EXAM PREPARATION AND PRACTICE
EXAM PREPARATION AND PRACTICE
Martin Noon, Katherine Pate and Dicky Susanto with Digital access
Martin Noon, Katherine Pate & Dicky Susanto with Digital access
There are extra digital questions for this title found online at Cambridge GO. For more information on how to access and use your digital resource, please see inside the front cover.
In this chapter you will answer questions on:
• identifying different types of numbers
• writing numbers as products of their prime factors
• calculating with negative numbers
• understanding the meaning of indices
• using the rules of indices
• recalling the order of operations for numbers
• rounding numbers to a given number of decimal places or significant figures.
In this chapter you will:
• show that you understand the command words ‘write’ and ‘write down’ and can answer ‘write’ and ‘write down’ questions
• show that you can understand and answer questions using a calculator and without a calculator.
When you read an examination question, look carefully at the command word used. It is important to understand what each command word means and what it is asking you to do. In this chapter, look out for the questions containing the command words ‘write’ and ‘write down’.
Write give an answer in a specific form.
Write down give an answer without significant working.
When an examination question uses the command words ‘write down’, it is asking for a brief, direct answer that you can find without doing much or any working. In some ‘write down’ questions, you may be able to copy some of the information given in the question.
If a question uses the command word ‘write’, it is asking you to write an answer in a particular form, for example as a decimal, as a fraction or as a power.
You will take two mathematics examinations. Paper 1 is a non-calculator paper so you will need to be able to answer some questions without a calculator. In this chapter, some questions are labelled . You should try to answer these without using a calculator.
1 5, √ 2 , 3 7 , 6, 13
From this list of numbers, write down
a an even number b an integer
c the rational numbers d an irrational number
e a prime number.
2 a List all the factors of 12.
b Write down the prime factors of 12.
3 List the first four multiples of 12.
4 Find the lowest common multiple (LCM) of 8 and 6.
5 Find the highest common factor (HCF) of 24 and 42.
6 Write 54 as the product of its prime factors.
7 60 = 2 × 2 × 3 × 5, 105 = 3 × 5 × 7
a Find the HCF of 60 and 105.
b Find the LCM of 60 and 105.
8 51, 52, 53, 54, 55, 56, 57, 58, 59
From this list of numbers, write down
a a multiple of 18 [1]
b a factor of 168 [1]
c the prime numbers. [2]
[Total: 4]
9 a Write 240 as a product of its prime factors. [2]
b Find the lowest common multiple (LCM) of 240 and 140. [2]
[Total: 4]
Each digit in a number has a place value.
a What is the value of the 7 in 47 206?
b What is the value of the 7 in 25 731?
How can you use place value to help you write a number in words?
For example, how do you write 25 731 in words?
• Integer
• Rational number
• Irrational number
• Prime number
• Factor
• Multiple
• Product
1 Copy and complete the statements with the correct sign type, < or >.
a −5 …… 4
2 Find the answers to these calculations.
a
3 Use a calculator to work out
a the difference between −40 and 175
b the sum of 130 and −84
c the product of 15 and −23.
4 Find two integers that give −21 when added, and give 38 when multiplied. [2]
[Total: 2]
5 Find the temperature that is 6 °C war mer than −2 °C. [1]
[Total: 1]
6 One day the temperature in Seoul is 2 °C and the temperature in Helsinki is −7 °C. Work out the difference in temperature between these two cities. [1]
[Total: 1]
Write a calculation to find the difference between 5 and 8.
Now write calculations to find
a the difference between −10 and 13
b the difference between −10 and −14.
Does knowing how to find the difference between two positive numbers help you to find the difference between two numbers where one or both are negative?
1 Work out
2 Find the value of
3 Use a calculator to find the value of
• Index
• Index notation
• Reciprocal
• Cube number
• Cube root
• Square number
• Square root
• Power
4 Evaluate
7−1
5 Write 45 as the product of its prime factors. Give your answer in index form.
6 Simplify each expression. Give your answer in index form.
7 Write down the reciprocal of 1 8 [1] [Total: 1]
8 24, 25, 26, 27, 28
From this list of numbers, write down a a cube number [1] b a square number. [1] [Total: 2]
9 a Write 5 3 × 5 4 5 7 as a single power of 5. [1]
b Write the value of 5−2 as a decimal. [1]
2]
What is 112? What is the cube root of 125?
Learning the square numbers from 12 to 122 and the cube numbers from 13 to 53 and 103 will help you find squares, cubes and roots without a calculator.
1 Write down what each letter stands for in ‘BODMAS’.
Work out
Work out
Evaluate
5 Add a pair of brackets to make this calculation correct. 5 × 9 + 12 ÷ 3 = 35 [1]
6 Find the value of 46 ÷ 25
1 Review of number concepts
7 a Work out −5 × −6 ÷ −2. [1]
b Work out i 13 + 6 × 4 − 1 [1] ii 13 + 6 × (4 − 1) [1]
[Total: 3]
1 Round each number correct to 2 decimal places.
a 36.548 b 0.732 c 0.295 d 0.999
2 Round each number correct to i the nearest 100 ii the nearest 1000.
a 23 406 b 15 870 c 9650 d 428 766
3 Round each number correct to i 1 significant figure ii 3 significant figures. a 2457 b 11.32 c 36 519 d 0.048 75
4 By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of
7.96 × 3.4 1.25 + 4.9
You must show all your working. [2]
[Total: 2]
5 a Write 32 485 correct to i the nearest thousand [1] ii the nearest ten. [1]
b By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of
4.6 2 + 98 8.3 − 2.7
You must show all your working. [2]
[Total: 4]
Look at all the non-calculator questions you answered in this chapter. Write a list of the number skills, facts and rules you used in these questions. How confident are you that you can remember all of these? Are there any that you need to practise to help you answer non-calculator questions?
Highlight any you need to learn. When you think you have learned them, ask someone to use your list to test you on them.
Let's revisit the Knowledge and Exam skills focus for this chapter. Decide how confident you are with each statement.
Now I can Show it Needs more work Almost there Confident to move on
1identify different types of number
2write numbers in prime factor form
3calculate with negative numbers
4recall and use the laws of indices
5recall the order of operations
6round numbers to a given number of decimal places or significant figures
7 estimate the answer to calculations by first rounding all the numbers in the calculation to 1 significant figure
8understand the command words ‘write down’ and ‘write’
9work out the answers to non-calculator and calculator questions.
Write the definitions of factor, integer, irrational number, multiple, rational number, prime number and product.
Write 30 as the product of prime factors.
Write 98 as the product of prime factors, in index form.
Work out
a −5 − 4
b −5 − −4
c −5 × −4
d 20 ÷ −5
Write as a single power
a 34 × 35
b 28 ÷ 22
c (53)0
Calculate 9 + 6 × 7 − 8 ÷ (6 − 4).
Round 4.6527
a to 3 decimal places b to 2 significant figures.
Estimate the value of 5.7 2 8.75 + 3.1
What is the difference between ‘write down’ and ‘write’?
Without using a calculator, work out
a 92
b 3√ 27
Use a calculator to work out
c 83 d √ 392.04