wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

Spring Semester 2022 Long Test - Geometry

Total questions: 50

Worksheet time: 3hrs 32mins

Name
Class
Date
1.

1. Write the equation of the circle.

a)

(x+1)2 + (y +1)2 = 3

b)

(x+1)2 + (y +1)2 = 9

c)

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

d)

(x-1)2 + (y -1)2 = 9

2.

In the equation (x-4)2+(x-3)2=25, the radius is

a)

3

b)

4

c)

5

d)

25

3.

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

4.

What is the center and radius of the circle with the equation x2 + y2 - 4x + 10y + 13 = 0?

a)

Center (2,5) r = 4

b)

Center (-2,5) r = 16

c)

Center (-2,-5) r = 16

d)

Center (2,-5) r = 4

5.

What must be done to show that quadrilateral CARE is a trapezoid and prove that two sides are parallel and the other two are nonparallel

a)

Use distance formula to calculate length of all four sides.

b)

Calculate the slopes of all four sides.

c)

Calculate the midpoint of the sides.

d)

Calculate the slopes of the diagonals.

6.

To prove that parallelogram JKLM is a rhombus, given the coordinates of its vertices, Aleia decided to show that one set of consecutive sides are congruent. To do so, which calculation must she perform?

a)

Find the length of 2 consecutive sides

b)

Find the length of all 4 sides

c)

Find the slope of two consecutive sides

d)

Find the length of two opposite sides

7.

To prove that quadrilateral ABCD is a parallelogram given the coordinates of its vertices, Matt decided to show that both pairs of opposite sides are parallel. To do so, which calculation must he perform?

a)

Find the slope of 2 sides

b)

Find the slope of the diagonals.

c)

Find the slope of all 4 sides.

d)

Find the length of all 4 sides.

8.

Write an equation of a line that passes through the point (5,-1) and is parallel to the line y = (-3/5)x -3

a)

y = (-3/5)x + 2

b)

y = (3/5)x + 2

c)

y = (-3/5)x -2

d)

y = (5/3) + 2

9.

Write an equation of a line that passes through the point (-9,2) and is perpendicular to the line y = 3x - 12

a)

y = (-1/3)x - 1

b)

y = -3x + 12

c)

y = (1/3)x - 2

d)

y = 3x - 1

10.

Given triangle ABC as shown with B(-3,-1), U(-3,3) and G(4,1). Find the area of triangle BUG.

a)

6 square units

b)

12 square units

c)

14 square units

d)

28 square units

11.

Given a parallelogram PQRS with P(-4,-2), Q(-2,3), R(4,3) and S(2,-2), find its area. (Use the formula A = b x h)

a)

22 square units

b)

30 square units

c)

32.31 square units

d)

64.62 square units

12.

A grid overlay is placed over a kite as shown at the right. Based upon the grid, find the perimeter of the kite to the nearest tenth of a unit.

a)

24.8 units

b)

25.3 units

c)

26.0 units

d)

30.2 units

13.

A can of chili has a radius of 5.25 cm and a height of 13 cm. Use 3.14 for π. Round answers to the nearest tenth if necessary. Find the volume.

a)

3012.4 cm 3

b)

1125.1 cm 3

c)

1456.9 cm 3

d)

2034.5 cm 3

14.

A cylindrical tank has a volume of 628 inches cubed. The height of the tank is 8 inches. What is the area of the base?

a)

78.5 in2

b)

9.8125 in2

c)

785.5 in2

d)

70.5 in2

15.

Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. How many cubic inches of soda are contained in a full can?

a)

12.0

b)

75.4

c)

24.0

d)

18.8

16.

Choir is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches.


Which equation can be used to find the volume of the container?

a)

V = π(9)

b)

V = π(9)2(32)

c)

V = π(4.5)2(32)

d)

V = π(4.5)(32)

17.

Find the volume of the cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

a)

124.6 in3

b)

97.5 in3

c)

78.9 in3

d)

87.9 in3

18.

Find the volume of the figure. Round to the nearest tenth.

a)

128.6 units³

b)

401.9 units³

c)

1,286.1 units³

d)

5,144.6 units³

19.

What is the volume of the following triangular prism?

a)

1120 cubic ft

b)

560 cubic ft

c)

373.3 cubic ft

d)

186.6 cubic ft

20.

A snack bar sells popped popcorn in cone-shaped containers. One container has a diameter of 8 inches and a height of 10 inches. How many cubic inches of popped popcorn does one container hold?

a)

502.7 in3

b)

261.8 in3

c)

167. 6 in3

d)

83.7 in3

21.

Find the volume.

a)

75 in3

b)

298.7m3

c)

62.4m3

d)

51.3 in3

22.

