MATHEMATICS
Number
AQA 8300 | Premium Learning Edition
What this pack does
Number is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
number, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
LEARN SEE IT
Plain-English teaching in short sections. Worked questions with every step explained.
TRY IT FIX IT
Questions immediately after each lesson. Answer sheet explains the method, not just the
result.
Independent resource
Original revision material aligned to the current AQA topic structure. ClearGrade is not affiliated with or
endorsed by AQA. Questions are independently written and are not reproduced past-paper questions.
ClearGrade GCSE | Premium Learning Edition Mathematics | 1
, Before you start
Number is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
number, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
By the end of this pack, you should be able to:
• explain and apply number skills and bidmas
• explain and apply factors, multiples, primes, hcf and lcm
• explain and apply fractions
• explain and apply percentages and reverse percentages
• explain and apply indices, roots and standard form
• explain and apply approximation, estimation and bounds
• explain and apply surds and recurring decimals
How to use the pack
1. Read one lesson. 2. Cover the page and explain it from memory. 3. Study the worked example. 4. Attempt
the three “Your turn” questions without looking back. 5. Mark them using the explained answers at the back. 6.
Re-do every question you got wrong.
ClearGrade GCSE | Premium Learning Edition Mathematics | 2
, LESSON 1
Number skills and BIDMAS
The idea in plain English
Order operations so everyone gets the same value from an expression. Brackets come first, then indices, then
multiplication/division left-to-right, then addition/subtraction.
What you need to know
• Keep negative signs attached to their numbers.
• Do multiplication and division before addition and subtraction.
• Estimate first if the arithmetic is messy.
WORKED EXAMPLE
Question: Work out 18 - 3 x (5 - 2).
Step 1: Bracket first: 5-2=3.
Step 2: Multiply next: 3x3=9.
Step 3: Subtract: 18-9=9.
Step 4: Check: the answer should be below 18 because you are subtracting a positive number.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Work out 7+4x6. [1-2 marks]
2. Work out 30/5+2^3. [2-3 marks]
3. Work out 12-2(7-4). [3-4 marks]
LESSON 2
Factors, multiples, primes, HCF and LCM
The idea in plain English
Prime factorisation gives a reliable way to find HCF and LCM. HCF uses shared prime factors with the lowest
powers; LCM uses every required prime factor with the highest powers.
What you need to know
• A prime has exactly two positive factors.
• Use a factor tree or repeated division to prime-factorise.
• Check an HCF divides both numbers and an LCM is a multiple of both.
ClearGrade GCSE | Premium Learning Edition Mathematics | 3
, WORKED EXAMPLE
Question: Find the HCF and LCM of 72 and 120.
Step 1: 72=2^3 x 3^2.
Step 2: 120=2^3 x 3 x 5.
Step 3: HCF uses common lowest powers: 2^3 x 3 = 24.
Step 4: LCM uses highest powers: 2^3 x 3^2 x 5 = 360.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Prime-factorise 180. [1-2 marks]
2. Find HCF of 84 and 126. [2-3 marks]
3. Find LCM of 18 and 30. [3-4 marks]
LESSON 3
Fractions
The idea in plain English
Fractions represent equal parts. For addition/subtraction make the denominators the same; for multiplication
multiply numerators and denominators; for division multiply by the reciprocal.
What you need to know
• Simplify by dividing numerator and denominator by a common factor.
• Convert mixed numbers to improper fractions before multiplying/dividing.
• Cross-cancel before multiplying to reduce arithmetic.
WORKED EXAMPLE
Question: Calculate 7/12 + 5/18.
Step 1: LCM of 12 and 18 is 36, so use denominator 36.
Step 2: 7/12=21/36 and 5/18=10/36.
Step 3: Add numerators: 31/36.
