Ratio, Rates and the Number Plane

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Student Book - Series I-1

Ratio, Rates and the Number Plane

Mathletics Instant

Workbooks

y = 2x + 1y = -x - 1

Ratio, rates and the number plane

Student Book - Series I

Contents

Topics

Topic 1 - Equivalent ratios __/__/__ Date completed

Topic 2 - Using ratios __/__/__ Topic 3 - Rates __/__/__ Topic 4 - Scale drawing __/__/__ Topic 5 - Graphing ordered pairs and number patterns __/__/__ Topic 6 - Graphing lines on the number plane __/__/__ Topic 7 - Graphing points of intersection __/__/__ Topic 8 - Graphing curves __/__/__ Topic 9 - Problem solving __/__/__

Ratio, rates and the number planeMathletics Instant Workbooks – Series I Copyright © 3P Learning

Author of The Topics and Topic Tests: AS Kalra

Practice Tests

Topic 1 - Topic test A __/__/__ Topic 2 - Topic test B __/__/__

1



Topic 1: Equivalent ratios

44 EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1

Ratio, rates and the number plane EXCEL MATHEMATICS YEAR 8

pages 177–179UNIT 1: Equivalent ratios

Question 1 Express the following ratios in simplest form.

a 3 : 6 b 5 : 5 c 6 : 18 d 4 : 12

= = = =

e 3 : 15 f 2 : 8 g 2 : 12 h 2 : 10

= = = =

i 8 : 64 j 4 : 16 k 9 : 27 l 12 : 48

= = = =

m 3 : 24 n 14 : 22 o 7 : 49 p 11 : 121

= = = =

q 5 : 30 r 25 : 75 s 36 : 72 t 8 : 84

= = = =

Question 2 Express as a ratio in its simplest form.

a 10 : 20 : 30 b 12 :

14 c 2

12 : 2 d

14 :

34

= = = =

e 112 : 1 f 2 :

25 g

17 :

57 h

311 :

711

= = = =

i 0.2 : 0.3 j 1.5 : 2 k 1 : 14 l 1.2 : 2.4

= = = =

Question 3 Simplify the following ratios.

a $4 : $12 b 30 cents : $6 c 10 hours : 1 day d 400 g : 1 kg

= = = =

e 50 cents : 90 cents f 3 days : 3 weeks g 12 cm : 1 metre h 20 seconds : 1 min

= = = =

i 2 kg : 800 g j 400 mL : 1 L k 3 km : 600 m l 8 cm : 60 mm

= = = =

m 60 cm : 112 m n 500 g : 3 kg o 30 min : 2 h p 1 h : 40 min

= = = =

Chapter 5

2




Chapter 5: Ratio, rates and the number plane 45

Question 1

a Divide $36 in the ratio of 4 : 5. _____________________________________________________________

b Divide $40 in the ratio of 3 : 2. _____________________________________________________________

c $200 is divided in the ratio 6 : 4. What is the smaller part? _______________________________________

d $45 is divided in the ratio 5 : 4. What is the larger part? __________________________________________

Question 2

a The ratio of boys to girls is 2 : 3. If there are 12 boys, how many girls are there? _____________________________________________________________________

b Two girls aged 12 years and 15 years divide $72 in the ratio of their ages. How much does each girl receive? _______________________________________________

c The three angles of a triangle are in the ratio 2 : 3 : 4. Find the size of each angle. ________________________________________________________________

d Find the ratio of the areas of two squares whose sides are 3 cm and 5 cm, respectively. ________________________________________________________________

e A piece of rope is cut into three lengths in the ratio 2 : 3 : 5. If the smallest length is 6 m, find the length of the original rope. ____________________________________

Question 3

a A rectangle has length 16 cm and breadth 8 cm. What is the ratio of its length to its perimeter? ___________________________________________________________

b In a class of 30 students, the ratio of passes to failures in a test was 5 : 1. Find the number of students who passed. __________________________________________

c Two brothers are to share an inheritance of half a million dollars in the ratio 12 : 13. How much is the smaller share? _______________________________________

d The ratio of adults to children on a train trip is 3 : 2. If the train carries 800 passengers, find the number of adults and children on the train. ____________________________________________________________

UNIT 2: Using ratios

EXCEL MATHEMATICS YEAR 8

pages 181–182Topic 2: Using ratios

3




Ratio, rates and the number plane EXCEL MATHEMATICS YEAR 8

pages 177–179UNIT 1: Equivalent ratios

Question 1 Express the following ratios in simplest form.

a 3 : 6 b 5 : 5 c 6 : 18 d 4 : 12

= = = =

e 3 : 15 f 2 : 8 g 2 : 12 h 2 : 10

= = = =

i 8 : 64 j 4 : 16 k 9 : 27 l 12 : 48

= = = =

m 3 : 24 n 14 : 22 o 7 : 49 p 11 : 121

= = = =

q 5 : 30 r 25 : 75 s 36 : 72 t 8 : 84

= = = =

Question 2 Express as a ratio in its simplest form.

