Unit 1 Pretest #2

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. The slope of a bike jump is 1.9 and it rises 4 feet. What is the horizontal distance covered by this jump?

a. 2.1 ft c. 1.7 ftb. 0.5 ft d. 7.6 ft

____ 2. If the slope of a hill is 0.60, which of the following would be the rise and run?

a. rise = 6 m, run = 5 m c. rise = 3 m, run = 5 mb. rise = 6 m, run = 3 m d. rise = 4 m, run = 6 m

____ 3. A contractor is designing a roof that will have a 6:13 pitch, which means the roof will rise 6 feet for every 13 feet of horizontal distance. Which of the following diagrams would represent a 6:13 roof?

a.

8 ft24 ft

c.

5 ft

22 ft

b.

10 ft

24 ft

d.

6 ft

26 ft

____ 4. A ladder on the West Coast Trail hike on Vancouver Island, BC, has a slope of 16 over a run of 3 m. What is the vertical distance covered by the ladder?

a. 57.6 m c. 0.2 mb. 5.3 m d. 48.0 m

____ 5. A sloped skate rail starts at 3.5 feet from the ground and slopes down to 20 inches from the ground. The rail travels 8 feet horizontally. Which of the following calculations will give the correct value for slope?

a. c.–

b. d.–

____ 6. A drainage pipe has an angle of elevation of 2.3° over a distance of 118 feet. What is the rise in height of the pipe?

a. 4.74 ft c. 7.58 ftb. 5.69 ft d. 3.79 ft

____ 7. What is the percent grade of a hill that rises to an elevation of 1500 m with a run of 16 km?

a. 9.4% c. 93.8%b. 1.1% d. 7.1%

____ 8. A skateboard rail rises 5 feet over a run of 8 feet. What is the length of the rail?

a. 11.3 ft c. 8.5 ftb. 6.2 ft d. 9.4 ft

____ 9. What is the slope of mountain with a 9% grade?

a. 0.13 c. 0.34b. 0.08 d. 0.09

____ 10. A roof has a pitch of 6:13. If it rises 6 feet, how long is the surface of the roof to the peak?

a. 8.6 ft c. 17.2 ftb. 13 ft d. 14.3 ft

____ 11. The slope shown in the graph represents:

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

a. negative slope. c. undefined slope.b. zero slope. d. positive slope.

____ 12. Two points of data are plotted: point A is at (–1, –3) and point B is 5 units in the negative x direction. How would you describe the slope of this line?

a. undefined slope c. zero slopeb. negative slope d. positive slope

____ 13. What is the slope of a line that includes (4, 8) and (15, 23) as coordinates?

a. 32

c. 1511

b. 1115

d. 1411

____ 14. Amrit is studying for an exam, reading his textbook at a rate of 0.5 pages/minute. The exam covers a 42-page chapter. How long will it take him to finish reading the chapter?

a. 1.1 hours c. 109.2 minutesb. 1.4 hours d. 25.2 minutes

____ 15. Which of the following graphs shows the largest slope?

a.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y c.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

b.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y d.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Short Answer

1. The windmill trap on a mini-putt course includes a ramp that vanishes underground for 1.2 m. If the slope of the ramp is 0.5, what is the vertical distance the ball will descend?

2. A bird taking off from a pond gains 9 m of height over the 85 m of the pond. What is the slope of the bird’s flight?

3. An airplane takes off with an angle of elevation of 26°. If it must clear the 37-m tall tree at the end of its runway, what length of runway does the plane require?

4. Plot coordinate (–5, 3) and label it A. Draw an arrow pointing 7 unit(s) in the positive x direction, using a dotted line. From this point, draw another arrow 3 unit(s) in the negative y direction. Label the end as point B.

Draw a solid line between A and B.

Describe the slope of this line as positive, negative, zero, or undefined.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

5. Plot coordinate (–3, –4) and label it A. Draw an arrow pointing 0 units in the positive x direction, using a dotted line. From this point, draw another arrow 4 unit(s) in the positive y direction. Label the end as point B.

Draw a solid line between A and B.

Describe the slope of this line as positive, negative, zero, or undefined.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

6. Starting from the coordinate (–5, –5), draw a line with a slope of 12 .

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

7. A+ Caterers is tracking the popularity of their cheese puff appetizers at a community event. The graph below shows the number of cheese puffs on the tray over the course of the afternoon. Calculate the slope of this line.

