Free Printable Extra Exam Review 2025

1.

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

a)

Parabola

b)

Circle

c)

Hyperbola

d)

Ellipse

2.

Identify the conic:
-6x² + 4y² + 9x + y = -7

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

3.

Write the standard form of the circle:
x² + y² +10y = 39

a)

x² + (y+5)² = 49

b)

x² + (y+5)² = 64

c)

(x+5)² + y² = 61

d)

(x+5)² + y² = 100

4.

Identify the polar equation:
r=1+sinθ

a)

cardioid

b)

circle

c)

limacon with inner loop

d)

spiral

5.

Which of the following could be the equation for...

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 6 - 6 sin θ

d)

r = 6 + 6 cos θ

6.

Which of these is an equation for this dimpled limaçon?

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 2 - 3cosθ

7.

Match the given polar equation with its corresponding graph.

r^2=9\cos2\theta

a)

rose

b)

lemniscate

c)

dimpled limacon

d)

cardioid

8.

Match the given polar equation with its corresponding graph.

$r=5\cos2\theta$

a)

rose

b)

lemniscate

c)

dimpled limacon

d)

cardioid

9.

Find the equation of the figure shown.

a)

(x-1)²/16 - (y+2)²/4= 1

b)

(x+1)²/16 - (y-2)²/4= 1

c)

(y+2)²/4 - (x-1)²/16= 1

d)

(x-1)²/4 - (y+2)²/2= 1

10.

What conic section is pictured?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

11.

What conic section is pictured?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

12.

a)

Vertical Ellipse

b)

Vertical Hyperbola

c)

Horizontal Ellipse

d)

Horizontal Hyperbola

13.

Identify the center and the length of a and b.

a)

C: (0,0) a= 25, b=4

b)

C: (0,0) a= 4, b=25

c)

C: (0,0) a= 2, b=5

d)

C: (0,0) a= 5, b=2

14.

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)

15.

What number would go in the blank?

a)

-2

b)

-4

c)

-8

d)

-16

16.

What is the value of a² for the given hyperbola?

a)

1

b)

-2

c)

25

d)

16

17.

Name the conic section and determine the vertices.9x² - 4y² - 54x-16y - 79 = 0

a)

hyperbola; (3, 4), (3, -8)

b)

hyperbola; (7, -2), (-1, -2)

c)

hyperbola; (9, -2), (-3, -2)

d)

hyperbola; (3, 2), (3, -6)

18.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

19.

Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9).

a)

6

b)

8.2

c)

10

d)

10.4

20.

$p=<3,\ -9>$

Find the magnitude to the nearest tenth.

a)

9.5

b)

10

c)

9

d)

2√3

21.

Determine the direction and magnitude of the vector 〈-11,5〉

a)

Direction 24.4°
Vertical 12.1

b)

Direction65.6°
Magnitude 12.1

c)

Direction -24.4°
Magnitude 12.1

d)

Direction 155.6°
Magnitude 12.1

22.

Find the angle between u and v.

a)

78.930^o

b)

33.691^o

c)

101.070^o

d)

146.310^o

23.

v - w

a)

-6i + 2j

b)

6i - 2j

c)

2i - 6j

d)

-2i + 6j

24.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

25.

Identify all angles where r=0 for:
r = 4 sin $2\theta$

a)

$0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2}$

b)

$\frac{\pi}{4},\ \frac{3\pi}{4},\ \frac{5\pi}{4},\ \frac{7\pi}{4}$

c)

$0,\ \pi,\ 2\pi,\ 3\pi$

d)

There are no angles where r=0

26.

Identify all angles that are the zeros.

r=1-2sinθ

a)

$\frac{\pi}{6},\frac{5\pi}{6}$

b)

$\frac{\pi}{3},\frac{2\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$\frac{7\pi}{6},\frac{11\pi}{6}$

27.

Find the solution point of the curves $r\ =\ \cos\theta$ and $r\ =\ 2\ +\ 3\cos\theta$ . Let answers be written as $\left(r,\ \theta\right)$ .

a)

(1, Π)

b)

(1, Π) (0, 0)

c)

(-1, Π) (0, 0)

d)

(-1, Π)

28.

At what values of theta do the following curves intersect? Select all that apply.

$r\ =\ \sin\theta$

$r\ =\ 1\ -\ \sin\theta$

a)

0

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{2}$

d)

$\frac{5\pi}{6}$

29.

Which point represents $\left(-4,\frac{4\pi}{3}\right)$ ?

(a)

Choose from the below words

A

F

E

B

C

D

30.

Find the polar coordinates for the rectangular point $\left(-3,0\right)$ .

a)

$\left(3,\pi\right)$

b)

$\left(3,0\right)$

c)

$(3,\frac{\pi}{2})$

d)

$(3,\frac{3\pi}{2})$

31.

Give the rectangular coordinates for the polar point $\left(4,\pi\right)$

a)

(-4,0)

b)

(4,0)

c)

(0,-4)

d)

(0,4)

32.

Give the rectangular coordinates for the polar point $\left(4,-\frac{3\pi}{2}\right)$

a)

(-4,0)

b)

(4,0)

c)

(0,-4)

d)

(0,4)

33.

Which of the following graphs is symmetric about the line $\theta=\frac{\pi}{2}$ ?

a)

b)

c)

d)

34.

Three of the following coordinates represent the same point. Which one represents a DIFFERENT point from the others?

a)

$\left(4,\frac{\pi}{3}\right)$

b)

$\left(4,-\frac{5\pi}{3}\right)$

c)

$\left(-4,\frac{5\pi}{3}\right)$

d)

$\left(-4,-\frac{2\pi}{3}\right)$

35.

find: B*A

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

36.

