AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 9

Working Hours and Time Calculations

📋 What This Question Tests

This question assesses your ability to interpret table data and solve problems involving time:

Adding time: Calculating finish times across 12-hour/24-hour boundaries and stating times with correct am/pm or 24-hour conventions.
Unit conversion: Converting between hours and minutes using 1 hour = 60 minutes .
Fractions of amounts: Calculating one quarter (¼) of a total quantity.
Reasoning & comparison: Comparing quantities with different units to justify a conclusion.

Question 9 (a)

Adding duration to a start time (1 mark)

✅ Correct Answer

Any of the following formats:

2:30 pm
14:30
Condone: 14:30 pm or "half past two in the afternoon"

[1 Mark] B1: Independent mark for correct time including clear am/pm designation or 24-hour format.

📐 Calculation Steps

Find Margot's total working time from table: 4 hours.
Start time: 10:30 am.
Add 4 hours:
10:30 am + 1h → 11:30 am
11:30 am + 1h → 12:30 pm
12:30 pm + 2h → 2:30 pm (or 14:30)

❌ Common Errors

Writing 2:30 without specifying pm (Awarded 0 marks!).
Writing 2:30 am by forgetting that adding 4 hours crosses the midday threshold into the afternoon.
Using Margot's online time (110 minutes) instead of her total working time (4 hours).

🧠 Exam Technique

Whenever a question uses 12-hour format (e.g., 10:30 am ), your final answer must specify am or pm, or be written unambiguously in full 24-hour notation ( 14:30 ). Never leave just "2:30".

Question 9 (b)

Comparing fractions and converting time units (3 marks)

✅ Correct Answer & Tick Box

Tick: [✔] Yes with complete supporting working comparing Zeke's online time to one quarter of his total working time.

📐 Method 1: Compare in Minutes (Recommended)

Find one quarter of total hours:
8 hours ÷ 4 = 2 hours [M1]
Convert quarter to minutes:
2 × 60 = 120 minutes [M1dep]
Compare & conclude:
Zeke spent 200 minutes online.
Since 200 > 120, tick Yes. [A1]

📐 Method 2: Convert Total to Minutes First

Convert 8 hours to minutes:
8 × 60 = 480 minutes [M1]
Find one quarter of total minutes:
480 ÷ 4 = 120 minutes [M1dep]
Compare & conclude:
200 minutes > 120 minutes, tick Yes. [A1]

📐 Method 3: Compare as Fractions / Decimals

Total time = 8 × 60 = 480 minutes [M1]
Fraction online = 200 / 480 = 5 / 12 (or 0.416...) [M1dep]
One quarter = 3 / 12 (or 0.25)
Since 5/12 > 3/12 (or 0.416... > 0.25), tick Yes. [A1]

📐 Method 4: Compare in Hours

One quarter of total time = 8 ÷ 4 = 2 hours [M1]
Convert 200 mins to hours: 200 ÷ 60 = 3 ⅓ hours (3 hours 20 mins) [M1]
Since 3 ⅓ hours > 2 hours, tick Yes. [A1]

💡 Key Knowledge

Golden Rule of Units: You cannot compare hours directly with minutes! Always convert both quantities to the same unit (either both in minutes or both in hours).
One quarter: "One quarter of X" means X ÷ 4 or ¼ × X .
1 hour = 60 minutes , so:
• Hours to minutes: multiply by 60
• Minutes to hours: divide by 60

❌ Common Student Traps

Ticking without working: Ticking "Yes" with no supporting calculations gets 0 marks.
Dividing 200 by 4: Calculating 200 ÷ 4 = 50 and stopping. This calculates one quarter of his online time, not his total time!
Assuming 1 hour = 100 minutes: Mistakenly thinking 200 minutes is 2 hours. Remember, 200 minutes is 3 hours and 20 minutes.
Using Margot's numbers: Looking at the wrong row in the table (Margot worked 4 hours, Zeke worked 8 hours).

Mark Breakdown:
• M1: Finding total minutes (8 × 60 = 480) OR finding quarter of total hours (8 ÷ 4 = 2).
• M1 (dep): Completing the conversion to compare directly (e.g. 480 ÷ 4 = 120, 2 × 60 = 120, or 200 / 480).
• A1: Correct values shown for comparison (e.g., 120 and 200, or 5/12 and 3/12) and "Yes" ticked.