1 2 3 4 5 6 Hours

15

30

45

60

75

90

105

Puffs

8. Joseph and Jolene are fraternal twins. Joseph is 80 cm tall at 4 years of age and 1.1 m tall at 10 years of age. Jolene is 80 cm tall at 5 years of age and 1.25 m tall at 9 years of age. Draw a rate of change graph showing Joseph and Jolene’s heights.

9. In an orienteering competition, two clues are located on the map at coordinates (–14, –36) and (15, 4). Each unit on the map represents 12 m. How far apart are these clues?

10. Starting from the coordinate (2, –1), draw a line with a slope of –14 .

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Problem

1. John is planning to book a roofing company to re-shingle his cottage, but he needs to tell them the pitch of his roof. His triangular roof is 32 feet wide and rises 9 feet.

a. What is the slope of John’s roof?

b. How many feet does John’s roof rise for every 8 feet of horizontal distance?

32 ft

9 ft

2. The staircase leading up to Lloyd’s front porch is 10 steps. The total rise is 1.52 m and the total run is 1.65 m. The steps are all built to identical dimensions.

a. What is the slope of the staircase?

b. What are the rise and run of each step, in millimetres?

b. What is the slope of each step?

3. A boardwalk along a lakeshore is built to slope towards the lake to allow for drainage. The boardwalk slopes 1.5 inches downward for every 3 feet of horizontal width.

a. How many inches of drop are there over the entire 13-foot width of the boardwalk?

b. What is the percent grade of this boardwalk?

4. A family returning from a camping trip have a 1000-km drive ahead of them. They will travel at an average speed of 70 km/h. The following equation shows their progress:

d = 1000 – 70h

In this equation, d is the distance remaining and h is the number of hours travelled.

a. What are the independent and dependent variables in this situation?

b. Create a table of values showing the distance remaining at 1-hour intervals, up to 6 hours.

Time travelled (h) Distance remaining (km)

c. Plot the data and calculate the slope of the line.

d. What does the slope represent?

5. Geoff used the GPS receiver on his phone to plot the corners of the tool shed he is building in his back yard.

a. Plot a graph showing the corners of his shed located at A(3, 3), B(7, 5), C(7, 4), and D(5, 2).

b. If the diagonals of his shed are equal, Geoff can verify that his corners are right angles. Calculate the lengths of AC and BD. Are the corners right angles?

Unit 1 Pretest #2Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: Moderate REF: 1.1OBJ: Algebra LOC: A-SO2 TOP: Rise Over RunKEY: slope

2. ANS: C PTS: 1 DIF: Moderate REF: 1.1OBJ: Algebra LOC: A-SO2 TOP: Rise Over RunKEY: slope

3. ANS: D PTS: 1 DIF: Difficult REF: 1.1OBJ: Algebra LOC: A-SO2 TOP: Rise Over RunKEY: slope

4. ANS: D PTS: 1 DIF: Moderate REF: 1.1OBJ: Algebra LOC: A-SO2 TOP: Rise Over RunKEY: slope

5. ANS: D PTS: 1 DIF: Difficult REF: 1.1OBJ: Algebra LOC: A-SO2 TOP: Rise Over RunKEY: slope

6. ANS: A PTS: 1 DIF: Easy REF: 1.2OBJ: Algebra LOC: A-SO2 TOP: Grade, Angle of Elevation, and DistanceKEY: angle of elevation

7. ANS: A PTS: 1 DIF: Easy REF: 1.2OBJ: Algebra LOC: A-SO2 TOP: Grade, Angle of Elevation, and DistanceKEY: percent grade

8. ANS: D PTS: 1 DIF: Moderate REF: 1.2OBJ: Algebra LOC: A-SO2 TOP: Grade, Angle of Elevation, and DistanceKEY: Pythagorean theorem

9. ANS: D PTS: 1 DIF: Easy REF: 1.2OBJ: Algebra LOC: A-SO2 TOP: Grade, Angle of Elevation, and DistanceKEY: percent grade

10. ANS: D PTS: 1 DIF: Moderate REF: 1.2OBJ: Algebra LOC: A-SO2 TOP: Grade, Angle of Elevation, and DistanceKEY: Pythagorean theorem

11. ANS: D PTS: 1 DIF: Easy REF: 1.3OBJ: Algebra LOC: A-SO2 TOP: Rate of ChangeKEY: slope

12. ANS: C PTS: 1 DIF: Moderate REF: 1.3OBJ: Algebra LOC: A-SO2 TOP: Rate of ChangeKEY: slope

13. ANS: C PTS: 1 DIF: Easy REF: 1.3OBJ: Algebra LOC: A-SO2 TOP: Rate of ChangeKEY: slope

14. ANS: B PTS: 1 DIF: Easy REF: 1.3OBJ: Algebra LOC: A-SO2 TOP: Rate of ChangeKEY: rate

15. ANS: C PTS: 1 DIF: Easy REF: 1.3OBJ: Algebra LOC: A-SO2 TOP: Rate of Change

KEY: slope

SHORT ANSWER

1. ANS:

The ball will descend 0.6 m.

