Free Printable T3 Final Exam Review 2025

1.

*

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

2.

Which of the following is not a Pythagorean identity?

a)

$\sin^2x+\cos^2x=1$

b)

$\sec^2x+1=\tan^2x$

c)

$\cot^2x+1=\csc^2x$

d)

$\tan^2x+1=\sec^2x$

3.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

4.

A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute. What is the angular speed in radians per hour?

a)

90π rad / 1 hr

b)

2700π rad / 1 hr

c)

5400π rad / 1 hr

d)

97200π rad / 1 hr

5.

A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute. What is the linear speed in feet per hour?

a)

90π ft / 1 hr

b)

2700π ft / 1 hr

c)

5400π ft / 1 hr

d)

4050π ft / 1 hr

6.

A car tire has a diameter of 14 inches and is spinning at a of 10 revolutions per second. What is the linear speed in miles per hour?

a)

7.95π mi / 1 hr

b)

15.90 mi / 1 hr

c)

3.28 rad / 1 hr

d)

2.84 rad / 1 hr

7.

A car tire has a diameter of 14 inches and is spinning at a rate of 10 revolutions per second. What is the angular speed in radians per hour?

a)

120π rad / 1 hr

b)

1,008,000π rad / 1 hr

c)

504,000π rad / 1 hr

d)

7200π rad / 1 hr

8.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

9.

Calculate the length of an arc with radius 15 cm and central angle of 30°.

a)

450 cm

b)

5π/2 cm or ≈ 7.9 cm

c)

225 cm

d)

5π/4 cm or ≈ 3.9 cm

10.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

11.

Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.

a)

5654.9 in/min

b)

1800 in/min

c)

2827.4 in/min

d)

900 in/min

12.

What is the radius of the circle with area of a sector equal to 7π cm²and central angle of 70°?

a)

6 cm

b)

1π/5 cm or .6 cm

c)

.8 cm

d)

36 cm

13.

Find the area of each sector.

a)

52.4 in²

b)

18,864 in²

c)

60 in2

d)

10.47 in

14.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

15.

The two pulleys in the figure have radii of 25 cm and 9 cm, respectively. The larger pulley rotates 52 times in 14 sec. Find the angular speed of each pulley in radians per second.

a)

Larger: 23.34 rad/sec; Smaller: 64.83 rad/sec

b)

Larger: 26.34 rad/sec; Smaller: 64.83 rad/sec

c)

Larger: 23.34 rad/sec; Smaller: 65.32 rad/sec

d)

Larger: 26.34 rad/sec; Smaller: 65.32 rad/sec

16.

A record spins at 33 rpm (revolutions per minute), which is an angular velocity of about 1.1pi radians per second. What is the approximate linear velocity of a fly that sits on the record, 12 cm from the center?

a)

3.4pi cm/s

b)

21.5pi cm/s

c)

13.2pi cm/s

d)

131.9pi cm/s

17.

$Find\ \cot\theta\ if\ \sin\theta=\frac{2}{3}$

a)

$\frac{3\sqrt[]{11}}{11}$

b)

$\frac{3}{2}$

c)

$\frac{2\sqrt[]{5\ }}{5}$

d)

$\frac{\sqrt[]{5}}{2}$

e)

none

18.

$Find\ \sin\theta\ if\ \csc\theta=\sqrt[]{5}$

a)

$\sqrt[]{5}$

b)

$\frac{\sqrt[]{5}}{5}$

c)

$2\sqrt[]{5}$

d)

$\frac{\sqrt[]{5}}{2}$

e)

none of these

19.

$Find\ the\ \sec\theta\ if\ \cot\theta=\frac{\sqrt[]{7}}{8}$

a)

$\frac{\sqrt[]{497}}{7}$

b)

$\frac{8\sqrt[]{7}}{7}$

c)

$\frac{8\sqrt[]{71}}{71}$

d)

$\frac{\sqrt[]{71}}{8}$

e)

none

20.

What is the angle of depression(in degrees - to nearest tenth) if the tower is 55 ft high and the object is 120 ft from top of the tower?

(a)

21.

Find the height of the tree (put answer to nearest tenth ) if angle of elevation of 61 degrees, 4.5 ft off of the ground and 55ft away from base of tree.

(a)

22.

Which trig function would you use with this diagram?

a)

^Sin

b)

^Cos

c)

^Tan

d)

^Wha??

23.

Use trig ratios (SOH CAH TOA) to solve for x

a)

5.0

b)

6.1

c)

7.7

d)

6.4

24.

Solve for the missing distance.

a)

18.9

b)

19.5

c)

47.3

d)

27.5

25.

