Book by Anthony
GCSE Maths Made Easy
The Short and Simple Guide
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CONTENTS
1. Number
2. Algebra
3. Ratio, Proportion and Rates of Change
4. Geometry and Measures
5. Probability and Statistics
6. Common Mistakes to Avoid
7. Quick Formula Recap
8. Final Practice Paper
9. Answer Key
10. Exam Day Tips
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1. NUMBER
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Place Value
Each digit has a value based on its position.
Example: In 4,532
· 4 is worth 4,000
· 5 is worth 500
· 3 is worth 30
· 2 is worth 2
Practice: What is the value of the 7 in 3,742?
Answer: 700
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Factors
Numbers that divide into a number exactly.
Example: Factors of 12 are 1, 2, 3, 4, 6, 12
Practice: List all factors of 20.
Answer: 1, 2, 4, 5, 10, 20
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Multiples
Times table answers.
Example: Multiples of 5 are 5, 10, 15, 20, 25...
Practice: Write the first 5 multiples of 7.
Answer: 7, 14, 21, 28, 35
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Prime Numbers
Only divisible by 1 and itself.
Example: 2, 3, 5, 7, 11, 13, 17, 19... (2 is the only even prime)
Practice: Is 21 prime?
Answer: No, because 21 = 3 x 7
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HCF and LCM
, HCF (Highest Common Factor) means the biggest number that goes into both.
Example: HCF of 12 and 18
· Factors of 12: 1, 2, 3, 4, 6, 12
· Factors of 18: 1, 2, 3, 6, 9, 18
· HCF = 6
LCM (Lowest Common Multiple) means the smallest number both go into.
Example: LCM of 4 and 6
· Multiples of 4: 4, 8, 12, 16...
· Multiples of 6: 6, 12, 18...
· LCM = 12
Practice: Find the HCF and LCM of 8 and 12.
Answer: HCF = 4, LCM = 24
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Fractions
Adding and Subtracting: Make denominators the same first.
Example: 1/2 + 1/3
· Common denominator = 6
· 3/6 + 2/6 = 5/6
Multiplying: Multiply tops, multiply bottoms.
Example: 2/3 x 3/4 = 6/12 = 1/2
Dividing: Flip the second fraction and multiply.
Example: 1/2 divided by 1/4 = 1/2 x 4/1 = 4/2 = 2
Practice: Work out 3/4 minus 1/3
GCSE Maths Made Easy
The Short and Simple Guide
---
CONTENTS
1. Number
2. Algebra
3. Ratio, Proportion and Rates of Change
4. Geometry and Measures
5. Probability and Statistics
6. Common Mistakes to Avoid
7. Quick Formula Recap
8. Final Practice Paper
9. Answer Key
10. Exam Day Tips
---
1. NUMBER
---
Place Value
Each digit has a value based on its position.
Example: In 4,532
· 4 is worth 4,000
· 5 is worth 500
· 3 is worth 30
· 2 is worth 2
Practice: What is the value of the 7 in 3,742?
Answer: 700
,---
Factors
Numbers that divide into a number exactly.
Example: Factors of 12 are 1, 2, 3, 4, 6, 12
Practice: List all factors of 20.
Answer: 1, 2, 4, 5, 10, 20
---
Multiples
Times table answers.
Example: Multiples of 5 are 5, 10, 15, 20, 25...
Practice: Write the first 5 multiples of 7.
Answer: 7, 14, 21, 28, 35
---
Prime Numbers
Only divisible by 1 and itself.
Example: 2, 3, 5, 7, 11, 13, 17, 19... (2 is the only even prime)
Practice: Is 21 prime?
Answer: No, because 21 = 3 x 7
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HCF and LCM
, HCF (Highest Common Factor) means the biggest number that goes into both.
Example: HCF of 12 and 18
· Factors of 12: 1, 2, 3, 4, 6, 12
· Factors of 18: 1, 2, 3, 6, 9, 18
· HCF = 6
LCM (Lowest Common Multiple) means the smallest number both go into.
Example: LCM of 4 and 6
· Multiples of 4: 4, 8, 12, 16...
· Multiples of 6: 6, 12, 18...
· LCM = 12
Practice: Find the HCF and LCM of 8 and 12.
Answer: HCF = 4, LCM = 24
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Fractions
Adding and Subtracting: Make denominators the same first.
Example: 1/2 + 1/3
· Common denominator = 6
· 3/6 + 2/6 = 5/6
Multiplying: Multiply tops, multiply bottoms.
Example: 2/3 x 3/4 = 6/12 = 1/2
Dividing: Flip the second fraction and multiply.
Example: 1/2 divided by 1/4 = 1/2 x 4/1 = 4/2 = 2
Practice: Work out 3/4 minus 1/3
