AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 20

Social Media Advert Views: Time Series & Money Estimation

📋 What this question tests

Graph Drawing: Accurate plotting of points on a scaled grid (1 small square = 1 000 views) and connecting sequential points with straight ruled lines to form a time series graph.
Extrapolation & Trend Estimation: Reading the downward trend from Day 2 onwards to make a sensible estimate for Day 7 views.
Unit Conversion with Money: Multiplying large quantities by fractional pence values ( 0.018p ) and converting pence to pounds ( ÷ 100 ).

Question 20 (a) — Drawing the Time Series Graph

2 Marks

💡 Key Knowledge

Scale inspection: The vertical axis spans from 0 to 100 000 across 10 major grid intervals. Each major division is 10 000 , meaning 1 small square = 1 000 views.
Time series rule: Successive points must be connected with straight line segments from point to point using a ruler, not a single curve or a line of best fit.

✅ Accurate Plotting Coordinates

Day 1: 49 000 (1 small square below 50 000)
Day 2: 95 000 (5 small squares above 90 000)
Day 3: 87 000 (7 small squares above 80 000)
Day 4: 77 000 (7 small squares above 70 000)
Day 5: 64 000 (4 small squares above 60 000)
Day 6: 48 000 (2 small squares below 50 000)

All 6 points connected sequentially: Day 1 → 2 → 3 → 4 → 5 → 6.

🧠 Exam Technique & Mark Scheme Rules

B2: All 6 points plotted correctly within a tolerance of ± half a small square and joined with straight lines.
B1: At least 4 of the points plotted correctly.
Use a sharp pencil and a 30 cm clear ruler. Dashed or slightly imperfect ruler lines are condoned if the intent is clearly straight lines connecting consecutive days.

❌ Common Errors to Avoid

Line of best fit: Drawing an overall single straight trendline instead of joining point-to-point. A time series requires point-to-point lines.
Curve sketching: Drawing a smooth curved line through points loses the straight-line requirement.
Misreading the y-axis: Plotting Day 1 (49 000) at 45 000 or 40 900. Remember, each single small square equals 1 000.

Question 20 (b) — Estimating Earnings on Day 7

3 Marks

📐 Step-by-Step Calculation

Identify trend and estimate Day 7 views:
Look at recent drops: Day 3 → Day 4 is -10 000, Day 4 → Day 5 is -13 000, Day 5 → Day 6 is -16 000.
A sensible continuation drops around 15 000 to 18 000 from 48 000.
Acceptable range: 20 000 to 40 000 views .
Example chosen: 30 000 views.
Calculate total earnings in pence:
30 000 × 0.018p = 540p
Convert pence to pounds (£):
540p ÷ 100 = £5.40

✅ Acceptable Final Answers

Depending on your sensible Day 7 estimate (between 20 000 and 40 000):

If Day 7 = 30 000 views → £5.40
If Day 7 = 32 000 views → £5.76
If Day 7 = 28 000 views → £5.04
If Day 7 = 35 000 views → £6.30

Full acceptable range: Any value from £3.60 to £7.20 matching your estimate.

🧠 Mark Breakdown

B1: Sensible estimate of views in the range [20 000, 40 000] (can be implied in your working or written explicitly).

M1: Multiplying your estimate by 0.018 and dividing by 100 (or multiplying directly by 0.00018 ). Condones using 0.02 for the method mark.

A1ft: Correct final answer in pounds in the range [3.60, 7.20] , rounded or truncated to the nearest penny.

❌ Common Traps & Lost Marks

Forgetting to divide by 100: Giving an answer like £540 instead of £5.40 . The prompt provides a £ sign, so writing pence without converting loses the final accuracy mark!
Rounding too early: Estimating 0.018 as 0.02 gives 30 000 × 0.02 ÷ 100 = £6.00 . The mark scheme caps this at B1 M1 A0 (maximum 2 marks). Always calculate with the exact given rate of 0.018p !
Unrealistic Day 7 estimate: Assuming views increase or stay at 48 000. The post has dropped steadily since Day 2, so Day 7 must be below 48 000.