Find the value of x rounded to the nearest tenth.

26.

Find the missing side length. Round to the nearest tenth.

type in just the number

27.

a)

$81\degree$

b)

$93\degree$

c)

$82\degree$

d)

$79\degree$

28.

a)

$25\degree$

b)

$26\degree$

c)

$23\degree$

d)

$22\degree$

29.

Find the angle at B.

a)

35

b)

209

c)

87

d)

29

30.

If a triangle has 1 angle and 2 sides, there are often two possible triangles. You solve law of sines to find the first possible angle for the triangle.

How do you find the second possible angle?

a)

Subtract your first answer from 180^o

b)

Subtract your first answer from 360^o

c)

Add your first answer to 180^o

d)

Subtract the angle on the triangle from your first answer

31.

Find side QR.

a)

34.7 km

b)

2.2 km

c)

13.74 km

d)

31.1 km

32.

Which Law would you use? (a)

Choose from the below words

Law of Sines

Law of Cosines

Law of the Jungle

Law of Gravity

33.

Use the Law of Sines to solve for BC

a)

33

b)

24

c)

12

d)

29

34.

Find AB

a)

10

b)

8

c)

6.1

d)

4.9

35.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?

a)

25.23

b)

23.19

c)

22.15

d)

20.85

36.

Two stakes are holding a small blimp in place. Stake A measures an angle of elevation of 49^o and Stake B measures an angle of elevation of 58^o. If the string attached to Stake A has a length of 148 feet, what is the length of the string attached to Stake B?

a)

152.7 feet

b)

166.3 feet

c)

157.3 feet

d)

131.7 feet

37.

Emma and Alyssa are 20 miles apart and spot a UFO in the sky between them. The angle of elevation from Emma to the UFO is 15^o, and from Alyssa to the UFO is 35^o(see diagram). How far away is the UFO from Emma?

a)

6.76 mi

b)

12.36 mi

c)

14.98 mi

d)

17.59 mi

38.

In an effort to recover Abraham's lost cell phone, two cell towers stationed 6000 feet apart detect the signal from the phone. Using strength of signal, the west tower measures the phone to be 5050 feet away and the east tower detects the phone to be 2420 feet away (see diagram). What angle $\theta$ should Abraham walk from the west tower to get to his phone?

a)

$\theta=18.48\degree$

b)

$\theta=23.33\degree$

c)

$\theta=24.17\degree$

d)

$\theta=27.91\degree$

39.

A GPS satellite measures the distances to two buildings to be 370 km and 350 km, and the angle between them to be 2.1^o (see diagram). How far apart are the two buildings?

a)

17.90 km

b)

30.32 km

c)

15.61 km

d)

23.96 km

40.

What is the area of a triangle with two sides that measure 6 m and 8 m with an included angle of 137°?

a)

17.8m²

b)

14.6m²

c)

16.4m²

d)

12.9m²

41.

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

42.

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

43.

Solve on the domain [0,2π)
1/4sin x + 1= 0

a)

0

b)

7π/4

c)

5π/4

d)

No solution

44.

Solve equation for $0\le\theta<2\pi$ .
$-\sin^2\theta=\sin\theta+1-3\sin^2\theta$

a)

$\theta=\frac{\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

d)

$\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$

45.

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)

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

46.

Solve equation for $0\le\theta<2\pi$ .
$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

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

c)

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

d)

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

47.

Solve equation for $0\le\theta<2\pi$ .
$-2=-5+3\sec\theta$

a)

$\theta=0,\frac{\pi}{3}$

b)

$\theta=0$

c)

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

d)

$No\ Solution$

48.

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

a)

$\theta=\pi$

b)

$\theta=\frac{7\pi}{4}$

c)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\frac{3\pi}{4}$

49.

Solve equation for $0\le\theta<2\pi$ .
$2=-4-3\csc\theta$

a)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

b)

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

c)

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

d)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}$

50.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

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

d)

$\theta=0,\pi$

51.

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)

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

52.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta+4=5+\sin^2\theta$

a)

$\theta=\frac{\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

b)

$\theta=\frac{\pi}{4},\frac{7\pi}{4}$

c)

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

d)

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

53.

Solve equation for $0\le\theta<2\pi$ .
$-3=\cot^2\theta-6$

a)

$\theta=\frac{\pi}{6},\frac{7\pi}{4},\frac{11\pi}{6}$

b)

$\theta=\frac{7\pi}{6},\frac{5\pi}{4},\frac{11\pi}{6}$

c)

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

d)

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

54.

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

a)

$\theta=\frac{5\pi}{6},\frac{4\pi}{3}$

b)

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

c)

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

d)

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

55.

