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Cambridge Lower Secondary Mathematics Workbook 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions

6 A dice has 10 faces. Each face is one of three colours, green, gold or black. Here are the results of 400 throws.a Find the experimental probability for each colour. b Make a conjecture about the number of faces of each colour. Give a reason for your answer. Here are the results of another 600
5 When you throw three coins you can get 0, 1, 2 or 3 heads. Here are the results of a computer simulation of 500 throws of three coins.a b Find the experimental probabilities of 0, 1, 2 and 3 heads. Work out the theoretical probabilities of 0, 1, 2 and 3 heads. How close are the experimental
4 A spinner has five equal sectors numbered 1, 2, 3, 4, 5. Here are the results of 400 spins.Find the experimental probabilities of a i 2 b Find the theoretical probabilities of an odd number iii 4 or 5 i 2 ii an odd number 4 or 5 C Do you think the spinner is fair? Give a reason for your answer.
3 A spinner has four equal parts coloured yellow, blue, green and red. Here are the results of 60 spins.a Find the experimental probability of each colour. b Compare the experimental probabilities with the theoretical probabilities. YRGRGGYYRBY GBYGGGGYGRBR YGYYR BBGGRRG YGGYRRBGGYBG BGBGRGBBBBGR
2 A dice is thrown 80 times. Here are the results.a b C d e Use the first two rows to find an experimental probability of getting a 1. Use the first four rows to find an experimental probability of getting a 1. Use all eight rows to find an experimental probability of getting a 1. Which of your
1 Arun makes a six-sided cardboard dice. He colours three faces orange, two faces pink and one face white. He throws his dice 80 times. Here are the results.Colour orange pink white Frequency 34 28 18 100 b Calculate the experimental frequency for each colour. Work out the theoretical frequency for
13 Here are two words on cards.S Q U A R E T R A N G L E One card is taken at random from each word. Find the probability that both cards show the same letter. Show how you found the answer.
12 A spinner has 3 equal sectors coloured red (R), green (G) and blue (B). The spinner is spun twice. a Copy and complete this tree diagram to show b the possible outcomes. Find the probability of ired on both spins ii green on both spins iii iv not getting green on both spins getting green on at
11 Here are four number cards. 3 4 5 6 Two cards are chosen at random to make a 2-digit number. a List all the 2-digit numbers you can make with these cards. Find the probability that the number has a 4 as one of the digits. Three cards are chosen at random to make a 3-digit number. C List all the
9 Two fair six-sided dice are thrown and the numbers are multiplied together.a Draw a table to show the possible outcomes.b What is the most likely product? What is the probability of this product?c Find the probability of getting more than 15.d Find the probability of getting an odd number.10 Two
8 Here are two sets of cards. Set A 2 3 Set B 2 4 3 One card is taken at random from each set and they are added together.a Copy and complete this table to show the possible totals.b Work out the probability that the total is i 3 iii less than 5 ii 5 iv an odd number. 32 3 2 1 3 7 1 2 3 4
7 Here are three numbered cards. 5 6 7 Sofia puts the cards in a line at random to make a 3-digit number. a List all the possible outcomes. Find the probability that the number is i an odd number iii less than 700. ii a multiple of 5
6 A spinner has 7 equally likely sectors numbered 1, 2, 3, 4, 5, 6 and 7. The spinner is spun and a coin is thrown. a Draw a table to show the possible outcomes. Work out the probability of b a head and a 5 C a tail and an even number d a head but not a 5.
5 A spinner has 3 equally likely colours, red (R), yellow (Y) and green (G). The spinner is spun twice. a Copy and complete this table of outcomes.Find the probability of b green on both spins C a red and a yellow d not getting red e getting red at least once. green red yellow
4 Arun throws a coin repeatedly until he throws a head. This table shows the probability for different numbers of throws.Find the probability that Arun takes a more than 1 throw b more than 2 throws. 1 2 Throws Probability 12 14 3 64 919 6 7 or more -3 64 518 4 16 32 16 1
3 A dice is biased.The probability of throwing 3 is - and the probability of throwing 6 is -Work out the probability of not throwing 3 ab not throwing 6.
