# GCSE Mathematics – Revision Notes Topic ‘Number’s and Algebra’

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Contents

1. Rounding and Approximating 3

2.Square, Cube and prime numbers 5

3. Distance-time graphs 7

4. Fractions 9

8. Best offer questions 21

9. Number Machine 23

10 Quadratic Equations 25

11. Substitution 28

12. Rearrange 29

14. Simultaneous equations 31

15 Inequalities 36

15 Graphing Inequalities 38

17. Linear Graphs and equations 46

# 1. Rounding and Approximating

Firstly it’s important to remember in what order we multiply, add, subtract, etc…

The order is

1. Brackets

2. Exponents (Roots and Powers)

3. Multiply or Divide

4. Add or subtract

Some people like to remember the word BEMDAS to help remember the order

(Brackets Exponents Multiply Divide Add Subtract)

When rounding to the nearest whole number, we pay attention to the first decimal place. If it is 5 or greater we round it up to the nearest whole number. If it is less than 5 we round it down to the nearest whole number.

Look at the first decimal place

6.8 8 is greater than 5. Round up to 7.0

9.2 2 is less than 5. Round down to 9.0

5.5 If 5 is in the first decimal place approximate up. 5.5 approximates up to 6.0

When rounding correct to one decimal place. We pay attention to the second decimal place

7.72 2 is less than 5. Round down to 7.70

16.89 9 is greater than 5. Round up to 16.90

4.55 5 is in the second decimal place so we round up. Round up to 4.60

Rounding off to 3 or 4 decimal places is done the exact same way

When doing approximations we round each number in the calculation to one significant figure and th...