Solve equation for $0\le\theta<2\pi$ .
$-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$

a)

$\theta=\frac{5\pi}{4},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{6},\frac{7\pi}{4}$

c)

$\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{5\pi}{4},\frac{7\pi}{4}$

56.

Solve equation for $0\le\theta<2\pi$ .
$0=-\sqrt{3}\sin\theta-2\sin^2\theta$

a)

$\theta=0,\frac{2\pi}{3},\pi,\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

c)

$\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$

d)

$\theta=0,\pi,\frac{5\pi}{3}$

57.

Solve equation for $0\le\theta<2\pi$ .
$0=-3\cot\theta+2\sqrt{3}\cot\theta\sin\theta$

a)

$\theta=\frac{3\pi}{2}$

b)

$\theta=0,\frac{5\pi}{6},\pi,\frac{11\pi}{6}$

c)

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

d)

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

58.

Solve equation for $0\le\theta<2\pi$ .
$\sec\theta\csc\theta-\csc\theta=\sqrt{2}\sec\theta-\csc\theta$

a)

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

b)

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

c)

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

d)

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

59.

Solve equation for $0\le\theta<2\pi$ .
$2\sqrt{3}\sec\theta\cos\theta=-3\sec\theta$

a)

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

b)

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

c)

$\theta=\frac{7\pi}{6},\frac{4\pi}{3}$

d)

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

60.

Solve equation for $0\le\theta<2\pi$ .
$\sec^2\theta+3=2\sec\theta+2$

a)

$\theta=0,\frac{\pi}{2},\frac{2\pi}{3},\frac{5\pi}{3}$

b)

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

c)

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

d)

$\theta=0$

61.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta=7\sin^2\theta+4\sin\theta+1$

a)

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

b)

$\theta=0,\frac{\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

d)

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

62.

Solve equation for $0\le\theta<2\pi$ .
$-\sin^2\theta=\sin\theta+1-3\sin^2\theta$

a)

$\theta=\frac{\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

d)

$\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$

63.

Solve equation for $0\le\theta<2\pi$ .
$2+3\csc\theta+2\csc^2\theta=\csc^2\theta$

a)

$\theta=\frac{3\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

d)

$\theta=\frac{\pi}{4},\frac{11\pi}{6}$

64.

Solve equation for $0\le\theta<2\pi$ .
$4\cot^2\theta=-1-2\cot\theta+3\cot^2\theta$

a)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

b)

$\theta=\frac{7\pi}{4}$

c)

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

d)

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

65.

Find all real numbers that satisy the equation.

\cos x=\frac{1}{2}

Choose all solutions that apply.

a)

$x=\frac{\pi}{3}+2\pi k$

b)

$x=\frac{5\pi}{3}+2\pi k$

c)

$x=\frac{2\pi}{3}+2\pi k$

d)

$x=\frac{4\pi}{3}+2\pi k$

66.

Find all real numbers that satisfy the equation.

\sin x=1

a)

$x=\frac{\pi}{2}+\pi k$

b)

$x=\frac{\pi}{2}+2\pi k$

c)

$x=\pi+2\pi k$

d)

$x=\pi+\pi k$

67.

Find all real numbers that satisfy the equation

\sin x=-\frac{1}{2}

a)

$x=\frac{\pi}{6}+2\pi k$

b)

$x=\frac{7\pi}{6}+2\pi k$

c)

$x=\frac{5\pi}{6}+2\pi k$

d)

$x=\frac{11\pi}{6}+2\pi k$

68.

Find the first two solutions to

\tan3x=-\sqrt{3}

in the interval

\left(0,2\pi\right)

.

a)

$\frac{2\pi}{9}$

b)

$\frac{5\pi}{9}$

c)

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

d)

$\frac{4\pi}{3}$

69.

$Solve\ 3\cot x\ +\ 5\ =\ 8\ \ for\ \ 0\ \le\ x\ <\ 2\pi$

a)

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

b)

$0,\ \pi$

c)

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

d)

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

70.

Evaluate: $\sin\frac{5\pi}{8}$

71.

If x is a positive acute angle and $\sin x=\frac{1}{2},$ what is $\sin2x?$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

72.

The expression $2\sin30^o\cos30^o$ has the same value as

a)

$\sin15^o$

b)

$\cos60^o$

c)

$\sin60^o$

d)

$\cos15^o$

73.

If $\cos\theta=\frac{1}{8},$ the positive value of $\sin\ \frac{\theta}{2}$ is

a)

$\frac{3}{2}$

b)

$\frac{\sqrt{7}}{4}$

c)

$\frac{9}{16}$

d)

$\frac{3}{4}$

74.

