Free Printable Trigonometric Ratios and Functions

1.

What is the acronym to help you remember the ratios to use in trigonometry?

a)

RIGHTANG

b)

SOHCAHTOA

c)

SHOCHATOA

d)

SAHCOHTAO

2.

What is the correct trigonometric ratio for the given right triangle?

a)

$\sin 40^\circ = \frac{w}{28}$

b)

$\cos 40^\circ = \frac{w}{28}$

c)

$\tan 40^\circ = \frac{w}{28}$

d)

$\sin 40^\circ = \frac{28}{w}$

3.

Solve for x in the equation . Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

9.7

4.

Choose the correct ratio for the given triangle.

a)

$\cos\ 33\degree\ =\ \frac{x}{14}$

b)

$\sin\ 33\degree\ =\ \frac{x}{14}$

c)

$\cos\ 33\degree\ =\ \frac{14}{x}$

d)

$\sin\ 33\degree\ =\ \frac{14}{x}$

5.

Set up the problem to solve for x:

a)

sin(47) = x/28

b)

cos(47) = x/28

c)

tan(47) = x/28

d)

cos(47) = 28/x

6.

What are the value of x and ( y ) in the given triangle.

In addition what is the area of the triangle.

Look up 45-45-90 triangles rules

a)

x = 10

y = 5sq root of 2

Area = 25

b)

x = 10

y = 5sq root of 2

Area = 50

c)

x = 20

y = 5sq root of 2

Area = 25

d)

x = 10

y = 5sq root of 3

Area = 25

e)

$None\ of\ these$

7.

What is the value of x and y ?

Look up rules for 30-60-90 Triangle

To go from 60 degree side to 30 degree side divide by sq root of 3,,then mult be 2 to fine the big side.

a)

x=14

y = 7

b)

$14\sqrt{3}$

c)

x= 7

y = 14

d)

$\frac{7\sqrt{3}}{2}$ $.$

e)

$\text{None of these}$

8.

Match the following for finding sides in a 30-60-90 right triangle.

a)

Short Leg

1.

Half of the hypotenuse

b)

Hypotenuse

2.

Double the short leg

c)

Long Leg

3.

Short leg times square root of 3

9.

Match the following for a 30-60-90 right triangle

a)

Short Leg

1.

Opposite the 30° angle.

b)

Long Leg

2.

Opposite the 60° angle.

c)

Hypotenuse

3.

Opposite the right angle.

10.

Which set of sides would make a right triangle?

Use: c² < a² + b²acute

c² = a² + b²right

c² > a² + b² obtuse

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

11.

Solve for the missing distance (d) in the right triangle shown in the image.

a)

18.9

b)

19.5

c)

47.3

d)

27.5

12.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

13.

Determine if this triangle is acute, right, or obtuse. Use:

c² < a² + b²

c² = a² + b²

c² > a² + b²

a)

Acute triangle

b)

Right triangle

c)

Obtuse triangle

d)

Cannot form a triangle

14.

Determine if this triangle is acute, right, or obtuse. Use:

c² < a² + b²

c² = a² + b²

c² > a² + b²

a)

Acute triangle

b)

Right triangle

c)

Obtuse triangle

d)

Cannot make a triangle

15.

Determine if this triangle is acute, right, or obtuse. Use:

c² < a² + b²

c² = a² + b²

c² > a² + b²

a)

Acute triangle

b)

Right triangle

c)

Obtuse triangle

d)

Cannot form a triangle

16.

Find $m\angle Y$ to the nearest tenth.

a)

39

b)

34

c)

35.1

d)

30

17.

Find the area of the triangle to the nearest tenth.

(s) sin(@) (s) then divide by 2

a)

18.5

b)

14.1

c)

19

d)

12.4

18.

Find Length CB and

The area of the triangle is (a) , to the nearest tenth.

First use Law of sine ,,then area formula

Choose from the below words

area 15.0,,,CB 20

Area 20.0

CB 25.0

Area 7.1,,CB 5.3

19.

Find the area of the triangle DEF to the nearest tenth.

First use Law of sine ,,then area formula

a)

29.8

b)

23.4

c)

27.6

d)

27

20.

What is the length of side x?

First use Law of sine

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

21.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

22.

Parker must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 860 feet from Point A and 175 feet from Point B. He measures the angle at Point C to be 78 degrees. Find the distance from Point A to Point B.

Law of Cosine is needed.

a)

707643.58

b)

841.22

c)

877.62

d)

842.01

23.

(a) feet.