You pour water from a full disposable conical cup into your mouth. How much water are you drinking?

a)

168.1 cm3

b)

4712.4 cm3

c)

28.1 cm3

d)

513,333.3 cm3

23.

If S denotes the number of students who take a certain sports, what is S'?

a)

24

b)

25

c)

23

d)

26

24.

The event that includes all the outcomes that are both in the two events.

a)

intersection of events

b)

complement of an event

c)

union of events

d)

independent events

25.

F denotes the number of students who take a foreign language, and S the number of students who take a certain sports, what is the union of F and S?

a)

14

b)

37

c)

24

d)

47

26.

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(orange,green)

a)

1/15

b)

3/31

c)

2/15

d)

1/5

27.

Find the probability of flipping a heads on a coin, and then getting the color yellow on a spinner with 6 colors.

a)

1/12

b)

3/7

c)

2/9

d)

7/19

28.

Lisa flipped the same coin 3 times. What is the probability she obtained all tails?

a)

1/2

b)

1/16

c)

1/4

d)

1/8

29.

A new credit card has been issued to 2000 customers. Of these customers, 1500 hold a Visa, 500 hold a Mastercard, and 40 hold a Visa and Mastercard. Find the probability that a random chosen customer holds a Mastercard, given they hold a Visa.

a)

.0267

b)

.02

c)

37.5

d)

.3333

30.

The weather forecaster predicted it will be 4/5 chance of rain for Monday and 2/3 chance of rain for Tuesday. What is the probability it will rain both days?

a)

1/2

b)

8/15

c)

20/15

d)

6/8

31.

A coin and a number cube with the numbers 1 through 6 are tossed. What is the probability of the coin showing tails and the number cube showing an even number?

a)

1/12

b)

1/8

c)

1/4

d)

3/4

32.

You flip a coin and roll a die. What is the probability, in a fraction, you flip a heads and roll a 5 or 6?

a)

1/6

b)

1/12

c)

1/2

d)

1/8

33.

There are 125 juniors at the high school. How many ways can they elect a president, vice president,and secretary?

a)

1,906,500

b)

375

c)

317,750

d)

1,953,125

34.

In the orchestra, there are eight violinists in the front row. How many different ways can they be seated?

a)

40,320

b)

64

c)

1

d)

8

35.

There are 12 kinds of Girl Scout cookies for sale. How many ways can Rachel choose three different kinds to buy?

a)

220

b)

1320

c)

36

d)

100

36.

A restaurant offers four appetizers, nine entrees,and three desserts. How many different ways can Angela choose a three course meal?

a)

36

b)

108

c)

100

d)

27

37.

Two lines that are perpendicular lines have ...

a)

Slope that is opposite reciprocals

b)

No Slope

c)

Slope that is the same

d)

none of the above

38.
y = 3x +2
y = 3x - 3
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
d)
The same line
39.
Which of the coordinates given could be the fourth point used to form a rectangle?
a)
(3, -6)
b)
(-3, -6)
c)
(-6, 3)
d)
(4, -6)
40.

What is the perimeter of a rectangle with corners at (2,2), (2,-4), (-5,-4), and (-5,2).

a)

13 units

b)

26 units

c)

42 units

d)

10 units

41.
What is the surface area of this figure?
a)
3000 cm 2
b)
164 cm 2
c)
236 cm 2
d)
328 cm 2
42.

What is the measure of the indicated arc?

a)

70

b)

140

c)

35

d)

90

43.
Find the measure of arc AB.
a)
17
b)
34
c)
68
d)
146
44.

What is the measure of angle K and angle M?

a)

mK=100    &   mM=100m\angle K=100\ \ \ \ \&\ \ \ m\angle M=100

b)

mK=50    &   mM=50m\angle K=50\ \ \ \ \&\ \ \ m\angle M=50

c)

mK=100   &   mM=50m\angle K=100\ \ \ \&\ \ \ m\angle M=50

d)

mK=50   &   mM=100m\angle K=50\ \ \ \&\ \ \ m\angle M=100

45.
Find m∠PRQ.
a)
39°
b)
90°
c)
51°
d)
15°
46.

What is m∠LMO?

(Segment LO is a diameter of Circle P)

a)

30°

b)

45°

c)

180°

d)

90°

47.

Find the value of x

a)

100

b)

105

c)

95

d)

90

48.
What is the probability that the person picked will be a boy given they speak german? 
a)
.7273
b)
.4
c)
.16
d)
.22
49.
What is the probability that a female is chose given they like a Toyota? 
a)
.525
b)
.4627
c)
.6774
d)
.3143
50.
There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color?
a)
2/5
b)
1/21
c)
4/25
d)
1/7