How to use this book Welcome to Collins Edexcel GCSE Maths Higher Practice Book. This book follows the structure of the Collins Edexcel GCSE Maths 4th edition Higher Student Book, so is ideal to use alongside it.
5
A sycamore tree is 40 cm tall. It grows at a rate of 8% per year. A conifer is 20 cm tall. It grows at a rate of 15% per year. How many years does it take before the conifer is taller than the sycamore?
6
The population of a small town is 2000. It is falling by 10% each year. The population of a nearby village is 1500. It is rising by 10% each year.
Colour-coded questions
After how many years will the population of the town be less than the population of the village?
7
Each week, a boy takes out 20% of the amount in his bank account to spend. After how many weeks will the amount in his bank account have halved from the original amount?
Know what level of difficulty you are working at with questions ranging from more accessible (green), through intermediate (blue) to more challenging (pink).
5.6 Reverse percentage (working out the original amount) Homework 5J 1
Find what 100% represents in each situation. a 20% represents 160 g
2
b 25% represents 24 m
a 40% represents 28 kg
3
c 5% represents 42 cm
Find what 100% represents in each situation. b 30% represents £54
c 15% represents 6 hours
VAT is a government tax added to goods and services. With VAT at 17.5%, what is the pre-VAT price of these goods? Jumper
£14.10
Socks
£1.88
Trousers
£23.50
Use of calculators
4
Paula spends £9 each week on CDs. This is 60% of her weekly allowance. How much is Paula’s weekly allowance?
5
Alan’s weekly pay is increased by 4% to £187.20. What was Alan’s pay before the increase?
Questions when you could use a calculator are marked with a icon.
6
Jon’s salary is £23 980. This is 10% more than he earned two years ago. Last year his salary was 3% more than it was two years ago. a How much was his salary last year? b By what percentage did he salary increase last year?
7
Twice as many people visit a shopping centre on Saturdays as on Fridays. The numbers visiting on both days increases by 50% in the week before Christmas. How many more visit on this Saturday than on this Friday? Give your answer as a percentage.
8
A man’s savings decreased by 10% in one year and then increased in the following year by 10%. He now has £1782. How much did he have two years ago?
40
5 Ratio and proportion and rates of change: Ratio and proportion
208105 GCSE Higher Practice Book CH05.indd 40
4
12/30/14 12:34 PM
A runner sets off at 8 am from point P to jog along a trail at a steady pace of 12 km/h. One hour later, a cyclist sets off from P on the same trial, at a steady pace of 24 km/h. After 30 minutes, the cyclist gets a puncture that takes her 30 minutes to fix. She then sets off at a steady pace of 24 km/h. At what time did the cyclist catch up with the runner?
Hints and tips Drawing a distance–time graph is a straightforward method of answering this question. Remember that the cyclist doesn’t start until 9 am.
Calculate the average speed of each journey. 50
b 250
250
40
40
200
200
30 20 10 0
6
30 20 10
0
0
0
1 1 Time (hours) Time (hours)
2
2
Distance (miles)
Distance (km)
These are provided where extra guidance can save you time or help you out.
50
Distance (miles)
a
Distance (km)
Hints and tips
5
150
150
100
100
50 0
50
0
0
0
1 1 2 2 Time (hours) Time (hours)
3
3
This graph shows a car’s journey from London to Brighton and back again. The car leaves at 8 am and returns at 3 pm. 50
Distance (miles)
40 30 20 10 0
8
9
10
11
12
13
14
15
Time
a For how long does the car stop in Brighton? b Was the car travelling faster from London to Brighton or on the return journey from Brighton to London? Describe how you can tell this from the graph.
Answers Check your own work – the answers are provided online at www.collins.co.uk/ gcsemaths4eanswers.
Homework 23B 1
200
13872_P004.indd 4
a
b
c
e
f
g
d
23 Algebra: Graphs
13834_P199_210.indd 200
4
Draw a graph of the depth of water in each of these containers as it is filled steadily.
03/01/15 7:57 PM
How to use this book
1/8/15 12:46 PM