Choose from the below words

15

25.22

25

30

24.

Use the Law of Cosines to find angle T.

a)

62.2 degrees

b)

53.1 degrees

c)

59.5 degrees

d)

64.7 degrees

25.

A post is supported by two wires (one on each side going in opposite directions), creating an angle of 80 degrees between the wires. The ends of the wires are 12m apart on the ground, with one wire forming an angle of 40 degrees with the ground. Find the lengths of the wires.

a)

7.8 and 10.6 meters

b)

9.4 and 12.2 meters

c)

4.3 and 7.3 meters

d)

7.8 and 11.3 meters

26.

Two ships are sailing from Halifax. The Nina is sailing due east, and the Pinta is sailing 43 degrees south of east. After an hour, the Nina has traveled 115 km, and the Pinta has traveled 98 km. How far apart are the two ships?

a)

85.1 km

b)

103.2 km

c)

79.7 km

d)

23.5 km

27.

Two people are standing on the shore 1/2 mile apart at points A and B and measure the angle to a sailboat at point C at the same time. Angle A is 63 degrees and angle B is 56 degrees. Find the distance from each person to the sailboat.

a)

Person A is 0.47 miles and person B is 0.51 miles from the sailboat.

b)

Person A is 0.51 miles and person B is 0.41 miles from the sailboat.

c)

Person A is 0.79 miles and person B is 0.35 miles from the sailboat.

d)

Person A is 0.35 miles and person B is 0.79 miles from the sailboat.

28.

Carl and Billy both start at point A. They each walk in a straight line at an angle of 105 degrees to each other. After 45 minutes, Carl has walked 4.5 km and Billy has walked 6 km. How far apart are they?

a)

10.5 km

b)

8.4 km

c)

13.1 km

d)

5.3 km

29.

Points A and B are on opposite sides of the Grand Canyon. Point C is 200 yards from A. Angle B measures 87 degrees and angle C measures 67 degrees. What is the distance between A and B?

a)

193.2 yds

b)

205.2 yds

c)

184.4 yds

d)

150.3 yds

30.

Jack is flying his kite. He runs 100 feet away from his house and lets out 75 feet of string. The angle of elevation from the ground to the kite is 65 degrees. How far away is the kite from the house?

a)

9285.73 ft

b)

96.36 ft

c)

24061.81 ft

d)

155.12 ft

31.

Using Heron's formula, find the area of the triangle with sides 7, 8, and 13.

A = √[s(s-a)(s-b)(s-c)]

s = (a + b + c)/2.

First,,,,,,Add the sides and divide by 2 to find S

a)

56

b)

28

c)

24.2

d)

104.4

32.

What is the correct setup to find side p?

a)

$p^2=16^2+19^2-2\left(16\right)\left(19\right)\cos48$

b)

$p^2=16^2-19^2+2\left(16\right)\left(19\right)\sin48$

c)

$p=16+19+2\left(16\right)\left(19\right)\cos48$

d)

$16^2=p^2+19^2-5\left(16\right)\left(19\right)\cos48$

33.

Match the following

a)

Sin A

1.

$\frac{8}{17}$

b)

Cos A

2.

$\frac{15}{17}$

c)

Tan A

3.

$\frac{8}{15}$

d)

Tan C

4.

$\frac{15}{8}$

e)

Size of Angle B

5.

$90\degree$

34.

Match the following

a)

Sin Z

1.

$\frac{12}{13}$

b)

Cos Z

2.

$\frac{5}{13}$

c)

Tan Z

3.

$\frac{12}{5}$

d)

Tan X

4.

$\frac{5}{12}$

e)

Area of the triangle

5.

120

35.

Match the following tables with their corresponding linear equations in the form of y=mx+b

a)

y = 3x - 3

1.

x	y
0	-3
1	-6
2	-9
3	-12
4	-15

b)

y = -3x + 3

2.

x	y
0	3
1	0
2	-3
3	-6
4	-9

c)

y = -3x - 3

3.

x	y
0	-3
1	0
2	3
3	6
4	9

d)

y = 3x + 3

4.

x	y
0	3
1	6
2	9
3	12
4	15

36.

Write a linear equation in the form of y = mx + b.

a)

y = x + 2

b)

y = 2x - 1

c)

y = 3x - 2

d)

y = 2x + 1

37.

What is the slope of the line represented by the table?

a)

1/2

b)

2

c)

7

d)

3

38.

Which table best represents this equation?

a)

b)

c)

d)

39.