2 A train can arrive early, on time or late. The probability the train arrives early is 5% and the probability it arrives late is 15%. Work out the probability that it is a not early b not late C not on time.
1 A spinner has sectors in different colours. The probability it is green is 0.15 and the probability it is brown is 0.4. Find the probability that it is a not green b not brown.
16 The ratio of women to men in a badminton club is ?:5. There are more men than women. The number of adults in the badminton club is 28. How many women are in the badminton club?
15 A builder makes concrete for a floor. He uses cement, sand and gravel in the ratio 1:2:4. a The builder makes 2.1 tonnes of concrete. What fraction of the concrete is sand? b How many kilograms of sand does he use?
14 Two clothes shops sell coats and jumpers. 'Clothes 4 U' has 24 coats and 60 jumpers for sale. 'Clothes 2 Keep' has 40 coats and 95 jumpers for sale. Which shop has the greater proportion of coats? Justify your choice.
13 Li and Su collect magazines and puzzle books.Li has 30 magazines and 12 puzzle books.Su has 45 magazines and 18 puzzle books.Who has the greater proportion of magazines? Justify your choice.
12 Gavin mixes a fruit drink. He uses orange juice and pineapple juice in the ratio 2: 7.Matt mixes a fruit drink. He uses orange juice and pineapple juice in the ratio 3: 10.What fraction of each fruit drink is pineapple juice?a bWhose fruit drink, Gavin's or Matt's, has the higher proportion of
11 Ru Shi mixes two shades of yellow paint. She uses the following ratios of yellow: white.Banana yellow 5:3 Mellow yellow 7:5 a What fraction of each shade of yellow paint is white? b Which shade of yellow paint is lighter? Show all your working. Justify your choice.
10 Work out. a b A bag contains blue and white counters. 1 of the counters are blue. What is the ratio of blue to white counters? A box contains CDs and DVDs. of the items are DVDs. What is the ratio of CDS to DVDs? 7 10 of the learners in a Madarin class are women. The rest are men. What is the
9 The ratio of men to women in a cafe is 7:6. The number of adults in the cafe is greater than 30 but less than 40. How many adults are in the cafe?
8 The ratio of boys to girls in a swimming club is 3:5. Which of these cards shows the number of children that could be in the swimming club?Justify your choice. A 29 B 35 C 68 88 D 72 E 82
7 A bag of dried fruit contains banana chips and apricots in the ratio 7:3. The bag contains 40 pieces of dried fruit. a What fraction of the pieces of dried fruit are apricots? b How many apricots are there in the bag?
6 Ken mixes two different fruit drinks. He uses the following ratios of grape juice: pear juice. Fruit drink A 2:7 a Fruit drink B 5:13 Copy and complete the workings to find the fraction of each drink that is pear juice. Fruit drink A: total number of parts =2+7= Fruit drink B: total number of
5 Copy and complete the workings to answer this question. A school cricket club has 45 members. The ratio of boys to girls is 5:4.
4 Jay mixes two shades of orange paint. He uses the following ratios of orange: white. Orange sunset 3:2 Orange flame 5:3 a Copy and complete the workings to find the fraction of each paint that is orange. Orange sunset: total number of parts=3+2= fraction orange: 5 Orange flame: total number of
]0\3 Copy and complete the workings to change each ratio into a fraction. a A bag of nuts has brazil nuts and almonds in the ratio 2:3. What fraction of the nuts are i brazil nuts ii almonds? Total number of parts=2+3=[ i Fraction that are brazil nuts ii Fraction that are almonds b A box of balls
2 Jake and Razi make light blue paint by mixing white paint and blue paint. Jake mixes white and blue in the ratio 4:20. Razi mixes white and blue in the ratio 5:15. Copy and complete the workings to find out who has the darker paint.Who makes the darker paint? Jake Razi 4:20 5:15 +4 4 5 5 1
1 Arshan and Oditi make pink paint by mixing white paint and red paint. Arshan mixes white and red in the ratio 3:6. Oditi mixes white and red in the ratio 4:12. Copy and complete the workings to find out who has the darker paint.Who makes the darker paint? Arshan Oditi 3:6 4:12 +3 +4 +4 1: 1:
14 Salim draws a quadrilateral. The angles are in the ratio 1:4:5:2. Salim thinks the largest angle is 110 more than the smallest angle. Is Salim correct? Explain your answer.