a 10 : 20 : 30 b 12 :

14 c 2

12 : 2 d

14 :

34

= = = =

e 112 : 1 f 2 :

25 g

17 :

57 h

311 :

711

= = = =

i 0.2 : 0.3 j 1.5 : 2 k 1 : 14 l 1.2 : 2.4

= = = =

Question 3 Simplify the following ratios.

a $4 : $12 b 30 cents : $6 c 10 hours : 1 day d 400 g : 1 kg

= = = =

e 50 cents : 90 cents f 3 days : 3 weeks g 12 cm : 1 metre h 20 seconds : 1 min

= = = =

i 2 kg : 800 g j 400 mL : 1 L k 3 km : 600 m l 8 cm : 60 mm

= = = =

m 60 cm : 112 m n 500 g : 3 kg o 30 min : 2 h p 1 h : 40 min

= = = =

Chapter 5

Topic 3: Rates

4





question 1 Write each of the following scales in the ratio form.

a 1 mm to 1 m b 1 cm to 1 m c 1 cm to 100 m

d 10 cm to 1 km e 4 mm to 1 m f 5 cm to 1 m

g 1 mm to 20 m h 20 cm to 1 m i 1 mm to 6 m

Question 2 Using a scale of 1 : 100 what length is represented by

a 1 cm b 3 cm c 5 cm

d 8 mm e 6 mm f 12 cm

Question 3 Using a scale of 1 : 1000 what is the real length represented by the following.

a 8 mm b 5 cm c 6 m

d 9.5 cm e 8.3 m f 63.25 m

Question 4 The distance between two points in real life is given. What will be the distance between these points on a scale drawing with a scale of 1 cm to 100 m?

a 500 m b 400 m c 1260 m

d 80 m e 3000 m f 2835 m

Question 5 A drawing of a block of land along with the proposed building has been drawn using a scale of 1 : 500. Measure the plan and answer the questions using metres.

a How wide is the block of land? _____________________________________________________________

b How deep is the block of land? _____________________________________________________________

c Find the area of the block of land in square metres. ____________________________________________________________________

d How far is the proposed building from the southern boundary? _______________________________________________________________

e Find the area of the proposed building in square metres. _________________________________________________________________

UNIT 4: Scale drawing

Scale 1 : 500

N


pages 186–188

Proposed building

Area I Area II

Topic 4: Scale drawing

5




Ratio, rates and the number planeUNIT 5: Graphing ordered pairs and number patterns

Question 1

a Plot the following ordered pairs on the number plane. A (–3, –2) , B (–2, –1) , C (–1, 0) , D (1, 2) , E (2, 3)

b Are the points collinear? __________________________________________________________________

c Join these points.

d State the rule. ___________________________________________________________________________

Question 2

a Complete the table for the rule y = x + 2.

b Write the set of ordered pairs formed.

c Plot this set of ordered pairs on the number plane.

d Are the points collinear? __________________________________________________________________

Question 3

a Plot the set of ordered pairs: A (–1, –1) , B (2, 3) , C (2, –1).

b What type of triangle is ∆ABC? ____________________________________________________________

c What is the length of side AC? _____________________________________________________________

d What is the length of side BC? _____________________________________________________________

e Use Pythagoras’ theorem to calculate the length of side AB.

f What is the perimeter of ∆ABC? ___________________________________________________________

g What is the area of ∆ABC? ________________________________________________________________

Question 4 Complete each of the following tables and write the set of ordered pairs formed alongside.

a b cy = x + 3

x y

0

1

2

3

y = x + 2

x y

–2

–1

0

1

2

y = 2x + 1

x y

–1

0

1

2

y = 2x –1

x y

–1

0

1

2

–x

–y

3

2

1

–1

–2

–4 –3 –2 –1 0 1 2 3 4

–3

y

x

–x

–y

3

2

1

–1

–2

–4 –3 –2 –1 0 1 2 3 4

–3

y

x

–x

–y

3

2

1

–1

–2

–4 –3 –2 –1 0 1 2 3 4

–3

y

x


pages 56–59

Topic 5: Graphing ordered pairs and number patterns

6





Question 1 Complete the following tables of values and then graph the equation on the number plane.

a b c

Question 2 Complete each of the following tables of values and then graph the equation on the number plane.

a b c

Question 3 On the same number plane, graph the following equations by first completing the tables of values. Find their point of intersection.