Which table represents the graph?

a)

b)

c)

d)

40.

Turkeys R Us delivers on Thanksgiving. A holiday meal costs $12.50 per person plus a delivery fee of $30. Which of the following functions best represents this? Choose 2 answers.

a)

y = 30 + 12.50x

b)

y = 12.50 + 30

c)

y = 12.50 + 30x

d)

y = 12.50x + 30

41.

Sandra has a $20 iTunes gift card and spends $3 each month.

Which function best represents this?

a)

y = 3x + 20

b)

y = 3 + 20x

c)

y = -3x + 20

d)

y = -20x + 3

42.

A gym charges an initial fee plus a monthly charge. Use the table to find the rate of change, which is the cost per month.

a)

$75 per month

b)

$55 per month

c)

$45 per month

d)

$35 per month

43.

What is the initial cost?

a)

12

b)

20

c)

36

d)

44

44.

Which of the following scenarios best represents this graph?

a)

Jane charges $28 an hour to clean.

b)

Fred paid someone $20 to come to his house and clean his car.

c)

Jeri paid $28 per hour for someone to clean her house.

d)

Fred paid an initial fee of $20 for a car cleaner to come out and then an additional $8 per hour.

45.

Match the following gym charges with their initial fees.

a)

$75

1.

Company A: y = 35x + 40

b)

$35

2.

Company B: y = 35x + 75

c)

$45

3.

Company C: y = 35x + 35

d)

$40

4.

Company D: y = 35x + 45

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

³/₄(6x + 2) = 15

a)

3

b)

6

c)

18

d)

20

49.

^x/₃+ 10 = 15

a)

75

b)

15

c)

25

d)

5

50.

Solve for x: $4-4|x+3|>8$

a)

$\left(-4,-2\right)$

b)

$\left(-\infty,-4\right)\cup\left(-2,\infty\right)$

c)

$x=\left\{\ \ \ \right\}$

d)

all real numbers

51.

a)

b)

c)

d)

52.

a)

b)

c)

no solution

d)

infinite solutions

53.

a)

Infinitely Many Solutions

b)

No Solution

54.

What is the solution to this system? Solve by substitution.
y= 4x + 3
2x - 3y = 21

a)

(3,-9)

b)

(-3,-9)

c)

(-3,9)

d)

(0,1)

55.

Match the following systems of equations with their solutions.

a)

( 3 , -1 )

1.

y = -x + 2 and y = 2x - 7

b)

( 7 , 7 )

2.

y = x + 0 and y = x + 7

c)

( -1 , 3 )

3.

y = x - 4 and y = -x + 2

d)

( 1 , 1 )

4.

y = 2x - 1 and y = x + 0

56.

What is the solution to this system of equations? Solve by substitution or graphing.

a)

(7, -8)

b)

(-7, 8)

c)

(-7, -8)

d)

(7, 8)

57.

Match the following points with the slope of the line passing through them.

a)

0

1.

(2, 3) and (5, 3)

b)

Undefined

2.

(4, 2) and (4, 5)

c)

-1

3.

(1, 2) and (3, 0)

d)

1

4.

(-3, -4) and (7, 6)

58.

Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0

a)

(−6, −4)

b)

Infinite number of solutions

c)

(−6, 10)

d)

(6, 4)

59.

When does a system of equations have no solutions?

a)

When the lines cross

b)

When slopes of the lines are different

c)

When the slopes are the same

d)

There is ALWAYS a solution sir!

60.

Two equations that produce the same line have _____ solution(s).

a)

no

b)

one

c)

infinitely many

61.

At the Wayne County bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

a)

t + n = 54

t = 3n + 8

b)

t + n = 54

n = 3t + 8

c)

t + n = 54

t = 3n - 8

d)

t + n = 8

t = 3n + 54

62.

Your family goes to Mississippi Fried for dinner. There are 6 people in your family. Some order the chicken fingers for $14.80, and some order the Deluxe Chicken Dinner for $17. If the total bill was $91, which system best represents the situation?

a)

x + y = 6

14.80x + 17y = 91

b)

x + y = 91

14.80x + 17y = 6

c)

x + y = 6

14.80y + 17x = 91

d)

x + y = 91

14.80x+ 17y = 6

63.

Which points are solutions to the system of inequalities. Select all that apply.

a)

(2,2)

b)

(0,0)

c)

(4,1)

d)

(0,1)

e)

(3,-1)

64.