13 Heidi makes her favourite colour paint by mixing blue, yellow and green in the ratio 0.8: 1.1:0.1. Copy and complete the table to show how much of each colour she needs to make the quantities shown. Size of tin Blue 1 litre Yellow Green 1.5 litres 2.5 litres
12 There are 24 coins in Zara's purse. The ratio of 50 cent to 25 cent to 10 cent coins is 2:3:7. Show that she has $4.90 in her purse in total.
11 Xiu, Zane and Mike buy a boat. The information shows how much each of them pays for the boat. Three years later, they sell the boat for $3300. They share the money from the sale of the boat in the same ratio in which they bought the boat. a How much does each of them receive from the sale of the
10 Tatiana, Lucia and Gianna buy a house for $120000. Tatiana pays $10000, Lucia pays $70000 and Gianna pays the rest. Four years later, they sell the house for $210000. They share the money in the same ratio in which they bought the house. Gianna thinks she will make $30000 profit on the sale of
9 Every year, Patrick shares 280 oranges between his children in the ratio of their ages. This year, the children are 3, 7 and 10 years old. How many more oranges will the youngest child receive in five years' time, than she received this year?
10 Tatiana, Lucia and Gianna buy a house for $120000. Tatiana pays $10000, Lucia pays $70000 and Gianna pays the rest. Four years later, they sell the house for $210000. They share the money in the same ratio in which they bought the house. Gianna thinks she will make $30000 profit on the sale of
9 Every year, Patrick shares 280 oranges between his children in the ratio of their ages. This year, the children are 3, 7 and 10 years old. How many more oranges will the youngest child receive in five years' time, than she received this year?
8 Four children are given a painting. They sell it and share the money in the ratio of their ages. The children are 6, 8, 11 and 13 years old. The painting sells for $4750. Show that the oldest child receives $1625.
7 Zara, Sofia, Arun and Marcus run their own business. They share the money they earn from each project in the ratio of the number of hours they work on the project. This is the time-sheet for one of their projects. How much does each of them earn from this project? Project earnings: $750 Time
6 A box of shapes contains triangles, squares and rectangles in the ratio 5:1:2. The box contains 56 shapes altogether. a How many shapes in the box are triangles i ii squares iii rectangles? 14 of the shapes are taken out. There are now 42 shapes left in the box.The ratio of the numbers of
5 The angles in a triangle are in the ratio 2:3:4. What are the sizes of the angles in the triangle?
4 A gardening club is made up of men, women and children in the ratio 5:4:11. Altogether, the club has 240 members. a i How many members of the gardening club are men ii women iii b Show how to check your answers to parta. children?b Show how to check your answers to part a.
3 Gita, Harry and Indira share their electricity bill in the ratio 2:4:5. How much does each of them pay when their electricity bill is a i b $110 $165 iii Show how to check your answers to parta. $352?