If $\sin\theta=\frac{\sqrt{5}}{3}$ , then $\cos2\theta$ equals

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

$\frac{1}{9}$

d)

$-\frac{1}{9}$

75.

$\sin96^o\cos24^o+\cos96^o\sin24^o\$ is equivalent to

a)

$\sin120^o$

b)

$\sin72^{o\ }$

c)

$\cos120^o$

d)

$\cos72^o$

76.

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$ and A and B are first quadrant angles, what is the value of $\sin\left(A+B\right)$ ?

a)

$\frac{63}{65}$

b)

$-\frac{33}{65}$

c)

$\frac{33}{65}$

d)

$-\frac{63}{65}$

77.

If $\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},$ what is the value of $\tan\left(A+B\right)?$

a)

$\frac{1}{8}$

b)

$\frac{7}{8}$

c)

$\frac{1}{4}$

d)

$\frac{7}{4}$

78.

If $\cos A=\frac{1}{3}$ , then the positive value of $\tan\ \frac{A}{2}$ ?

a)

$\sqrt{2}$

b)

$\sqrt{3}$

c)

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

d)

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

79.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

a)

$-\frac{2}{3}$

b)

$\frac{4\sqrt{5}-6}{15}$

c)

$\frac{4\sqrt{5}+2}{5}$

d)

$\frac{4\sqrt{5}+6}{15}$

80.

$\cos70^o\cos40^o-\sin70^o\sin40^o\$ is equivalent to

a)

$\cos30^o$

b)

$\cos70^{o\ }$

c)

$\cos110^o$

d)

$\sin70^{o\ }$

81.

Perform scalar multiplication on the matrix

a)

A

b)

B

c)

C

d)

D

82.

What do m, n, p and q equal in this scalar matrix multiplication?

a)

m=8, n=9, p=-4, q=4

b)

m=15, n = -45, p=20, q=-5

c)

m=20, n=-5, p=15, q=-45

d)

m=-5, n=20, p=-45, q=15

83.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

84.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

85.

What is the value of element M_3,4?
(Think about what is in the 3rd row and 4th column)

a)

34

b)

42

c)

37

d)

π

86.

Find A-B

a)

-3 1
7 -1

b)

1 0
1 -4

c)

-4 0
6 -1

d)

not possible because rows do not match columns

87.

Given these matrices find B - A

a)

b)

c)

d)

88.

These matrices are being multiplied. Determine the dimension/size of the new matrix.

a)

Can't multiply them

b)

4 x 2

c)

3 x 3

d)

4 x 3

89.

Find the product of the two matrices.

a)

undefined

b)

-3 16
17 12
8 -10

c)

3 12
-15 -8
-1 -3

90.

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

91.

What is the inverse of this matrix?

a)

_{(1/25) (-4/25)}
_{(3/25) (13/25)}

b)

_{(1/5) (-4/5)}
_{(3/5) (13/5)}

c)

_{(6/25) (-2/25)}
_{(2/25) (9/25)}

d)

_{(1/150) (-4/150)}
_{(3/150) (13/150)}

92.

What is A^-1?

a)

b)

c)

d)

93.

Are these matrices inverses of each other?

a)

Yes

b)

No

c)

Unable to Determine

94.

Solve the system by elimination and write your solution as an ordered triple (a,b,c). If there is no solution, write "none". If there are an infinite number of solutions, write "infinite".

(a)

95.

Solve the system by elimination and write your solution as an ordered triple (r,s,t). If there is no solution, write "none". If there are an infinite number of solutions, write "infinite".

(a)

96.

Solve the system by elimination and write your solution as an ordered triple (x,y,z). If there is no solution, write "none". If there are an infinite number of solutions, write "infinite".

(a)

97.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

98.

Solve the system.

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(-3, 2, -1)

d)

Infinitely many solutions

99.

Solve the system.

a)

(1, 2, -2)

b)

(1, -3, -2)

c)

(-1, 3, 2)

d)

No Solution

100.

Solve the system of equations:
x + y + z = 4
x = -2y
z = -3y

a)

(2, -1, 3)

b)

(2, 3, 1)

c)

None of these

d)

(4, 1, -1)

101.

The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?

a)

One

b)

Two

c)

Three

d)

Four

e)

No Solution

102.

What are the solutions to the system of equations graphed below?

a)

(2, 0)

b)

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

c)

(-2,0)

d)

(0, -4), (0,4)

e)

No Solution

103.

