Extra Practice Answers BLM 2 GR - HRSBSTAFF Home Page

49 downloads 17313 Views 402KB Size Report
This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher. Extra Practice Answers. BLM 2 GR.
Extra Practice Answers

BLM 2 GR

Chapter 2 Get Ready 1. a)

3. There would be 65 sides showing.

9

4. a) C  2.356 d) w = 4 g) q = 6.3

11

b) Number of Triangles 1 2 3 4 5 10 50 nth

Number of Sticks 3 5 7 9 11 21 101 2n + 1

6. For example: (5, 0) y 6 4 2 Missing Point (5, 0)

(–1, 0) –6

–4

–2 0

2

4

6

x

–2 (–4, –3) –4

(2, –3)

–6

13

16

b) Number of Squares 1 2 3 4 5 10 50 nth

Number of Sticks 4 7 10 13 16 31 151 3n+ 1

c) A = 42 f) z = 24

5. A (–4, 6), B (0, 3), C (4, 6), D (4, –4), E (0, –8), F (–4, –4)

–8

2. a)

b) m = 200 e) m = 17

–8

7. Ratio = 2:1 Cost of 8 bars = $16 Cost of 1 bar = $2 Equation for nth term: 3n + 2

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Extra Practice Answers

BLM 2.1

2.1 Represent Patterns in a Variety of Formats 1. a) x y –3 13 –2 10 –1 7 0 4 5 –11 Determine the equation: y = –3x + 4 Or, plot the points and extrapolate. b) x y –3 –1 –2 1 –1 3 1 7 5 15 Determine the equation: y = 2x + 5 Or, plot the points and extrapolate. y

y

a)

y –7 –63 –143 9 –79 Speedy ($) 8.25 13.05 20.25 29.25 35.25 Comparing Taxi Prices

Get You There Taxi y = 0.75x + 3.75 Speedy Taxi y = 0.6x + 5.25

30

12 10

Get You There ($) 7.50 13.50 22.50 33.75 41.25

42 36

(5, 15)

14

d) y = –8x – 7 x 0 7 17 –2 9 3. a) Distance (km) 5 13 25 40 50 b)

24

8 6 4

18

(1, 7)

12

(0, 4)

2

–12 –10

–8

–6

–4 b)

–2 0

6 2

4

6

8

–2

x

0

–4

10

20

30

40

50

60

x

Distance (km)

–6 –8 –10 (5, –11)

2. a) y = 7x – 8 x 1 2 3 4 9 b) y = 4x – 10 x 0 1 2 –5 8 c) y = –3x – 6 x 2 9 20 14 1

10

y –1 6 13 20 55 y –10 –6 –2 –30 22 y –12 –33 –66 –48 –9

c) Speedy Taxi is cheaper for longer trips. Speedy Taxi becomes cheaper than Get You There Taxi at 10 km. i) Make a table of values: Distance Speedy Get You There (km) ($) ($) 5 8.25 7.50 8 10.05 9.75 9 10.65 10.50 10 11.25 11.25 13 13.05 13.50 ii) Use the formulas and calculate answers using number of kilometres. Speedy Taxi: 5.25 + 0.60/km = cost 5.25 + 0.6 × 10 = 11.25 Get You There Taxi: 3.75 + 0.75/km = cost 3.75 + 0.75 × 10 = 11.25 iii) Graph the data and find the point where the two lines intersect.

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Extra Practice Answers

BLM 2.2

2.2 Interpret Linear and Non-Linear Relationships 1. a)

3. x –2 –1 0 1 2

y –5 –2 1 4 7

x –2 –1 0 1 2

y 13 4 1 4 13

x –2

y

Length of Side 1 2 3 4 5 10 nth

b)

yTriangle

100 80

1. 1

60

1. 3 2 4 10

0 1 2

40 20

0

14

x –2 0 2 4

y = 3x + 1 8 6

y = 3x + 1 4 2

–4

–2 0

6

8

4. a)

10

–6

4

y = 3x 2 + 1

12

–8

2

Length of Side

y

–12 –10

Problem

120

c)

–1

Number of Small Triangles 1 4 9 16 25 100 n2

2

4

6

8

10

x

y=

–2 –4 –6

1 x 2

b)

–8 –10

2. a) Exponential: There is a pattern of repeated multiplication between the y values. b) Linear: There is a constant difference of –4 between each y value. c) Exponential: There is a pattern of repeated multiplication between the y values. d) Quadratic: Since there is no repeated multiplication nor a constant difference between consecutive values of y, it must be a quadratic.

y –1 0 1 2

x –1 0 1 2 3 y = x +1

y 0 1 2 3 4

x –2 –1 0 1 2 y = x2

y 4 1 0 1 4

c)