a y = x y = –x

x x

y y

b y = x – 3 y = –x + 3

x x

y y

UNIT 6: Graphing lines on the number plane

y = x + 1

x –1 0 1 2

y

–x

–y

0

y

x

y = x – 1

x –1 0 1 2

y

y = 2x

x –1 0 1 2

y

–x

–y

0

y

x –x

–y

0

y

x –x

–y

0

y

x

x = 2

x

y –1 0 1 2

y = 3

x –1 0 1 2

y

x = –3

x

y –1 0 1 2

–x

–y

0

y

x –x

–y

0

y

x –x

–y

0

y

x


pages 59–60Topic 6: Graphing lines on the number plane

7





Question 1 Graph each pair of lines on the same number plane and find their point of intersection.

a x = 1; y = 2

x = 1 y = 2

x x

y y

b x = 2; y = 3

x = 2 y = 3

x x

y y

Question 2 Graph each pair of lines and find their point of intersection.

a y = 2x + 1; y = –x – 1

y = 2x + 1 y = – x – 1

x x

y y

b y = 2x + 3; y = –x + 3

y = 2x + 3 y = –x + 3

x x

y y

UNIT 7: Graphing points of intersection

3

2

1

6

5

4

–1

–2

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

–3

–4

y

x

3

2

1

6

5

4

–1

–2

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

–3

–4

y

x

3

2

1

6

5

4

–1

–2

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

–3

–4

y

x

3

2

1

6

5

4

–1

–2

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

–3

–4

y

x


pages 62–63Topic 7: Graphing points of intersection

8





Question 1 Complete the following table of values and then graph the equation on the number plane.

a y = x2

x –3 –2 –1 0 1 2 3

y

b y = x3

x –2 –1.5 –1 – 0.5 0 0.5 1 1.5 2

y

Question 2 Complete the following table of values and then graph the equation on the number plane.

a x = y2

x

y –3 –2 –1 0 1 2 3

b y = x2 + 1

x –3 –2 –1 0 1 2 3

y

UNIT 8: Graphing curves

3

2

1

6

7

8

5

4

–1

–2

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

–3

–4

–5

–6

–7

–8

y

x

3

2

1

6

7

8

5

4

10

9

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

y

x

–3

–4

0

1

2

–1

–2

4

3

1 2 3 4 5 6 7 8 9 10

y

x

3

2

1

6

7

8

5

4

10

9

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

y

x


page 64Topic 8: Graphing curves

9





1 In a class of 30 students, there are 18 boys. What is the ratio of a boys to girls?

b girls to boys?

2 Michael delivered 480 bottles of milk every morning between 6:00 am and 9:00 am. Find his hourly rate of delivery.

3 Tony buys a pen for $30 and sells it for $40. What is the ratio of a the cost price to the selling price?

b the selling price to the cost price?

4 John drives 240 km in 4 hours. Find his average speed.

5 Divide $300 in the ratio 2 : 3.

6 Two angles of a triangle are 40º and 60º. What is the ratio of a the third angle to the angle sum of the triangle?

b the smallest angle to the largest angle?

7 A car travels at 450 km in 5 hours. What is the speed of the car per hour?

8 If a 20 kg box of oranges cost $15, calculate the price for 1 kg of oranges.

9 A person wishes to divide $120 000 in the ratio of 3 : 7 to give to his son and his wife respectively. How much does each one get?

10 A concrete mixture is made up of five parts of metal, three parts of sand and two parts of cement. Find the quantity of each needed to make 50 cubic metres of concrete.

UNIT 9: Problem solving


pages 181–184Topic 9: Problem solving

Total marks achieved for PART A 12

Ratio, rates and the number planeTOPIC TEST PART AInstructions • This part consists of 12 multiple choice questions • Each question is worth 1 mark • Fill in only ONE CIRCLE for each question • Calculators may be used

Time allowed: 15 minutes Total marks = 12


Marks


1 Write 15 : 25 in its simplest form.

A 5 : 3 B 3 : 5 C 3 : 25 D 1 : 5 2 $180 is divided in the ratio 2 : 7 : 9. Find the largest share.

A $20 B $160 C $90 D $70 3 The angles of a triangle are in the ratio 2 : 3 : 4. Find the largest angle.

A 60° B 80° C 40° D 100° 4 If $24 000 is divided in the ratio 2 : 3, find the smaller share.

A $9600 B $14 400 C $10 500 D none of these 5 A cake recipe requires 500 g of flour, 200 g of sugar and 250 g of butter. If I only have 200 g of

butter, how much flour should I use?

A 250 g B 300 g C 500 g D 400 g 6 $9000 is divided in the ratio of 1 : 3. How much is the smaller share?

A $2250 B $1550 C $6750 D $3500 7 In a school of 957 students, boys and girls are in the ratio 6 : 5. How many girls are there?

A 552 B 87 C 435 D 348 8 4032 hectares are divided in the ratio 24 : 16 : 16. How much is the smaller share?