Which points are solutions to the system of inequalities? Select all that apply.

a)

(0,0)

b)

(-1,1)

c)

(1,-1)

d)

(0,-4)

e)

(0,1)

65.

Which two inequalities make up the given system?

a)

$y<\frac{-1}{2}x+1$

b)

$y>\frac{-1}{2}x+1$

c)

$y\ge4x-4$

d)

$y\le4x-4$

66.

Which two inequalities create the system pictured?

a)

$y>\frac{1}{4}x+2$

b)

$y<\frac{1}{4}x+2$

c)

$y\le-3x+4$

d)

$y\ge-3x+4$

67.

find the value of a

a)

a=-5

b)

a=4

c)

a=5

d)

a=-4

68.

what is the value of y in the system

a)

y=3

b)

y=-1

c)

y=-4

d)

y=2

69.

Lizzy has 30 coins that total $4.80. All of her coins are dimes, D, and quarters, Q. Which system of equations models this situation?

a)

D + Q = 4.80

0.10D + 0.25Q = 30

b)

D + Q = 30

0.10D + 0.25Q = 4.80

c)

D + Q = 30

0.25D + 0.10Q = 4.80

d)

D + Q = 4.80

0.25D + 0.10Q = 30

70.

The perimeter of a rectangle is forty inches. The length is two inches more than three times the width.

a)

2L + 2w = 40

L = 3w + 2

b)

2L + 2w = 40

w = 3L + 2

c)

2L + 2w = 40

L = 2w + 3

d)

2L + 2w = 40

w = 2L + 3

71.

x + y + z = 4
x = -2y
z = -3y
Solve the system.

a)

x = 2
y = -1
z = 3

b)

x= -5
y = 3
z = 1

c)

x = 10
y = -2
z = 0

d)

x= 4
y = 1
z = -1

72.

Which shape would you use this volume formula for?

a)

Spheres

b)

Cones

c)

Cylinders

d)

Prisms

73.

Find the volume

a)

960 cm³

b)

240 cm³

c)

960 cm ²

d)

1920 cm³

74.

What is the volume of a sphere with the radius of 4 inches ? Use 3.14 for pi.

a)

561.5 in³

b)

267.9 in³

c)

201 in³

d)

803.8 in³

75.

Find the value of x.

a)

18°

b)

28°

c)

38°

d)

118°

76.

Angle 3 and Angle 6 are examples of which type of angle pair?

a)

Alternate exterior angles

b)

Alternate interior angles

c)

Vertical angles

d)

Corresponding angles

77.

a)

x = 118

b)

x = 108

c)

x = 28

d)

x = 58

78.

Vertical angles are always

a)

acute

b)

total 180 degrees

c)

congruent (equal measures)

d)

adjacent angles

79.

What is the area of this triangle?

a)

14.494 meters squared

b)

108.184 meters squared

c)

54.092 meters squared

d)

54.35 meters squared

80.

The area of the trapezoid is (a)

Choose from the below words

41

45

44

43

81.

What is the area of this triangle?

a)

35 units²

b)

30 units²

c)

70 units²

82.

Find the area:

a)

104.5 units²

b)

120 units²

c)

80.5 units²

d)

2400 units²

83.

Match the following triangles with their areas:

a)

20 cm²

1.

Base = 5 cm, Height = 8 cm

b)

56 cm²

2.

Base = 8 cm, Height = 14 cm

c)

28 cm²

3.

Base = 8 cm, Height = 7 cm

d)

27 cm²

4.

Base = 9 cm, Height = 6 cm

84.

A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun.

a)

34 degrees

b)

56 degrees

c)

72 degrees

d)

15 degrees

85.

Given the illustrations above, determine the angle of elevation

a)

JK

b)

JL

c)

KL

d)

S

86.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

c)

An 8 foot ramp leans
against a building 5 feet away. What angle does the ramp make with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

87.

Match the following

a)

Sin Z

1.

$\frac{12}{13}$

b)

Cos Z

2.

$\frac{5}{13}$

c)

Tan Z

3.

$\frac{12}{5}$

d)

Tan X

4.

$\frac{5}{12}$

e)

Area of the triangle

5.

120

88.

Match the following

a)

Sin Z

1.

$\frac{9}{41}$

b)

Cos Z

2.

$\frac{40}{41}$

c)

Tan Z

3.

$\frac{9}{40}$

d)

Area of the triangle

4.

180

e)

Tan X

5.

$\frac{40}{9}$

89.

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

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

90.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

91.

a)

A

b)

B

c)

C

d)

D

92.