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

10

x

Extra Practice Answers

BLM 2.3

2.3 Discover the Slope of a Line 1. a) The y-axis represents the number of chocolate bars left in the box and the x-axis represents the time over which the bars are eaten. b) The y-axis represents the number of assignments collected and the x-axis represents the time elapsed since the assignment was given. c) The y-axis represents the number of water bottles in the machine and the x-axis represents time. The first horizontal line represents the machine when no one is buying a bottle. The second horizontal line represents the machine being refilled. d) Attached lines mean that non-integer numbers are permitted but it is not possible to sell a fraction of a chocolate bar, collect a fraction of an assignment in math, or sell a portion of a water bottle from a vending machine.

2. a) slope = –1 b) slope = 1 c) slope = 3 3. a) slope = 6 b) slope = –8 c) slope = –12 5. a) Slope = 2 b) Slope = 5 c) Slope = –1 d) Slope = –0.25 y

a)

y

b)

14 10 7 8 –6

6

–4

–2 0

2

4

x

4

6

x

–7 4

4.

–14 y

a)

2

y

b)

6

6

4

4

2

2

–21 –6

–4

–4

–2 0

2

4

x

–6

–4

–4

–2 0

4

x

–28

2

4

–35

y

x

y

d)

6

1.5

–4

4

1

–6

–6

2

0.5

–8

–8

–2

–2

–4

y

c)

–6

2

–2

c) –6

–2 0

–6

y

d)

–4

–2 0

2

4

x

–4

–2 0

6

6

–2

4

4

–4

–1

2

2

–6

–1.5

–8

–2

–2 0

2

4

x

–6

–4

–2 0

–2

–2

–4

–4

–6

–6

–8

–8

2

4

x

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

–0.5

2

Extra Practice Answers

BLM 2.4

2.4 The Equation of a Line 1. a) slope = –3; y-intercept = –6; x-intercept = –2; equation: y = –3x – 6 b) slope = –2; y-intercept = 5; x-intercept = 2.5; equation: y = –2x + 5 c) slope = 8; y-intercept = 10; x-intercept = –1.25; equation: y = 8x + 10

c) y

Tourists Travelling to Cape Tormentine

200 180 160 140

d) slope = 4; y-intercept = –12; x-intercept = 3; equation : y = 4x – 12

120

Bus: y = –80x + 180

100

2. a) y = –5x + 7 b) y = 6x – 4 c) y = –x + 7 d) y = –7x + 2

80 60 40 20

3. a) Bus group b)

0

Time (h) 0 1 2 3

Bus Distance (km) 180 100 20 0

Time (h) 0 1 2 3

Bicycle Distance (km) 75 50 25 0

Bicycle: y = –25x + 75

1

2 Time (h)

3

x

d) Bus: y = –80x + 180 Bicycle: y = –25x + 75 e) Bus (0, 180); Bicycle (0, 75) The y-intercept represents how the number of kilometres they have to travel. f) Bus (2.25, 0); Bicycle (3, 0) The x-intercepts represent how much time it takes to arrive at the bridge. g) –80x + 180 = –25x + 75 –55x = –105 x = 1. 90 h or about 1 h 54.5 min

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Extra Practice Answers

BLM 2.5

2.5 Graphs of Horizontal and Vertical Lines 1. y

a)

2. a), b)

y

b)

6

6

4

4

2

2

y a), b) 6 4

–6

–4

–2 0

2

4

x

–6

–4

–2 –4

–6

–6

–8

–8

6

4

4

2

2

–2 0

2

4

x

–4

–6

–4

–2

–4

–4

–6

–6

–8

–8

4

4

2

2

2

4

x

–6

–4

–2 0

–2

–2

–4

–4

–6

–6

–8

–8

4 2

–0.5 0 –2 –4 –6 –8

x

0.5

1

y=2

2

–6

–4

–2 0

2

x

4

–2

y = –2

–4 –6

x = –2

x=2

–8

c) 2

4

x

y

c)

6

y=x+2

4

y=2

–6

6

6

–1.5 –1

4

2

y

f)

y

g)

–2 0

–2

–2 0

2

y

d)

6

6

–6

–2 0

–4

y

e)

–4

–2

y

c)

–6

–4

–2 0

2

4

x

–2

y = –2 –4 2

4

–6

x

y=x–2

–8

b) x = 2; x = –2 c) Answers may vary: y = x + 2, y = x – 2 d) Answers may vary: y = 3, y = –3, x = 3, x = –3 e) Answers may vary: y = 3, y = –3, y = x + 3, y = x–3 f) Answers may vary: Rectangles: y = 2, y = -2, x = 4, x = –4; Triangle: y = x + 1, y = –x + 1, y = –1

x

3. Answers may vary. Assume the axes scales are in units of 1. a) y = 2, y = 12 b) y = –x + 12, y = x c) y = 2, y = 12, y = 2x + 2, y = 2x – 8 d) y = 2, y = 12, y = –2x + 12, y = –2x + 2

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Extra Practice Answers

BLM 2R

Chapter 2 Review ii) y = –2x; exponential There is a pattern of repeated multiplication between the y-values.