A 1728 ha B 1296 ha C 1152 ha D none of these 9 A car travels 441 km in 5

14 hours. Calculate the average speed per hour.

A 48 km/h B 77 km/h C 80 km/h D 84 km/h 10 A car travels at the speed of 20 m/s. How far does it travel in 1 hour?

A 70 km B 72 km C 74 km D 75 km 11 Change 90 km/h into km/min.

A 1 km/min B 1.5 km/min C 2 km/min D 2.5 km/min 12 10 litres per hour equals how many litres per day?

A 210 B 220 C 230 D 240

1

1

1

1

1

1

1

1

1

1

1

1

Ratio, rates and the number planeTOPIC TEST PART AInstructions • This part consists of 12 multiple choice questions • Each question is worth 1 mark • Fill in only ONE CIRCLE for each question • Calculators may be used



Marks


1 Write 15 : 25 in its simplest form.

A 5 : 3 B 3 : 5 C 3 : 25 D 1 : 5 2 $180 is divided in the ratio 2 : 7 : 9. Find the largest share.

A $20 B $160 C $90 D $70 3 The angles of a triangle are in the ratio 2 : 3 : 4. Find the largest angle.

A 60° B 80° C 40° D 100° 4 If $24 000 is divided in the ratio 2 : 3, find the smaller share.

A $9600 B $14 400 C $10 500 D none of these 5 A cake recipe requires 500 g of flour, 200 g of sugar and 250 g of butter. If I only have 200 g of

butter, how much flour should I use?

A 250 g B 300 g C 500 g D 400 g 6 $9000 is divided in the ratio of 1 : 3. How much is the smaller share?

A $2250 B $1550 C $6750 D $3500 7 In a school of 957 students, boys and girls are in the ratio 6 : 5. How many girls are there?

A 552 B 87 C 435 D 348 8 4032 hectares are divided in the ratio 24 : 16 : 16. How much is the smaller share?

A 1728 ha B 1296 ha C 1152 ha D none of these 9 A car travels 441 km in 5

14 hours. Calculate the average speed per hour.

A 48 km/h B 77 km/h C 80 km/h D 84 km/h 10 A car travels at the speed of 20 m/s. How far does it travel in 1 hour?

A 70 km B 72 km C 74 km D 75 km 11 Change 90 km/h into km/min.

A 1 km/min B 1.5 km/min C 2 km/min D 2.5 km/min 12 10 litres per hour equals how many litres per day?

A 210 B 220 C 230 D 240

1

1

1

1

1

1

1

1

1

1

1

1

10Ratio, rates and the number planeMathletics Instant Workbooks – Series I Copyright © 3P Learning

Ratio, rates and the number planeTopic Test PART AInstructions This part consists of 12 multiple-choice questions Each question is worth 1 mark Fill in only ONE CIRCLE for each question Calculators are NOT allowed


Marks

Total marks achieved for PART B 15

Marks

Ratio, rates and the number planeTopic Test PART B

11Ratio, rates and the number planeMathletics Instant Workbooks – Series I Copyright © 3P Learning

Instructions This part consists of 15 questions Each question is worth 1 mark Write answers in the answers-only columnTime allowed: 20 minutes Total marks = 15

Questions Answers only

Ratio, rates and the number planeTOPIC TEST PART B



Instructions • This part consists of 15 questions • Each question is worth 2 marks • Write answers in the answers-only column • Calculators may be used

Time allowed: 15 minutes Total marks = 30 Questions Answers only Marks

21 10 books cost $260, what is the price of 18 books?

2 Express 0.09 : 0.27 in its simplest form.


4 The three angles of a triangle are in the ratio of 2 : 3 : 4. What is the size of the largest angle?

5 Write 445 : 3

110 in its simplest form.

6 Change 72 km/h to m/s.

7 A car is travelling at 120 km/h. How far will it travel in 40 minutes?

8 How much time will it take to travel 600 km at 75 km/h?

9 If the cost of cooking oil is $2 for 100 mL, how much would 1 L cost?

10 Adam delivered 1080 bottles of milk in 6 hours. Find his hourly rate of delivery.

11 A distance of 90 km is represented by a length of 3 cm. What scale is used?

12 Find the distance represented by 8 cm, if the scale is 1 cm : 72 m?

13 Divide 320 m in the ratio 3 : 5.

14 The four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 6. Find the size of the smallest angle.


2

2

2

2

2

2

2

2

2

2

2

2

2

2










5 Write 445 : 3












1

1

1

1

1

1

1

1

1

1

1

1

1

1










5 Write 445 : 3












1

1

1

1

1

1

1

1

1

1

1

1

1

1

Ratio, Rates and the Number Plane

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Transcript of Ratio, Rates and the Number Plane