Factor completely: 3x²-36x+96

a)

(x-4)(x-8)

b)

3(x-4)(x-8)

c)

3(x+1)(x+32)

d)

3(x-2)(x+16)

93.

Factor completely: 49x²+28x+4

a)

(49x+4)(x+1)

b)

(7x+2)²

c)

(7x+1)(7x+4)

d)

(7x-2)²

94.

Which of the following is a difference of perfect squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

95.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

96.

What is the first step in solving
(x + 2)(x - 3) = 0 ?

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

97.

Which formula is used to factor the difference of squares?

a)

a² - b² = (a + b)(a - b)

b)

a² - b² = (a² + b²)

c)

a² - b² = a - b

d)

a² - b² = (a - b)(a + b²)

98.

Factor $27x^3-1$ using the difference of cubes formula.

a)

$(3x-1)(9x^2-3x+1)$

b)

$(3x-1)(9x^2+3x+1)$

c)

$(27x-1)(x^2+x+1)$

d)

$(3x^2-1)(9x+1)$

99.

What is the factored form of $x^3+8$ ?

a)

$(x+2)(x^2-2x+4)$

b)

$(x+2)(x^2+2x+4)$

c)

$(x^3+2)$

d)

$(x+2)(x+4)$

100.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

101.

Factor the difference of two perfect cubes: 125x³ - 1

a)

(5x - 1)(25x² - 5x + 1)

b)

(5x + 1)(25x² + 5x + 1)

c)

(5x + 1)(25x² - 5x + 1)

d)

(5x - 1)(25x² + 5x + 1)

102.

1. P4 - A rectangular prism is subdivided into four smaller rectangular prisms as shown. The volumes of the smaller prisms are given below. Match them with their side measurements.

a)

$V=4x^2$

1.

$s^3=4\cdot x\cdot x$

b)

$V=2x^2$

2.

$s^3=2\cdot x\cdot x$

c)

$V=8x$

3.

$s^3=2\cdot4\cdot x$

d)

$V=x^3$

4.

$s^3=x\cdot x\cdot x$

103.

A. P7 - The steps and their justifications for factoring the polynomial $4x^3+8x^2-9x-18$ by grouping are shown. Reorder the factoring steps into the correct order.

a)

$4x^3+8x^2-9x-18$

b)

$\left(4x^3+8x^2\right)+\left(-9x-18\right)$

c)

$4x^2\left(x+2\right)-9\left(x+2\right)$

d)

$\left(4x^2-9\right)\left(x+2\right)$

e)

$\left(2x+3\right)\left(2x-3\right)\left(x+2\right)$

1)

2)

3)

4)

5)

104.

Factor completely:

8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

105.

Factor completely:

64x³+125

a)

(4x+5)(16x²-20x+25)

b)

(4x-5)(16x²+20x+25)

c)

(4x-5)(4x²+20x-25)

d)

(4x-5)(4x²+20x+25)

106.

A rectangle has an area of 2x² – 19x +45 ft². What are the dimensions of the rectangle?

a)

(2x - 9)(x - 5)

b)

(2x + 9)(x + 5)

c)

(2x - 5)(x - 9)

d)

(2x - 5)(x + 9)

107.

A rectangle has an area of 4x²+19x + 12 and a length of (x + 4). What is the width?

a)

4x - 3

b)

4x + 3

c)

2x + 6

d)

2x + 3

108.

Which of the following is a factor of
4n²-17n-15?

a)

n+5

b)

4n-5

c)

4n-3

d)

4n+3

109.

Which of the following is a factor of 3x² - 7x + 2?

a)

x - 1

b)

x - 2

c)

3x - 2

d)

3x + 1

110.

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

111.

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)

112.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

113.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

114.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

115.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

116.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

117.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

118.

What does the quadratic function that has a vertex of (3,4) look like?

a)

y = a(x+3)² + 4

b)

y = a(x-3)² + 4

c)

y = -a(x+3) - 4

d)

y = a(x-3)² - 4

119.

What is the vertex form of a quadratic function?

a)

f(x) = 2a(x-h)² + k

b)

f(x) = a(x-h)² + k

c)

f(x) = (x+h)² + k

d)

f(x) = a(x-h) - k

120.

Convert f(x) = 3x²+ 6x - 5 to vertex form.

a)

f(x) = 3(x + 1)² - 8

b)

f(x) = 3(x - 1)² - 8

c)

f(x) = 3(x + 2)² - 8

d)

f(x) = 3(x - 2)² - 8

121.