2 Share these amounts among Ali, Bob and Carl in the given ratios. Use the same method as in Question 1. a $90 in the ratio 1:3:5 b $240 in the ratio 3:4:5 C d $350 in the ratio 5:2:7 $1000 in the ratio 3:5:2
1 Copy and complete the workings to share $72 between Ali, Bob and Carl in the ratio 4:1:3. Total number of parts: Value of one part: Ali gets: Bob gets: Carl gets: 4+1+3= $72 4x - 1x 3x |=
14 a On a piece of paper, draw three squares with side lengths 3 cm, 4 cm and 5 cm. Measure the length of the diagonal of each square, correct to the nearest millimetre. Copy and complete the table below. You can use a calculator to work out the value for n in the last column of the table. Write
13 Any ratio can be written in the form 1:n or n: 1, like this:Write these ratios i in the form 1:n ii a 2:4 b 3:12 C 5:25 in the form n: 1. d 25:200 In the form 1:n, +4 4 10- In the form n: 1, 10 1 2.5- 4 10- 4 410 0.4 14 +10
12 Abbie is trying to find the quickest way to drive to her new job. She tries three different routes and writes down how long each one takes. a Abbie thinks the ratio of her times for routes 1, 2 and 3 is 5:6:7. Without doing any calculations, explain how you know that Abbie is wrong.b Abbie's mum
11 Simplify each ratio.a 0.4:2 b 2.5:5 C 0.8:3.2 d 0.5:2.5 e 3.6:1.8 f 2.1:1.5 g 2.5:6 h 2.1:1.4 i 0.05:0.3:1
10 Work out. a Two cups hold 450 ml and five mugs hold 1.25 litres. b Which holds more liquid, one cup or one mug? Three bags of red rice have a mass of 960 g and four bags of brown rice have a mass of 1.22kg. Which has a greater mass, one bag of red rice or one bag of brown rice? Jules can text 16
9 Zara and Marcus are baking a huge cake. They mix 450 g of butter with 550 g of sugar and 1.1 kg of flour.Is either of them correct? Explain your answer. The ratio of butter to sugar to flour is 4:5:11. The ratio of butter to sugar to flour is 45:55:11.
8 Simplify each ratio. a 400m: 0.8 km: 60m b 4g:2200 mg:0.8g C hour: 1 minute: 20 seconds d 45 cents: $0.15:$2 2 e 6m:0.09 km: 300 cm f 48 cm: 88mm: 0.4m
7 Arun uses 600 g of walnuts and 1 kg of dates in a fruit loaf.Is Arun correct? Explain your answer. The ratio of walnuts to dates is 6:1.
6 Simplify each ratio. 250m: 1 km $1.26:60 cents e 1 minute: 42 seconds f b 2m: 15cm d 2.4 kg:600g 1.75t:500 kg
5 This is part of Karen's homework.a Explain the mistake Karen has made.b Work out the correct answer. Question Simplify the ratio 6:20:10 Answers 6:20 simplifies to 3:10 20:10 simplifies to 2:1 So the ratio is 3:10:2:1
4 Simplify each ratio. a 25:30:10 b 32:8:64 C 36:9:15
3 Simplify each ratio. Divide all the numbers in the ratio by the highest common factor (written in the bracket). The first one is done for you. a 2:10:12 (divide by 2) Answer is 1:5:6 b 8:12:16 (divide by 4) Answer is...... C 12:9:15 (divide by 3) Answer is
2 Simplify each ratio. Some of them have been started for you. 6: a +2 b 4 8 12 +4 +4 C 12:15 d 15:25 e 25:35 32 24- -3624- f 8 +8 g +12 12 h 27:24 i 36:27 j 40:24
1 Simplify each ratio. Some of them have been started for you. a 3 b 18 2 C 5:40 d 3:12 e 6:18 10 21 -30 f +2 g +3 h 27:3 i 700: 10 j 16:4
10 A company offers two types of cement mixer for hire. The graph shows the costs of hiring these cement mixers. a For each type of cement mixer, A and B, find the charge for 4 days' hire. Suppose the charge for x days is Sy. b Show that, for mixer A, the equation of the line is y=20x+180. C Find a
8 The heights of two plants are measured each week. The results are shown on this graph. a 29 b C d Work out the initial height of each plant. How does the graph show that each plant grows an equal amount each week? How much does each plant grow each week? After x weeks, the height of a plant is