Which of the following is a solution to the system

5x - 4y - 11 = 0

y = x² - x - 6

a)

(1, 8)

b)

(0, 4)

c)

(-1, -4)

d)

(2, 0)

e)

No Solution

104.

y²- x = 4

x² + y²= 4

a)

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

b)

(-1, √3), (-1, -√3)

c)

(0, 2), (0, -2), (-1, √3), (-1, -√3)

d)

(2, 0), (0, -2), (√3, ±1)

105.

Solve using elimination.

a)

no solution

b)

(2,3), (2, -3), (-2,3), and (-2,-3)

c)

(3,5), (-3,-5), (3, -5), and (-3,5)

d)

(2,3), (-2,-3), (3,5), and (-3,-5)

106.

Solve the following system using elimination.

a)

no solution

b)

(3,4), (-3,-4), (3, -4), and (-3, 4)

c)

(4,3), (-4,3), (4, -3), and (-4, -3)

d)

(3,4) and (4,3)

107.

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular shows. One night the theater sells 578 tickets and collects $3365 in total ticket sales.

Which system best represents the situation?

a)

b)

c)

d)

108.

Solve each system by matrices.

7x + 9y = 25

-7x - 5y = -17

a)

(1, 2)

b)

(1, -5)

c)

(-2, 1)

d)

(1, -2)

109.

Solve the system by matrices (x,y)
3x + 2y = –13
3x + 4y = 1

a)

(-9,7)

b)

(7,-9)

c)

(4,-7)

d)

(-7,-4)

110.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

111.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

112.

Change the following equation to standard form
x²+y²-4x+12y-8=0

a)

(x+2)²+(y-6)²=48

b)

(x-2)²+(y+6)²=48

c)

(x-6)²+(y-2)²=48

d)

(x+2)²+(y-6)²=48

113.

What is the center for the circle with this equation x²+y²+4x+6y-36=0?

a)

(-2,5)

b)

(2,7)

c)

(-2,-3)

114.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

115.

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)

116.

What are the vertices of the hyperbola?

a)

(0, 5) and (0, -5)

b)

(5, 0) and (-5, 0)

c)

(0, 25) and (-25, 0)

d)

(0, 0) and (0, 5)

117.

What is the value of a² for the given hyperbola?

a)

1

b)

-2

c)

25

d)

16

118.

What is the center of this hyperbola?

a)

(4,-2)

b)

(4,2)

c)

(-2,4)

d)

(2, 4)

e)

(7.5,3)

119.

Classify the conic section.

a)

Circle

b)

Ellipse

c)

Line

d)

None of these

120.

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

a)

Ellipse

b)

Circle

c)

Hyperbola

d)

Parabola

121.

What type of conic section is

2x^2+2y^2-4x-16y-9=0

?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

122.

What is the center and radius?

a)

Center: (-3,4)

Radius: 3

b)

Center: (3,4)

Radius: 3

c)

Center: (4,-3)

Radius: 9

d)

Center: (4,3)

Radius: 9

123.

The equation 6x² + 6y² – 3x + 4y = 0 will be a ....

a)

Circle

b)

Parabola

c)

Hyperbola

d)

Ellipse

124.

Is the hyperbola vertical or horizontal?

a)

Vertical

b)

Horizontal

125.

What are the vertices of the hyperbola?

a)

(0, 3) and (0, -3)

b)

(-4, 3) and (-4, -3)

c)

(0, 1) and (0, -1)

d)

(4, 0) and (-4, 0)

126.

Which direction will the major axis go in the given ellipse?

a)

horizontal

b)

vertical

127.

a)

(x + 2)² + (y - 1)² = 2

b)

(x + 2)² + (y - 1)² = 1

c)

(x - 2)² + (y + 1)² = 1

d)

(x + 2)² + (y - 2)² = 1

128.

Which of the following is the equation of the circle with a center at (5, 10) and diameter = 10

a)

(x - 5)² + (y - 10)² = 10

b)

(x - 5)² + (y - 10)² = 100

c)

(x + 5)² + (y + 10)² = 25

d)

(x - 5)² + (y - 10)² = 25

129.

Which conic section is represented by the equation

4x² + 25y² - 8x + 150y + 129 = 0

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

130.

a)

b)

c)

d)

131.

a)

5

b)

6

c)

3

d)

10

132.

a)

Horizontal

b)

Vertical

c)

Neither

133.

a)

b)

c)

d)

134.

a)

Horizontal

b)

Vertical

c)

Neither

135.

The vertices of a hyperbola are located at (1,1) and (5 ,1). Which are the coordinates of the center?

a)

(3,1)

b)

(3,0)

c)

(1,3)

d)

(9,1)

T3 Final Exam Review 2025

Total questions: 135

Worksheet time: 10hrs 12mins

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