PTS: 1 DIF: Moderate REF: 1.1 OBJ: AlgebraLOC: A-SO2 | A-SO1 TOP: Rise Over RunKEY: slope

2. ANS:

The slope of the bird’s flight is about 0.106.

PTS: 1 DIF: Easy REF: 1.1 OBJ: AlgebraLOC: A-SO2 TOP: Rise Over Run KEY: slope

3. ANS:

The plane needs a runway at least 75.9 m long.

PTS: 1 DIF: Moderate REF: 1.2 OBJ: AlgebraLOC: A-SO2|A-SO1 TOP: Grade, Angle of Elevation, and DistanceKEY: angle of elevation

4. ANS:

A

B1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

The slope of this line is negative.

PTS: 1 DIF: Moderate REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: plotting graph|slope

5. ANS:

A

B1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

The slope of this line is undefined.

PTS: 1 DIF: Moderate REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: plotting graph|slope

6. ANS:

A

B

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

PTS: 1 DIF: Easy REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: plotting graph|slope

7. ANS:Choose two points on the graph, such as (0, 105) and (1, 90).

The slope of the graph is –15.

PTS: 1 DIF: Easy REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: slope

8. ANS:

1 2 3 4 5 6 7 8 9 Age (y)

10

20

30

40

50

60

70

80

90

100

110

120

130

140Ht (cm)

Dotted line - JosephSolid line - Jolene

PTS: 1 DIF: Moderate REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: plotting graph

9. ANS:

The clues are 592.8 m apart.

PTS: 1 DIF: Moderate REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: Pythagorean theorem

10. ANS:

A

B1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

PTS: 1 DIF: Easy REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: plotting graph|slope

PROBLEM

1. ANS:

a.

The slope of John’s roof is about 0.56.

b. Divide the run of the roof by 8 ft.16 ft ÷ 8 ft = 2

Divide the rise of the roof by 2.9 ft ÷ 2 = 4.5 ft

The roof rises 4.5 ft for every 8 ft of horizontal distance.

PTS: 1 DIF: Moderate REF: 1.1 OBJ: AlgebraLOC: A-SO2 TOP: Rise Over Run KEY: slope

2. ANS:

a.

The slope of the staircase is about 0.92.

b. Divide the total rise by the number of steps.

The rise of each step is 152 mm.

Divide the total run by the number of steps.

The run of each step is 165 mm.

c. The slope of one step is the same as the slope of the entire staircase.

The slope of each step is about 0.92.

PTS: 1 DIF: Moderate REF: 1.1 OBJ: AlgebraLOC: A-SO2 TOP: Rise Over Run KEY: slope

3. ANS:a. Convert the run of the boardwalk to inches.

Calculate the slope of the boardwalk.

Convert 13 ft to inches.

Find the total drop.

The total drop of the boardwalk over the entire 13-ft width is 6.55 in.

b.

The grade of the boardwalk is 4.2%.

PTS: 1 DIF: Moderate REF: 1.2 OBJ: AlgebraLOC: A-SO2 TOP: Grade, Angle of Elevation, and DistanceKEY: percent grade

4. ANS:a. The independent variable is the number of hours travelled and the dependent variable is the distance

travelled.

b.Time travelled (h) Distance remaining (km)0 10001 9302 8603 7904 7205 6506 580

c.

1 2 3 4 5 6 7 8 9 10 Time (h)

100

200

300

400

500

600

700

800

900

1000

1100

1200

Dst (km)

Choose two points on the graph, such as (1, 930) and (5, 650).

The slope of the line is –70.

d. The slope represents a rate of change, the speed at which the family is driving. They are driving at 70 km/h.

PTS: 1 DIF: Moderate REF: 1.3 OBJ: AlgebraLOC: A-SO2 TOP: Rate of Change KEY: slope|plotting graph

5. ANS: a.

A

B

C

D

1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

b.

Since AC is not equal to BD, the angles are not right angles.