You can multiply a 2X3 matrix by which matrix?

a)

2X2

b)

2X12

c)

3X12

d)

2X3

37.

Find the determinant of the matrix and determine of the matrix is invertible.

a)

det = -14, inverse exists

b)

det = 0, no inverse exists

c)

det = 166, inverse exists

d)

det = 14, inverse exists

38.

Find the area of triangle ELI where E=(2, 11), L=(7, 1) and I=(2, 1)

a)

25

b)

36

c)

50

d)

12.5

39.

What is A^-1?

a)

b)

c)

d)

40.

Solve the following systems of equations.

-x+6y-z=6

2x+y-3z=16

-x+5y+3z=-7

a)

A (0, -6, 0)

b)

B (0, 0, -6)

c)

C (3, 1, -3)

d)

D (-6, 4, -3)

41.

What is the direction angle (in degrees) for a boat traveling
S20°E?

a)

160

b)

70

c)

340

d)

290

42.

Given p = <4, -6> and q = <-5, 2> find ||2p - q||

a)

√269

b)

√365

c)

√179

d)

√109

43.

Find the determinant of the matrix

a)

A

b)

B

c)

C

d)

D

44.

Find the value of x that makes the equation true.

a)

x = 7

b)

x = -11/3

c)

x = 19

d)

x = -7

45.

Perform the matrix operations.

a)

b)

c)

d)

46.

An airplane on course bearing 105° at 400 mph encounters a wind blowing 35 mph due east. Find the direction of the resultant vector.

a)

S13.8°W

b)

S76.2°W

c)

S13.8°E

d)

S76.2°E

47.

A feliex dances at a constant speed of 100 mph on a heading of N 45 E. There is a wind blowing 500 mph south. Use the options below to find the direction:

(a) (b) (c)

Choose from the below words

S

9.4

E

W

N

8.3

9.8

7.6

8.8

10.9

48.

A feliex dances at a constant speed of 100 mph on a heading of N 45 E. There is a wind blowing 500 mph south. Find the objects ground speed and round to the nearest tenth.

(a)

49.

Find the dot product: $u=\left(-12,30\right)$ and $v=\left(\frac{1}{2},-\frac{5}{4}\right)$

a)

$\frac{-87}{2}$

b)

(-6, $\frac{-75}{2}$ )

c)

$\frac{63}{2}$

50.

Determine one cycle for the polar curve.

$r=5\cos2\theta$

a)

0 $\le$ Θ $\le$ Π

b)

0 $\le$ Θ $\le$ $\frac{\pi}{2}$

c)

0 $\le$ Θ $\le2\pi$

d)

0 $\le$ Θ $\le$ $\frac{3\pi}{2}$

51.

Simplify: $\secθ\sinθ$

a)

cos θ

b)

csc θ

c)

tan θ

d)

cot θ

52.

Select all that are Pythagorean Identities.

a)

sin²(u) + cos²(u) = 1

b)

sin²(u) - cos²(u) = 1

c)

tan²(u) + 1 = sec²(u)

d)

cot²(u) + csc²(u) = 1

e)

cot²(u) + 1 = csc²(u)

53.

Please select the correct solution
cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

54.

Please select the correct solution

a)

csc x

b)

sec x

c)

cot x

d)

tan x

55.

Find the exact value.

a)

A

b)

B

c)

C

d)

D

56.

a)

A

b)

B

c)

C

d)

D

57.

a)

A

b)

B

c)

C

d)

D

58.

$\sec\left(5\degree\right)=$

Complete this equation using a cofunction identity.

a)

$\csc\left(5\degree\right)$

b)

$\csc\left(85\degree\right)$

c)

$\sec\left(85\degree\right)$

d)

$\frac{1}{\cos\left(5\degree\right)}$

59.

Which expression is always equivalent to sin x when 0°< x < 90°?

a)

cos(90°−x)

b)

cos(45°−x)

c)

cos(2x)

d)

cos x

60.

State the correct cofunction identity

$\cos\left(\frac{\pi}{2}-\theta\right)=$

a)

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

b)

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

c)

$\sec\left(\theta\right)$

d)

$\tan\left(\theta\right)$

61.

State the correct cofunction identity

$\tan\left(\frac{\pi}{2}-\theta\right)=$

a)

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

b)

$\cot\left(\theta\right)$

c)

$\cos\left(\theta\right)$

d)

$\tan\left(\theta\right)$

62.

Write the expression as the sine or cosine of a single angle: $\sin\left(\frac{\pi}{3}\right)\cos\left(\frac{\pi}{7}\right)-\sin\left(\frac{\pi}{7}\right)\cos\left(\frac{\pi}{3}\right)$

a)

$\cos\left(\frac{4\pi}{21}\right)$

b)

$\sin\left(\frac{4\pi}{21}\right)$

c)

$\cos\left(\frac{10\pi}{21}\right)$

d)

$\sin\left(\frac{10\pi}{21}\right)$

63.

$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$ is equivalent to.. #11

a)

$\tan75^o$

b)

$\tan\ 15^o$

c)

$\frac{\sin45^o}{\cos30^o}$

d)

$\tan90^{o\ }$

64.

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)

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

65.

Solve equation for $0\le\theta<2\pi$ .
$1+\tan^2\theta=4\tan^2\theta$

a)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

d)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6}$

Extra Exam Review 2025

Total questions: 65

Worksheet time: 4hrs 4mins

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