7 The cost of hiring a coach depends on the number of people.This graph gives the costs for two different companies, A and B.Find the cost of a coach for 30 people with acompany A.b When is company A cheaper than company B?Copy and complete this table of values for ccompany A.For each company,
6 Arun and Marcus are 400 metres apart. They run towards each other. This graph shows their distances from Arun's starting point. a b How long does Arun take to run 200m? How far does Arun run every 10 seconds? How far does Marcus run every 10 seconds? d What does the point where the lines cross
5 This graph shows the charges for two plumbers. Each plumber has a fixed charge and an hourly charge. a b C Which plumber is cheaper for a job that lasts 1.5 hours? Find the fixed charge for each plumber. Copy and complete this table for Plumber A.d e Work out the hourly charge for Plumber A. Work
4 A car and a lorry use petrol. The graph shows the amount of petrol left in each vehicle.a How much petrol is in the lorry initially?b How much petrol does the lorry use each hour?c How much petrol is in the car initially?d Copy and complete this table for the car.e How much petrol does the car
3 Zara and Sofia live together. Zara leaves home at 09:00 and cycles to the shops. When she gets there she waits for Sofia. a How long did Zara take to get to the shops? b How far are the shops from Zara's house? Sofia leaves home after Zara and cycles to the shops. C What time did Sofia leave
2 Two buckets are being filled with water. a How much water is in each bucket initially? b Find the number of litres in each bucket after 1 minute. C d e How many litres are added to Bucket 1 each minute? How many litres are added to Bucket 2 each minute? When do the two buckets contain the same
1 Sofia and Zara are walking along the same path.a How far does Zara walk every 10 minutes?b Sofia starts after Zara. How long after?c How far does Sofia walk every 10 minutes?d The lines cross. What does the point where they cross show you? Kilometres 4 3 2 - + 0 0 10 20 20 30 40 50 Minutes Sofia
12 The cost of a holiday depends on the number of nights. The cost for n nights is Sc where c=100n+50. a b Construct a table to show the cost for different values of n. Draw a graph to show the cost. C Explain what the gradient of the line represents.
11 Here are three parallel lines. a The equation of one of the lines is y = 10x+20. b C Which line is this? Find the equations of the other two lines. Write the equation of a parallel line that passes through (0, -10). 30 20 20 B C 10 x
10 The water in a tank is leaking out. The number of litres (y) left in the tank after x hours is given by the function y=18-3x. a Copy and complete this table.b Plot a graph to show the quantity of water in the tank over time.c What happens after 6 hours?d What does the y-intercept tell you?e What
9 Four lines are plotted on this diagram. They all cross the y-axis at (0, 6). The gradients of the lines are 1, -1, 2 and -2. Write the equation of each line. a b Write the coordinates of the x-intercept of each line. C-1 D-2 6 B A 0 x C B2 D
8 a Copy and complete this table.b Plot a graph of y=10x+20.c On the same axes, plot a graph of y=5x+20.d Write the gradient and the y-intercept of each line. x -2 -1 0 1 2 3 10.x+20 10 50
7 Here is the equation of a line: y=10-5.x a What is the gradient of the line? b Where does the line cross the y-axis? C Where does the line cross the x-axis? d Write the equation of a parallel line that passes through the origin.
6 a Copy and complete this table.b Copy and complete this table.c On the same axes, plot graphs of y=-x+7 and y=-x+2. d Write the gradient of each line. e f Write the y-intercept of each line. Write the x-intercept of each line. x -2 -1 0 1 2 -x+7 9 3 3 4
5 Here are the equations of three lines. y=x y=2x y=3x a On the same axes, plot a graph of each line. b Write the gradient of each line.
