AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 8

Mark scheme

Show the mark scheme

$Mark scheme for Question 8 shows three marks: M1 for a correct method to divide by 1/2 (implied by 0.4, 2/5, or 1/2.5); M1 for a correct method to add two fractions with different denominators; A1 for 2/3 or equivalent fraction such as 10/15. A special case SC2 is awarded for 14/15 from performing addition first.$

Q Answer Mark Comments

12 1

Correct method to divide by M1 implied by 0.4 or or

25 2 5.

Correct method to add two fractions 7

with different denominators M1 implied by

2 10

oe fraction eg

3 15

A1

SC2 oe fraction

Additional Guidance

41 1

SC2 is from + ÷

15 5 2

Ignore incorrect simplification of a correct fraction to another fraction

10 4

eg = M1M1A1

15 5

Correct answer in working but answer given as a decimal M1M1A0

How to answer it

Order of Operations with Fractions

What this question tests

Key Mathematical Skills Assessed:

Order of Operations (BIDMAS / BODMAS): Recognizing that division takes priority over addition.
Dividing Fractions: Using the reciprocal method ("keep-change-flip") to evaluate fractions divided by fractions.
Adding Fractions: Finding a common denominator to add two fractions with different denominators.
Simplifying & Formatting: Expressing the final answer strictly as a fraction (simplified or equivalent).

Question 8 • 3 Marks

Evaluate: 4/15 + 1/5 ÷ 1/2

Calculate the exact value and express your answer as a fraction.

📐 Step-by-Step Calculation

Apply BIDMAS: Identify operations. There is an addition (+) and a division (÷). Division must be calculated first:
Calculate 1/5 ÷ 1/2
Perform Division (Keep, Change, Flip):
1/5 ÷ 1/2 = 1/5 × 2/1 = (1 × 2) / (5 × 1) = 2/5
[Method Mark M1 awarded here]
Perform Addition:
Now rewrite the expression: 4/15 + 2/5
Find a common denominator (lowest common multiple of 15 and 5 is 15):
Convert 2/5 to fifteenths: multiply numerator and denominator by 3:
2/5 = (2 × 3) / (5 × 3) = 6/15
[Method Mark M1 awarded for a valid common denominator method]
Add the Numerators:
4/15 + 6/15 = (4 + 6) / 15 = 10/15
Simplify (Optional but recommended):
Divide top and bottom by 5:
10/15 = 2/3
[Accuracy Mark A1 awarded here]

✅ Acceptable Final Answers

2/3 (Fully simplified)
10/15 (Equivalent fraction accepted)
Any equivalent fraction such as 20/30

💡 Key Rules to Remember

BIDMAS: Division comes before Addition. Working left-to-right without checking priority is wrong!
Fraction Division: a/b ÷ c/d = a/b × d/c
Fraction Addition: Denominators must be identical before adding numerators: a/d + b/d = (a + b)/d .

🧠 Exam Technique & Examiner Insights

Show each step explicitly: Writing 2/5 or 0.4 instantly secures the first method mark (M1).
Simplification Grace: The mark scheme notes: "Ignore incorrect simplification of a correct fraction". If you correctly reach 10/15 , you already have full marks, even if you make an algebra slip afterwards (e.g. writing 10/15 = 4/5).
Fraction Form: The question states "Give your answer as a fraction". If you calculate 0.666... or 0.67 without stating the fraction, you lose the final accuracy mark (scoring M1M1A0).

❌ Common Traps & Lost Marks

Working Left to Right (The BIDMAS Trap):
Doing (4/15 + 1/5) ÷ 1/2 :
4/15 + 3/15 = 7/15 , then 7/15 ÷ 1/2 = 14/15 .
Examiner Note: This scores a special case of only 2 marks (SC2) instead of 3.
Adding Denominators: Never add denominators together (e.g. 4/15 + 2/5 ≠ 6/20).
Dividing by 1/2 misconception: Dividing by a half is equivalent to multiplying by 2, NOT dividing by 2 or halving.

Mark Scheme Breakdown:
• M1: Correct method to divide by 1/2 (implied by 2/5, 0.4, or 1/2.5).
• M1: Correct method to add two fractions with different denominators (common denominator shown).
• A1: Correct fraction: 2/3 or equivalent fraction (e.g. 10/15 ).
• Special Case: Award SC2 for an answer of 14/15 (from adding first).

Topics

Number · 3.1.1 Structure and calculation · 3.1.2 Fractions, decimals and percentages