Step 4: 31 and 36 have no common factor, so it is already simplified.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
ClearGrade GCSE | Premium Learning Edition Mathematics | 4
Number
AQA 8300 | Premium Learning Edition
What this pack does
Number is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
number, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
LEARN SEE IT
Plain-English teaching in short sections. Worked questions with every step explained.
TRY IT FIX IT
Questions immediately after each lesson. Answer sheet explains the method, not just the
result.
Independent resource
Original revision material aligned to the current AQA topic structure. ClearGrade is not affiliated with or
endorsed by AQA. Questions are independently written and are not reproduced past-paper questions.
ClearGrade GCSE | Premium Learning Edition Mathematics | 1
, Before you start
Number is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
number, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
By the end of this pack, you should be able to:
• explain and apply number skills and bidmas
• explain and apply factors, multiples, primes, hcf and lcm
• explain and apply fractions
• explain and apply percentages and reverse percentages
• explain and apply indices, roots and standard form
• explain and apply approximation, estimation and bounds
• explain and apply surds and recurring decimals
How to use the pack
1. Read one lesson. 2. Cover the page and explain it from memory. 3. Study the worked example. 4. Attempt
the three “Your turn” questions without looking back. 5. Mark them using the explained answers at the back. 6.
Re-do every question you got wrong.
ClearGrade GCSE | Premium Learning Edition Mathematics | 2
, LESSON 1
Number skills and BIDMAS
The idea in plain English
Order operations so everyone gets the same value from an expression. Brackets come first, then indices, then
multiplication/division left-to-right, then addition/subtraction.
What you need to know
• Keep negative signs attached to their numbers.
• Do multiplication and division before addition and subtraction.
• Estimate first if the arithmetic is messy.
WORKED EXAMPLE
Question: Work out 18 - 3 x (5 - 2).
Step 1: Bracket first: 5-2=3.
Step 2: Multiply next: 3x3=9.
Step 3: Subtract: 18-9=9.
Step 4: Check: the answer should be below 18 because you are subtracting a positive number.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Work out 7+4x6. [1-2 marks]
2. Work out 30/5+2^3. [2-3 marks]
3. Work out 12-2(7-4). [3-4 marks]
LESSON 2
Factors, multiples, primes, HCF and LCM
The idea in plain English
Prime factorisation gives a reliable way to find HCF and LCM. HCF uses shared prime factors with the lowest
powers; LCM uses every required prime factor with the highest powers.
What you need to know
• A prime has exactly two positive factors.
• Use a factor tree or repeated division to prime-factorise.
• Check an HCF divides both numbers and an LCM is a multiple of both.
ClearGrade GCSE | Premium Learning Edition Mathematics | 3
, WORKED EXAMPLE
Question: Find the HCF and LCM of 72 and 120.
Step 1: 72=2^3 x 3^2.
Step 2: 120=2^3 x 3 x 5.
Step 3: HCF uses common lowest powers: 2^3 x 3 = 24.
Step 4: LCM uses highest powers: 2^3 x 3^2 x 5 = 360.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Prime-factorise 180. [1-2 marks]
2. Find HCF of 84 and 126. [2-3 marks]
3. Find LCM of 18 and 30. [3-4 marks]
LESSON 3
Fractions
The idea in plain English
Fractions represent equal parts. For addition/subtraction make the denominators the same; for multiplication
multiply numerators and denominators; for division multiply by the reciprocal.
What you need to know
• Simplify by dividing numerator and denominator by a common factor.
• Convert mixed numbers to improper fractions before multiplying/dividing.
• Cross-cancel before multiplying to reduce arithmetic.
WORKED EXAMPLE
Question: Calculate 7/12 + 5/18.
Step 1: LCM of 12 and 18 is 36, so use denominator 36.
Step 2: 7/12=21/36 and 5/18=10/36.
Step 3: Add numerators: 31/36.
Step 4: 31 and 36 have no common factor, so it is already simplified.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
ClearGrade GCSE | Premium Learning Edition Mathematics | 4
