# 1.

The volume of a sphere is 100 cm3. Find the diameter of the

sphere. 3

3

4rV

We need to find the radius and multiply by 2.

433 V

r

3

4

3

V

r

3

)14.3(4

)100(3r

3

56.12

300r

3 89.23r

88.2r

d = 2.88 • 2 = 5.76

# 2.

Two cylinders have the exact volume. Cylinder A has a radius

of 4 in. and a height of 12 inches. What is the height of

cylinder B if it has a radius of 3 inches?

hrV 2Find the volume

of Cylinder A:)12()4( 2V

192)12)(16( V

The volume of Cylinder B is the

same:

192)()3( 2 hV

192))(9( h192))(9( h

h = 21.3

# 3.

A car rental charges $ 30 for a day plus 5 cents a mile. What is the most amount of miles John

can drive if he plans to spend no more than $ 80 for a car rental?

x = amt. of miles.05 x + 30 ≤

80.05 x ≤ 505 x ≤

5000x ≤ 1000

# 4.

Jack’s house is 3 miles north and 2 miles east of downtown. Sally’s house is 1 mile north and 5 miles

west of downtown.

(a.) Find the distance between their houses. Round answer to the

nearest tenth.

3 midowntow

n

2 mi

Jack’s house

1 mi

5 mi

Sally’s house

5 mi2

mi d

d2 = 22 + (5 + 2)2d2 = 4 + 72

d2 = 4 + 49

d2 = 53

53dd = 7.3

# 4.

Jack’s house is 3 miles north and 2 miles east of downtown. Sally’s house is 1 mile north and 5 miles

west of downtown. (b.) Mary’s house is exactly halfway between Jack’s and Sally’s houses. Find the location of Mary’s house.

Mary’s house: is ½ (7.3) = 3.65 miles between Jack’s and Sally’s

house

# 4.

(c.) Square ABCD has the coordinates (- 2, 3), (1, 5), (3, 2), and (0, 0).

Which is larger, perimeter or area? Explain your reasoning.

Area and perimeter are measured in two different units—cannot

compare.

# 5.

Chad is trying to save at least 400 dollars to buy a smart phone. Write the inequality that he could use to

find out how many weeks he needs to save if he earns 40 dollars a week. x = number of

weeks

40 x ≥ 400

# 6.

Which of the following equations have the same solution? Explain.

I. x + 3 = 5 x – 4

II. 2 x + 8 = 5 x – 3

III. 10 x – 8 = 2 x + 6

IV. 2(x + 4) = 19 – x

V. x – 3 = 5 x + 4

VI. 10 x + 6 = 2 x – 8

VII. 0.3 x + 10 x = 12 x – 0.4

- 4 x = - 7

x = 7/4

- 3 x = - 11

x = 11/3

8 x = 14 x = 14/8 = 7/4

2 x + 8 = 19 – x

3 x = 11

x = 11/3

- 4 x = 7

x = - 7/4

8 x = - 14 x = - 14/8 = - 7/4

3 x + 100 x = 120 x – 4

- 17 x = 4

x = - 4/17

I and III have the same solution.

II and IV have the same solution.

V and VI have the same solution.

# 7.

Find the mistake(s) in the following problem (if any).

10 – (2 x + 6) = 12 10 – 2 x + 6 = 1216 – 2 x = 12- 2 x = - 4 x =

2

# 8.

C x + 9 = x + 29. For what value of x makes this a true statement when C

is three?

3 x + 9 = x + 29

2 x + 9 = 29

2 x = 20

x = 10

# 9.

A door is 8 ft tall and 4 ft wide. Can a dining room table that is 10 ft tall get

through the door? Explain.

Too tall both vertical and

diagonal

# 10.

If 2 (x – 5) = x + 5, what is the value of

- 3 x – 2?

2 x – 10 = x + 5

2 (x – 5) = x + 5

x – 10 = 5

x = 15

- 3 (15) – 2 = - 45 – 2 = - 47

# 11.

Solve for the given variable:

3 a – 4 b = c + 4 a for a

3 a – 4 b = c + 4 a - 4 a- 4 a

- a – 4 b = c+ 4

b+ 4 b

- a = c + 4 ba = - c – 4

b

# 12.

Solve for the given variable:

yfora

yx12

32

1232

a

yxa • • a

2 x + 3 y = 12 a- 2 x - 2 x

3 y = 12 a – 2 x3 3

y = 12 a – 2

x3

# 13.

Solve for the given variable:

2 x – 3 y = 12 for x

2 x – 3 y = 12 + 3

y+ 3 y

2 x = 12 + 3 y2 2

x =

12 + 3 y2

# 15.

A smaller plane and a larger plane leave an airport and travel in the same

direction. The larger plane leaves 1 hour after the smaller plane and travels 600

miles per hour. The smaller plane travels 400 miles per hour. How long have they

traveled before they are next to each other?We will the formula d

= rt.Smaller plane distance = 400 • tLarger plane distance = 600 • (t – 1)When they are beside each other, their distances are equal.

400 • t = 600 (t – 1)400 t = 600 t – 600

- 200 t = - 600 t = 3 In 3 hours, they were beside each other.

# 16.

Jane ran 3 miles in 20 minutes. Jack ran 10,560 feet in 15

minutes. Who ran faster? By how many miles per hour?

There are 3 “20-minute” increments in 1 hour and 4 “15-minute” increments in 1 hour.

Jane’s speed: 3 • 3 = 9 miles per hourJack’s speed: 10560/5280 miles • 4 =

2 • 4 miles per hour = 8 miles per hourJane ran 1 mile per hour faster.

# 17.

Find two consecutive even integers such that the larger is four less than twice the smaller.

x = first integer

x + 2 = second integerx + 2 = 2 x – 4 - x + 2 = – 4 - x = – 6 x = 6

The integers are 6 and 8.

# 18.

Find two consecutive integers such that their product is 110.

x = first integer

x + 1 = second integer

x(x + 1) = 110

x2 + x = 110

x2 + x – 110 = 0(x + 11) (x – 10) = 0

x = - 11 or x = 10

The integers are – 11, and – 10 or 11 and 10.

# 19.

The hypotenuse of a right triangle is 3 more than twice the

smaller leg. The larger leg is three less than twice the smaller

leg. Find the length of the larger leg.

x = smaller leg

2 x + 3

2 x – 3 x2 + (2 x – 3)2 = (2 x + 3)2 x2 + 4 x2 – 12 x + 9 = 4 x2 +

12 x + 9 5 x2 – 12 x + 9 = 4 x2 + 12 x + 9 x2 – 24 x

= 0 x (x – 24) = 0

{0, or 24}24

45

51