4 a Copy and complete this table.b Copy and complete this table.c On the same axes, plot the lines y=x+3 and y=2x+3.d Find the gradient of each line.e Find the y-intercept of each line. x -3 -2 -1 0 1 2 3 x+3 0 6
4 a Copy and complete this table.b Copy and complete this table.c On the same axes, plot the lines y=x+3 and y=2x+3. d e Find the gradient of each line. Find the y-intercept of each line. x -3 -2 -1 0 1 2 3 x+3 0 6
3 a Copy and complete this table of values.b On the same axes, plot graphs of y=5x and y=5x+10. C Find the gradient of each line. d Find the y-intercept of each line. x 5.x 5.x+10 -4 -3 -2 -1 -15 0 1 2 3 4 10 -5 20
1 a Copy and complete this table of values.b a graph of y=x+2. Plot plot a graph On the same axes, of y= x.C Find the gradient of each line. = -4 42 x+2 -2 -3 -2 -1 0 1 2 35 5 3 4
13 The cost ($y) of hiring a drill for x days is given by the function y=4x+10. a b Draw a graph to show the cost of hiring the drill for up to 7 days. Explain what the 10 in the function tells you. C Explain what the 4 in the function tells you.
12 The temperature (7C) after m minutes is given by the function T = 706m. a b C d Construct a table for values of m, from 1 to 6, and T. Use the table to draw a graph of T-70-6m. Put m on the horizontal axis. How does the graph show that the temperature is decreasing at a constant rate? Use your
11 An electrician visits a customer's home. The total cost is in two parts: a fixed charge of $50 and an hourly rate of $30. a The total charge for 1 hours is y dollars. Write a formula for y. Copy and complete this table of values.Use your table to draw a graph. Put t on the horizontal axis.c
10 The width of this rectangle is .xcm. The length is 3 cm more than the width. a The perimeter is pcm. Write a function for p. b Copy and complete this table of values.c Use the table to draw a graph. Put p on the vertical axis.d The perimeter of the rectangle is 20cm. Use your The graph to find
9 Here is the equation of a line: y=25x-10 Copy and complete the coordinates of these points on the line. a d (5,) (15) b (8, e 90) 3 (-2,)
8 a Copy and complete this table of values for 5x+20.b Draw a graph of y=5x+20.c Copy and complete this table of values for 30-5.x.d a graph of y=30-5.x. On the same axes as for partb, draw e lines cross? Where do the two x -2 -1 0 5.x+20 15 I 2 3 4 35
8 a Copy and complete this table of values for 5x+20.b y=5x a graph of +20. Draw c Complete this table of values for 30-5.x. Copy and x -2-1 0 1 2 3 4 5.x+20 15 35
7 a Copy and complete this table of values for 60-x.b Use your table to draw a graph of y=60-x.c Where does the line cross the y-axis?d If the line is extended, where does it cross the x-axis? r -20 -10 0 10 20 30 40 60-x 80 20
6 y=15x+10 a Copy and complete this table.b Draw a graph of y=15x+10.c Where does the line cross the y-axis? -2 -1 0 1 2 3 4 y=15x+10
5 Here is a function: y=6-2x a y= 10. If x =- 2 show that b Copy and complete this table.c Use the table to draw a graph of y=6-2x.d If the line is extended, which of these points will be on the line? .x r -2 -1 0 1 2 3 4 y=6-2x
4 Here is a function: y=4x-1 a b If x=3 work out the value of y. Copy and complete this table.c Use the table to draw a graph of y=4x-1. -3 -2 -1 0 1 2 3 y=4x-1
3 Here is a function: y=5-x a Copy and complete this table.b Use the table to draw a graph of y=5-x. -2 -1 0 1 2 3 4 5 6 y=5-x 7 +4 0
2 b Use the table to plot a graph of y=2x-2. Here is a function: y=3x+4 a Copy and complete this table of values.b Use the table to draw a graph of y=3x+4. r -3 -2 -1 0 1 2 3 y=3x+4 -5 4
1 A function is y=2x-2. a Copy and complete this table of values. -2 -1 0 1 2 y=2x-2 -6 3 4 5 8
12 Here is a function: y=5n+ 10 It shows the cost, in dollars, of hiring a bike for n days.Show that the cost for 14 days is less than twice the cost for a7 days.b Zara pays to hire the bike for a certain number of days but she returns the bike one day early. She gets a refund for the day she did

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