Math 421K

Final exam Review January 2017

Chapter 1

1. If a store sells 2L containers of milk for $2.46 what is the unit price of the milk?a. $0.81/L b. $0.46/L c. $1.23/L d. $4.92/L

2. The regular price of a hockey stick is $85. What is the sale percentage if the stick goes on sale for $63.75?

a. 25% b. 30% c. 35% d. 40%

3. Pure gold can be purchased for $40.13/1 g. If you buy a gold ring with a weight of 17.8 g, what will you have to pay for the ring?

a. $2.25 b. $714.31 c. $0.40 d. $22.33

4. If the exchange rate is (C$1 = US$0.87), how much American money could you get for C$850?a. $977.01 b. $850.00 c. $1.15 d. $739.50

5. If (1km = 1000m), how many kilometers have you gone if you walk 1250m?a. 0.80km b. 1.25km c. 125km d. 12.5km

6. If you buy a package of 3 golf balls for $12.95 which is the correct unit price?a. $4.32 b. $4.31 c. $4.316 d. $4.30

7. If your car can hold 55L of fuel, how many gallons will you need to fill your fuel tank in the United States? ( 1 gal = 3.79 L )

a. 209 gal b. 55 gal c. 14.00 gal d. 14.47 gal

8. Convert 28⁰C into Fahrenheit.a. 82.4⁰F b. 47.6⁰F c. 108⁰F d. 37.5⁰F

Part B: Complete each of the following questions. Please show your work as that is where most of the marks come from.

1. What is the unit price of a 3.5kg bag of oranges if it costs $2.75

2. A store sells granola bars in packs of 16 for $4.19. You can also buy the bars in packs of 8 for a cost of $2.80. Calculate the unit price of each pack and state which is the best buy.

3. At the Bulk Barn you can buy suckers for $1.12/100g. If a bag weighs 450g how much will it cost?

4. If you have US$325, how much will you have in C$ if the exchange rate is (US$1 = C$1.32) ?

5. Convert each of the following measurementsa. 6 gallons = ? L (1 gal = 3.79 L)

b. 70 kg = ? lbs (1 kg = 2.20 lbs)

c. The average overpass on the highway is 4.5 m high. How many feet is this? (1 m = 3.28 ft)

6. Convert 72⁰F into the Celsius scale.

Chapter 2

1. How many centimeters are in 4’ 3”? (1 in = 2.54cm) (1 ft = 12 in)a. 51cm b. 129.54cm c. 121.92cm d. 20.08cm

2. The average badminton racket is 670 mm in length. How many meters is this?(k, h, da, m, d, c, m)

a. 0.670 m b. 6.67 m c. 67.0 m d. 6700m

3. What is the perimeter of this figure?

a. 17.5 in b. 9.5 in c. 19 in d. 16.5 in

4. Which circle has a circumference of 18.8 m? (C= πd) (C=2πr)

a. b. c. d.

5. Convert 5 yards to feet. (1 yd = 3 ft)a. 1.67 ft b. 0.60 ft c. 15 ft d. 8 ft

Part B: Work must be shown for the problems to receive full marks. Make sure you read the instructions for each question.

1. Express each number in feet and inches (1ft = 12in)

a. 77 in

b. 4ft 3in + 42 in

2. A training wall for rock climbers is 48 ft tall. If a new package of safety rope is 18 yards long, will it reach the top of the climbing wall? (1 yd = 3 ft)

a. Find the perimeter of the following figure. (not to scale)

3. A construction worker needs to cut two pieces of wood. One is 14 ½ inches in length. The other is 25 ¼ inches. What is the total length of the two pieces of lumber?

4. Convert each of the following distances to the required units.Remember to use (k h da m d c m)

a. 63.45 km = ___________ hmb. 22.7 m = ___________ cmc. 357 mm = ___________ md. 0.632 hm =_____________ cme. 347600 cm = ____________ km

5. A regulation baseball bat is 106.68cm in length. Express this in feet and inches. (2.54 cm = 1 in) (1 ft = 12 in)

6. The concrete support at the base of the CN Tower is in the shape of a circle. The radius of the support is 43.5 ft. What is the circumference of the support of the tower? (C = πd) (C = 2πr)

