find S₁₄
7, 2, -3, ...

a)

-812

b)

119

c)

-945

d)

-357

33.

What is the period of the equation shown?

a)

3π

b)

2π

c)

3π / 2

d)

2π / 3

34.

What is the period of the equation shown?

a)

8π

b)

4π

c)

π / 4

d)

π / 2

35.

Describe the horizontal shift.

a)

left π / 2

b)

left 2π

c)

right 2π

d)

right π / 2

36.

Describe the horizontal shift.

a)

left 3π / 4

b)

left 4π / 3

c)

right 3π

d)

right 3π / 4

37.

Describe the horizontal and vertical shifts.

a)

left π , up 4

b)

left π , down 3

c)

right π , up 4

d)

right π , down 3

38.

Describe the horizontal and vertical shifts.

a)

right 3π/2 , down 5

b)

left 2π/3 , up 5

c)

right 2π/3 , up 5

d)

left 2π , down 5

39.

What is the equation of the graph shown?

a)

y = 2sin(θ + π/2) + 3

b)

y = 3cos(θ - π/2) + 2

c)

y = 3sin(θ - π/2) + 2

d)

y = 2cos(θ + π/2) + 3

40.

What is the equation of the graph shown?

a)

y = 2sin(θ + π/2) + 2

b)

y = 2cos(θ - π/2) + 2

c)

y = 2sin(θ - π/2) + 2

d)

y = 2cos(θ + π/2) + 2

41.

What is the equation of the graph shown?

a)

y = 3sin(θ + π/4) - 1

b)

y = 3cos(θ - π/4) -1

c)

y = 3sin(θ - π/4) + 1

d)

y = 3cos(θ + π/4) + 1

42.

What is the directrix of the parabola
(x - 4)²= 8(y + 3)?

a)

y = - 3

b)

x= 5

c)

y= - 5

d)

y= 2

43.

What is the focus of the following parabola?
(y + 5)²= -12 (x - 2)

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

44.

True or False?
When the x-part is squared, the parabola opens up or down.

a)

True

b)

False

45.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

46.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -2, -4), (-2, 8)
Length of minor axis is 10
What is the center of the ellipse?

a)

( - 2, 2)

b)

(- 2, 4)

c)

(2, -2)

d)

(-2, 1)

47.

What direction does the parabola open?
(y-9)²= -40(x+4)

a)

Up

b)

Down

c)

Left

d)

Right

48.

What is "a" in the equation:
(y-9)²=-40(x+4)

a)

- 10

b)

10

c)

- 40

d)

40

49.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what is the center of this ellipse?

a)

(4, 6)

b)

( - 4, 3)

c)

(6, 4)

d)

(4, -3)

50.

What number would go in the blank?

a)

-2

b)

-4

c)

-8

d)

-16

51.

Given the following, write the equation of the ellipse.

a)

A

b)

B

c)

C

d)

D

52.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

53.

Simplify

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

54.

Simplify

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

55.

Simplify: tanxcotx-cos²x

a)

tanx

b)

cotx

c)

sin²x

d)

cos²x

56.

a)

1/cos x

b)

1

c)

cot x

d)

-1

57.

If sinθ = 3 / 5 and θ is in Q II, find tan θ.

a)

3 / 4

b)

-3 / 4

c)

4 / 3

d)

- 4 / 3

58.

Simplify the expression $\csc^2x\left(1-\sec^2x\right)$

a)

$-\csc^2x$

b)

$\cos x$

c)

$-\sec^2x$

d)

$\tan x$

59.

Simplify (Hint: you will need to FOIL first)

a)

sinθ

b)

cot²θ

c)

tan²θ

d)

cos²θ

60.

Simplify: tanxcotx-cos²x

a)

tanx

b)

cotx

c)

sin²x

d)

cos²x

61.

Determine the exact value of $\sin\ \left(\frac{\pi}{6}\right)$

a)

1/2

b)

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

c)

-1

d)

1

62.

$\cos\ \left(-\frac{11\pi}{3}\right)$

a)

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

b)

$\frac{1}{2}$

c)

$-\frac{1}{2}$

d)

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

63.

sin π =

a)

0

b)

1

c)

-1

d)

undefined

64.

tan 270=?

a)

0

b)

1

c)

-1

d)

undefined

65.

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

66.

tanθ 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

67.

cos π =

a)

0

b)

1

c)

-1

d)

undefined

68.

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

a)

y

b)

x

c)

x/y

d)

y/x

69.

a)

b)

c)

70.

cos 300°

a)

$\frac{1}{2}$

b)

0

c)

$-\frac{1}{2}$

d)

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

71.

a)

b)

c)

d)

e)

72.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

73.

Find the measure of the angle marked in red.

a)

-230°

b)

130°

c)

230°

d)

50°

74.

What is the direction angle for a vector whose component form is $<0,\ -3>$

a)

0 degrees

b)

90 degrees

c)

180 degrees

d)

270 degrees

75.

A vector is a quantity that has both _______ and _________.

Select all that apply.

a)

direction

b)

amplitude

c)

acceleration

d)

magnitude

e)

velocity

76.

Which of the following describes the vector above?

a)

45 cm

b)

45 cm at 30 degrees North of East

c)

45 cm at 30 degrees East of North

d)

45 cm North East

77.

What type of conic section is $3x^2–y^2–11x–6y+4=0$ ?

a)

Ellipse

b)

Hyperbola

c)

Circle

d)

Parabola

78.

What type of conic section is $2x^2+2y^2-4x-16y-9=0$ ?

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

79.

Identify the conic: 6y² – 5x – 2y + 5 = 0

a)

Parabola

b)

Circle

c)

Hyperbola

d)

Ellipse

80.

Identify the conic:
25x² + 5y² + 6x + 4y +2 = 0

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

81.

If plane is parallel to the base of the cone, a (a) formed.

82.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

83.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

84.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

85.

(x+3)² = 4(y+5)
What is the equation of the directrix?

a)

x = 4

b)

x = 2

c)

y = -4

d)

y = -6

86.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

a)

y² = 24(x+4)

b)

(y+4)² = -12x

c)

x² = 16(y+4)

d)

(x+4)² = -20y

87.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

88.

What is the focus of the following parabola?
(y + 5)²= -12 (x - 2)

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

Pre-Calc Final Review

Total questions: 88

Worksheet time: 5hrs 32mins

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