1. a) 23 and 28 b) Asterisk E’s y 28

y

26

2

24 22 20

–8

–6

–4

–2 0

2

4

6

x

–2

18 16

–4

14 12

–6

10

–8

8 6

–10

4

–12

2

0

2

4

6

8

10

12

14

b) linear. Answers may vary.

x

Figure Number

c) y = 5x + 3 d) 278 e) linear f) It is not logical to attach the points on this relation because the letter E’s are discrete data.

4. Graph times and distances may vary, but the shapes of the graphs will be similar. Students are encouraged to elaborate and add details. y

Liam’s Trip to School

School 2

2. a) $60 b) $50 c) y = 50x + 60 d) $410 e) 5.5 hours

1

Doughnut Shop 5 min Mailbox

3. a)

i) y = 2x2 + 2 quadratic There is no repeated pattern in the y-values.

10 min

0

8:00 a.m.

x

8:30 a.m.

Time (min)

y 10

5. a) y = –4x + 7; slope = –4 b) y = 6x – 5; slope = 6

8 6

c) y = 3, x ∈R; Slope is 0 because

4

d) x = 4, y ∈R

2

–8

–6

–4

–2 0 –2 –4

2

4

6

x

Slope is undefined because impossible to calculate.

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

rise 0

0 run is

is 0.

Extra Practice Answers

BLM 2PT

Chapter 2 Practice Test 1. 2. 3.

C slope C quadratic C –4

4.

B

5.

D 8

ii) 3 + 2x = y

1 2

6. Answers may vary but students must include an equation, table of values, and a graph. Students must also explain how the ratio of the vertical change (rise) to the horizontal change (run) gives the steepness or slope of a line.

x y –2 –1 –1 1 0 3 1 5 2 7 Slope is 2; x-intercept is –1.5; y-intercept is 3. y 6 4 2

7. A quadratic relation is a relation between two variables that appears as a parabola or a U-shaped curve when graphed. In y = x2, there is no repeated pattern in the table of consecutive y-values. An exponential relation is a relation between two variables where one of the variables is an exponent. In y = 2x, there is a repeated multiplication pattern in the table of consecutive y-values. 8. Situations may vary. Horizontal graphs have no slope because the line has no rise. The values for y are all the same no matter what the value of x. Vertical graphs have an undefined slope because there is no run. The values for x are all the same no matter what the values of y.

–8

–6

–4

–2 0

2

4

x

6

–2 –4 –6 –8

iii) y = –4 + x x y –2 –6 –1 –5 0 –4 1 –3 2 –2 Slope is 1; x-intercept is 4; y-intercept is –4. y

9. a) i) y = –2x + 5 x y –2 9 –1 7 0 5 1 3 2 1 Slope is –2; x-intercept is 2.5; y-intercept is 5.

6 4 2

–8

–6

–4

–2 0

2

4

6

x

–2 –4 –6 –8

y 6 4 2

–8

–6

–4

–2 0

2

4

6

x

–2 –4 –6 –8

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

iv) y = –x – 1

11. a)

x y –2 1 –1 0 0 –1 1 –2 2 –3 Slope is –1; x-intercept is –1; y-intercept is –1.

Additional Days (d) 0 1 3 6 10

Cost ($) 15 17 21 27 35

b)

y 6

y

4 2 28

–8

–6

–4

–2 0

2

4

–2

6

x

24 20 16

–4

12

–6 8

–8 4

b) See above. c) See above.

0

10. a) slope = –2; y-intercept = (0, –1); x-intercept = (–0.5, 0); equation: y = –2x – 1 b) slope =

3 ; 2

y-intercept = (0, 4); x-intercept = (–2 equation: y =

2 , 0); 3

2

4

6 8 10 Number of Days

12

14

x

c) The y-intercept is 15. It represents the least amount of money one will pay to advertise. d) The x-intercept is –7.5. An x-intercept is not possible in this question because the x-axis represents the number of days and one cannot have a negative number of days (otherwise, the newspaper would owe everyone money). e) Cost = $2 × number of days + $15 or y = 2x + 15

3 x+4 2

Copyright 2006 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.