Base of tower

Chapter 3

1. The base of a lighthouse has a diameter of 14.5 m. What is the surface area at the base? (SA = πr2)

a. 7.25 m2 b. 22.78 m2 c. 165.1 m2 d. 660.5 m2

2. Calculate the surface area of the following field. (SA = l x w)

a. 588 m2 b. 408 m2 c. 98 m2 d. 308 m2

3. Calculate the surface area of the following cylinder.(SA = 2πr2 + 2πrh)

a. 659.7 in2 b. 1847.3 in2 c. 307.9 in2 d. 923.6 in2

4. The front door of a house is 3.5 ft wide and is 7 ft high. What is the surface area of the door? (SA = l x w)a. 24.5 ft2 b. 10.5 ft2 c. 12.25 ft2 d. 21 ft2

5. Find the surface area of this circle.(SA = πr2)

a. 1385.4 yd2 b. 66.0 yd2 c. 346.4 yd2 d. 33.0 yd2

Part B: Work must be shown for the problems to receive full marks.

1. The jib sail on a sailboat is in the shape of a triangle. For a certain boat the sail must have the following dimensions. Calculate the area of cloth that is needed to make the sail (SA = b x h ) 2

2. A community hockey rink is going to be used to host a hockey training camp. Find the surface area of the rink. (SA = l x w) (SA = πr2)

3. What is the minimum area of paper required to wrap this object? (SA = 2(lw + lh + hw))

4. What is the area of the following shape? (SA = l x w) ( SA = πr2)

5. What is the surface area of this L-shaped room? (SA = l x w)

6. Calculate the surface area of this cylinder (SA = 2πr2 + 2πrh)

Chapter 4

1. Which statement is correct?a. Hourly wage x 1.5 = net payb. Gross pay – deductions = net payc. Hourly wage x hours worked = net payd. Gross pay + vacation pay = net pay

2. What method of payment always pays the same amount each year?

a. commission b. hourly wage c. salary d. tips

3. Jack sells cars at a Mazda dealership. If he sells $43 584 of product this month, what will his commission pay be if he earns 5% of sales?

a. $2179.20 b. $41404.80 c. $8716.80 d. $217920

4. Erin notices her gross pay is $843.42. At the bottom of her pay stub she finds her net pay is $684.75. Calculate the deductions taken from Erin.

a. $684.75 b. $1528.17 c. $843.42 d. $158.67

5. Laura works for an investing business. Her normal rate of pay is 22.75 per hour. When she works overtime her employer offers her time and a half. What is Laura’s rate of pay when she works overtime?

a. $45.50/hr b. $11.38/hr c. $34.13/hr d. $22.75/hr

Part B: Show your work for the following problems. Full marks will only be awarded when work is shown.

1. Carly babysits for her neighbor. At the end of one evening, she is paid $50.75. If she babysat for 3.5 hours, how much did she earn each hour? (2 marks)

2. A restaurant server’s regular hourly wage is $10.50/hr, plus tips. If she works 30 hours this week and earns $200 in tips, what is his gross weekly pay? (3 marks)

3. Terry examines his hours for this month. (5 marks)Week 1: 43 hours Week 2: 40 hoursWeek 3: 38 hoursWeek 4: 42 hours

His regular hourly wage is $14.50/hr. If he works more than 40 hours in 1 week, he receives time-and-a-half for his overtime hours. Calculate Terry’s gross pay for the month.

4. George earns an hourly wage of $19.75/hr. He earns double time for overtime hours. This week, he worked 40 regular hours and 5.5 overtime hours.

a. What is George’s gross weekly pay? (5 marks)

b. The deductions from his pay total $160.85. What is his weekly net pay? (2 marks)

5. Jessica earned $950 gross last month. Her deductions were ● CPP: 4.95%● EI: 1.73%●Taxes: 22.7%

a. Find Jessica’s total deductions. (4 marks)

b. Calculate Jessica’s net pay. (3 marks)

6. A saleswoman at a clothing store earns 3% of sales, plus an hourly wage of $13.25/hr. Last week, she worked 38 hours and sold $2740 worth of clothing. What is her gross pay for last week? (5 marks)

