UNIT 2: TEST REVIEW

# 1. The volume of a sphere is 100 cm3. Find the diameter of the sphere. We need to find the radius and multiply by 2. d = 2.88 • 2 = 5.76

Find the volume of Cylinder A: The volume of Cylinder B is the same: # 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? Find the volume of Cylinder A: The volume of Cylinder B is the same: h = 21.3

x = amt. of miles .05 x + 30 ≤ 80 .05 x ≤ 50 5 x ≤ 5000 x ≤ 1000 # 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 ≤ 50 5 x ≤ 5000 x ≤ 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. 5 mi 2 mi Jack’s house 2 mi d 3 mi 5 mi Sally’s house 1 mi downtown (a.) Find the distance between their houses. Round answer to the nearest tenth. d2 = 22 + (5 + 2)2 d2 = 53 d2 = 4 + 72 d2 = 4 + 49 d = 7.3

Mary’s house: is ½ (7.3) = 3.65 miles between Jack’s and Sally’s house # 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. I and III have the same solution. Which of the following equations have the same solution? Explain. I and III have the same solution. I. x + 3 = 5 x – 4 - 4 x = - 7 x = 7/4 II and IV have the same solution. II. 2 x + 8 = 5 x – 3 - 3 x = - 11 x = 11/3 V and VI have the same solution. III. 10 x – 8 = 2 x + 6 x = 14/8 = 7/4 8 x = 14 IV. 2(x + 4) = 19 – x x = 11/3 2 x + 8 = 19 – x 3 x = 11 V. x – 3 = 5 x + 4 - 4 x = 7 x = - 7/4 VI. 10 x + 6 = 2 x – 8 8 x = - 14 x = - 14/8 = - 7/4 VII. 0.3 x + 10 x = 12 x – 0.4 3 x + 100 x = 120 x – 4 - 17 x = 4 x = - 4/17

Find the mistake(s) in the following problem (if any). # 7. Find the mistake(s) in the following problem (if any). 10 – (2 x + 6) = 12 10 – 2 x + 6 = 12 16 – 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

Too tall both vertical and diagonal # 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

If 2 (x – 5) = x + 5, what is the value of # 10. If 2 (x – 5) = x + 5, what is the value of - 3 x – 2? 2 (x – 5) = x + 5 2 x – 10 = x + 5 x – 10 = 5 x = 15 - 3 (15) – 2 = - 45 – 2 = - 47

Solve for the given variable: # 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 b a = - c – 4 b

Solve for the given variable: # 12. Solve for the given variable: a • • a y = 12 a – 2 x 3 2 x + 3 y = 12 a - 2 x - 2 x 3 y = 12 a – 2 x 3 3

Solve for the given variable: # 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 y 2 2 12 + 3 y 2 x =

# 15. We will the formula d = rt. Smaller plane distance = 400 • t 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 • t Larger plane distance = 600 • (t – 1) When they are beside each other, their distances are equal. - 200 t = - 600 400 • t = 600 (t – 1) t = 3 400 t = 600 t – 600 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 hour Jack’s speed: 10560/5280 miles • 4 = 2 • 4 miles per hour = 8 miles per hour Jane ran 1 mile per hour faster.

# 17. x = first integer x + 2 = second integer x + 2 = 2 x – 4 Find two consecutive even integers such that the larger is four less than twice the smaller. x = first integer x + 2 = second integer x + 2 = 2 x – 4 The integers are 6 and 8. - x + 2 = – 4 - x = – 6 x = 6

Find two consecutive integers such that their product is 110. # 18. Find two consecutive integers such that their product is 110. x = first integer x = - 11 or x = 10 x + 1 = second integer x(x + 1) = 110 The integers are – 11, and – 10 or 11 and 10. x2 + x = 110 x2 + x – 110 = 0 (x + 11) (x – 10) = 0

# 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. 51 2 x + 3 x2 + (2 x – 3)2 = (2 x + 3)2 2 x – 3 x2 + 4 x2 – 12 x + 9 = 4 x2 + 12 x + 9 45 5 x2 – 12 x + 9 = 4 x2 + 12 x + 9 x2 – 24 x = 0 x = smaller leg x (x – 24) = 0 24 {0, or 24}