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

122.

Find the equation of the figure shown.

a)

(x-5)² + (y-3)²= 25

b)

(x+5)²/4 + (y+3)²/9= 1

c)

(x-5)²/2 + (y-3)²/3= 1

d)

(x-5)²/4 + (y-3)²/9= 1

123.

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

124.

Classify the conic section.

a)

Circle

b)

Ellipse

c)

Line

d)

None of these

125.

Which is the equation of a circle with center (2, 1) that passes through (2, 4)?

a)

(x – 2)² + (y – 1)² = 9

b)

(x – 2)² + (y – 1)² = 3

c)

(x + 2)² + (y + 1)² = 9

d)

(x + 2)² + (y + 1)² = 3

126.

Is the hyperbola vertical or horizontal?

a)

Vertical

b)

Horizontal

127.

What is the radius of (x + 2)²+(y - 5)² = 5

a)

5

b)

25

c)

√5

d)

(-2,5)

128.

a)

(x - 3)²+ (y + 4)² = 9

b)

(x - 3)²+ (y + 4)² = 3

c)

(x)²+ (y)² = 9

d)

(x - 1)²+ (y + 1)² = 7

129.

a)

Vertical Ellipse

b)

Vertical Hyperbola

c)

Horizontal Ellipse

d)

Horizontal Hyperbola

130.

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

131.

What are the coordinates of the focus?

a)

(-9, 2)

b)

(-5, 2)

c)

(-7, 2)

d)

(-3, 2)

132.

What is the missing value for the coefficient in the equation?

$x-4=\ldots\left(y+1\right)^2$

a)

-3

b)

-12

c)

$-\frac{1}{12}$

d)

$-\frac{1}{3}$

133.

Which graph represents $\frac{\left(y-1\right)^2}{16}-\frac{\left(x+1\right)^2}{4}=1$

a)

b)

c)

d)

134.

Determine the equation of the hyperbola.

a)

$\frac{x^2}{4}-\frac{y^2}{1}=1$

b)

$\frac{x^2}{2}-\frac{y^2}{1}=1$

c)

$\frac{x^2}{4}+y^2=1$

d)

$\frac{x^2}{2}+y^2=1$

135.

What are the co-vertices of the given ellipse?

a)

$\left(5,\ -4\right)\ and\ \left(5,\ 2\right)$

b)

$\left(-2,\ -1\right)\ and\ \left(12,\ -1\right)$

c)

$\left(-1,\ -2\right)\ and\ \left(-1,\ 12\right)$

d)

$\left(-4,\ 5\right)\ and\ \left(2,\ 5\right)$

136.

Find the standard equation of the given ellipse

a)

b)

c)

d)

137.

Write the equation of the hyperbola with co-vertices at (4, 0) and (-4, 0) and foci at (0, 5) and (0, -5).

a)

b)

c)

d)

138.

Does this function represent Exponential Growth or Exponential Decay?
$f\left(x\right)\ =\ \frac{1}{2}\left(\frac{1}{4}\right)^x$

a)

Exponential Growth

b)

Exponential Decay

139.

(2²y³)⁵

a)

2⁷y⁸

b)

256y⁸

c)

1024y¹⁵

d)

None

140.

$\left(10m^4\right)^8$

a)

$10m^{12}$

b)

$10^8m^{12}$

c)

$10^8m^{32}$

d)

$10m^{32}$

141.

$\left(4x^2y^3z\right)^3$

a)

$4x^5y^3z^3$

b)

$4^3x^5y^6z^3$

c)

$4x^6y^9z^3$

d)

$4^3x^6y^9z^3$

142.

a)

x¹²y³⁰

b)

1/(x⁴y)

c)

1/(x^-8y^-11)

d)

x⁸y¹¹

143.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

144.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

145.

Expand

a)

A

b)

B

c)

C

d)

D

146.

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

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

147.

6^-3x=216

a)

x=3

b)

x=-1

c)

x=6

d)

x=-3

148.

What is the formula for simple interest?

a)

A=P(1+r)^t

b)

I=Prt

c)

I=P(1+r)t

d)

A=Prt

149.

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)

150.

a)

√3/3

b)

√3

c)

1

d)

undefined

151.

The reciprocal of cosine is

a)

sine

b)

secant

c)

cosecant

d)

cotangent

152.

The reciprocal of tangent is

a)

secant

b)

cosecant

c)

cotangent

Trigonometric Ratios and Functions

Total questions: 152

Worksheet time: 37hrs 31mins

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