Chapter 5

1. What is the angle of the bisector for the 34⁰ angle below?

a. 34⁰ b. 17⁰ c. 68⁰ d. 24⁰

2. Identify the transversal in the following diagram.

a. AB b. CD c. EF d. There is no transversal

3. Determine the unknown measure of angle “x”.

a. 125⁰ b. 180⁰ c. 360⁰ d. 55⁰

4. Which pair of angles are opposite angles?

a. ∠B and ∠C b. ∠B and ∠D c. ∠A and ∠C d. ∠A and ∠B

5. Find the measure of ∠F.

a. 115⁰ b. 180⁰ c. 25⁰ d. 65⁰

6. Select the correct relationship between line AB and line CD.

a. Parallel b. Transversal c. Perpendicular d. There is no relationship

7. What is the complementary angle to a 30⁰ angle?

a. 60⁰ b. 150⁰ c. 330⁰ d. 210⁰

Part B: Show your work for the following problems. Make sure to clearly state any relationship used to find the answer if asked to do so.

1. Using a ruler , sketch a pair of parallel lines. Make sure to indicate they are parallel. (2 marks)

2. Determine the measure of each of the following angles. Extend the lines with a ruler if necessary. Also, identify the type of angle. (4 Marks)

a. Angle:___________________

Type of angle:___________________

b.

Angle:_____________________

Type of angle:______________________

3. With the aid of a protractor, draw each angle stated. Indicate the angle and measured arc. Make sure the angle is drawn as accurate as possible. (6 marks)

a. 74⁰

________________________________________________

b. 200⁰

_________________________________________________

*Do not use a protractor for the following problems. Use angle relationships to determine the answers.

4. Determine the measure of angle “X”. State the relationship between the two angles. (3 marks)

5. Determine the measure of angle “X”. State the relationship between the two angles. (3 marks)

6. Determine the measure of angle “X”. State the relationship between the two angles. (3 marks)

7. If angle “A” is found to be 117⁰ find the measure of each angle asked below. (4 marks)

a. ∠B = __________⁰ b. ∠D = _________⁰ c. ∠H = _________⁰ d. ∠G =_________⁰8. Look at the following diagram. Determine if the lines with a transversal passing through them

are parallel or not parallel. Explain how you know the answer. Make sure you state the relationship used to make your decision. (3 marks)

*Use a protractor for this question

9. Construct a 70⁰ angle using a protractor. Once the angle is made, bisect the angle and draw the angle bisector. Indicate the angle of the bisector when finished. (3 marks)

Chapter 6

Pythagorean Formula: (A2 + B2 = C2) (B2 = C2 - A2)

Part A: Multiple choice questions: (1 mark each)

1. Identify the hypotenuse in the following triangle.

a. Side 1 b. Side 2 c. Side 3 d. There is no hypotenuse

2. Find the length of the missing side.

a. 436 b. 20.9 c. 11.3 d. 128.48

3. Identify the right triangle below.

a. b. c. d.

4. Find the value of the missing side that will make angle x be a 90⁰ angle.

a. 625 b. 175 c. 13.2 d. 25

x

5. Find the value of side x.

a. 5.9 b. 16.6 c. 25.3 d. 62.4

6. The measurements of a corner are given below. Find the length of the missing side which makes the corner “square”.

a. 6.3 in b. 28.0 in c. 21.9 in d. 14.4 in

7. Find the diagonal distance across a field with the following dimensions.

a. 137.8 yds b. 110.7 yds c. 67 yds d. 183 yds

8. The edge of a roof is 21 feet from the ground. What length of ladder would be able to reach the edge of the roof it the base is placed 8 feet from the side of the house?

a. 19.4 ft b. 20 ft c. 21 ft d. 22.5 ft

Part B: Show your work for the following questions. Round answers to one decimal place.

Pythagorean Formula: (A2 + B2 = C2) (B2 = C2 - A2)

1. Find the missing side of each triangle. (4 marks each)

a.

b.

2. A vehicle’s hatch opening measures 112 cm high and 158 cm wide. Will a round table with a diameter of 185 cm fit in the hatch? ( 5 marks)

3. Mr. Scully wants to buy a television that will fit in a 60” wide opening. Suppose he buys a television off of Kijiji that has a diagonal measurement of 72” and is 42” tall. Will the television fit? Assume the corners of the television are right angles. (5 marks)

4. Check if the following triangles contain a right angle. ( 3 marks each)

a.

b.

5. In baseball, the bases are 90 ft apart. If player x catches the ball halfway between the second and third base, how far is the throw from where they are standing to first base? (6 marks)