OxfordAQA International AS and A-level Economics: Ratios, percentages, averages (9640) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions practise quantitative skills QS1, QS2 and QS3 from section 3.5 of the OxfordAQA International AS and A-level Economics (9640) specification, version 1.2. The skills could be assessed in any assessment. Sections 3.1 and 3.2 are International AS content and 3.3 and 3.4 are the extra International A2 content. Questions 9 to 11 use quantiles, which the specification adds for A2 assessments. Every country, firm and number is invented. Start with the study guide or the revision notes if you need them. The OxfordAQA Economics hub, the printable checklist and the free diagnostics are also useful.

Questions

1. A bakery chain employs 36 full-time and 60 part-time staff. Write the ratio of full-time to part-time staff in its simplest form, and give part-time staff as a fraction of all staff. [2]

2. A regional government shares a 360 cu million budget between roads, schools and clinics in the ratio 3 : 4 : 5. Calculate the amount for each. [3]

3. In Town T the price of a good rises from 4.80 cu to 5.52 cu. Monthly quantity demanded falls from 2,000 to 1,740 units.

(a) Find the percentage rise in price. [1] (b) Find the percentage fall in quantity demanded. [1] (c) Calculate the change in total revenue and comment on it. [2]

4. In Country E, inflation rises from 2.5% to 4.0%.

(a) State the change in percentage points. [1] (b) Calculate the percentage change in the inflation rate. [2]

5. A good sells for 36 cu including a 20% sales tax. Calculate the price before tax and the tax collected. [3]

6. Country G’s real GDP is 500 cu billion. It then changes by +3%, −2% and +4% in three successive years. Calculate GDP after three years and the overall percentage change. Explain why this is not +5%. [4]

7. Seven workers earn hourly pay (cu) of 5, 6, 6, 7, 8, 10 and 14.

(a) Calculate the mean and the median. [2] (b) A manager on 40 cu an hour joins. Calculate the new mean and median. [2]

8. A workshop has 20 workers. Ten earn 5 cu an hour, six earn 7, three earn 9 and one earns 14. Calculate the mean hourly pay and the median hourly pay. [5]

9. (A2) Twelve households have annual incomes (thousand cu): 14, 16, 18, 21, 24, 27, 31, 38, 46, 60, 85, 150. Using position (n + 1) × fraction, calculate the lower quartile, the median, the upper quartile and the interquartile range. [6]

10. (A2) Quintile shares of national income, from poorest to richest fifth:

Quintile	1st	2nd	3rd	4th	5th
Country H, year 1 (%)	6	10	15	23	46
Country H, year 5 (%)	8	12	16	23	41

(a) Calculate the ratio of the top to the bottom quintile share in each year. [2] (b) Calculate the percentage change in the combined share of the bottom two quintiles. [2] (c) Calculate the percentage change in the top quintile’s share. [1] (d) Evaluate whether the poorest households are better off in year 5. [3]

11. (A2) Country F raises its legal minimum weekly pay from 40 cu to 48 cu. Ten workers’ weekly pay (cu) before the change was 40, 44, 48, 50, 52, 56, 60, 66, 80 and 140. Everyone else’s pay is unchanged.

(a) Calculate the mean and median before the change. [2] (b) Calculate the mean and median after the change. [1] (c) Calculate the percentage change in the mean. [1] (d) Using position (n + 1) × fraction, calculate the interquartile range before and after. [3] (e) Evaluate whether the change reduced pay inequality among these workers. [3]

Answers

1. 36 : 60 = 3 : 5 (divide by 12) [1]. Part-time = 60/96 = 5/8 [1]. [2] Examiner insight: Simplify by the highest common factor, and say which group comes first. A ratio written the wrong way round tells a different story.

2. Parts = 3 + 4 + 5 = 12 [1]. One part = 360 / 12 = 30 [1]. Roads 90, schools 120, clinics 150 (sum 360) [1]. [3] Examiner insight: Checking that the shares sum to the total is a quick way to catch a slip before it costs the final mark.

3. (a) (5.52 − 4.80) / 4.80 × 100 = +15% [1]. (b) (1,740 − 2,000) / 2,000 × 100 = −13% [1]. (c) Old revenue = 4.80 × 2,000 = 9,600; new revenue = 5.52 × 1,740 = 9,604.8 [1]. Revenue rises by 4.8 cu, about +0.05%, so it is almost unchanged [1]. [4] Examiner insight: Each percentage change needs its own old value as the base. Using the price base for the quantity change is a common slip.

4. (a) 4.0 − 2.5 = +1.5 percentage points [1]. (b) (4.0 − 2.5) / 2.5 = 0.6 [1], so +60% [1]. [3] Examiner insight: Show both versions of a change in a rate. Saying “rose by 1.5%” is ambiguous and may not earn credit.

5. Price before tax = 36 / 1.20 [1] = 30 cu [1]. Tax = 36 − 30 = 6 cu [1]. [3] Examiner insight: Taking 20% off 36 gives 28.80, which is wrong because the tax is 20% of the pre-tax price. Work out what the base is first.

6. Year 1: 500 × 1.03 = 515 [1]. Year 2: 515 × 0.98 = 504.7 [1]. Year 3: 504.7 × 1.04 = 524.888, about 524.89 cu billion [1]. Overall change = 24.888 / 500 = +4.98% (2 d.p.). It is below 5% because each rate applies to a different base, so changes multiply rather than add [1]. [4] Examiner insight: A one-line explanation that the base changes each year is what turns a calculation into a reasoned answer.

7. (a) Sum = 56, mean = 56 / 7 = 8 [1]; median = 4th value = 7 [1]. (b) Sum = 96, mean = 96 / 8 = 12 [1]; median = (7 + 8) / 2 = 7.5 [1]. [4] Examiner insight: The mean moves a lot and the median hardly moves. Noting that contrast is what makes the working useful to an economic argument.

8. Total pay = 10 × 5 + 6 × 7 + 3 × 9 + 1 × 14 = 50 + 42 + 27 + 14 = 133 [1]; workers = 20 [1]; mean = 133 / 20 = 6.65 cu [1]. The 10th worker earns 5 and the 11th earns 7 [1], so median = (5 + 7) / 2 = 6 cu [1]. [5] Examiner insight: Multiply each pay level by its frequency before adding. Dividing by the number of pay levels (4) instead of the number of workers (20) is a common error.

9. n + 1 = 13 [1]. Q1 position 3.25: 18 + 0.25 × (21 − 18) = 18.75 [1]. Median position 6.5: (27 + 31) / 2 = 29 [1]. Q3 position 9.75: 46 + 0.75 × (60 − 46) = 56.5 [1]. IQR = 56.5 − 18.75 = 37.75 [1]. The method (position rule and interpolation) is stated [1]. [6] Examiner insight: Naming the position rule you use shows the method, so the marker can follow your approach.

10. (a) Year 1: 46 / 6 = 7.67 : 1 [1]. Year 5: 41 / 8 = 5.13 : 1 (2 d.p.) [1]. (b) Year 1: 6 + 10 = 16%. Year 5: 8 + 12 = 20% [1]. Change = 4 / 16 = +25% [1]. (c) (41 − 46) / 46 = −10.9% (1 d.p.) [1]. (d) The bottom two fifths take a larger share, which suggests improvement [1]. Shares show only how income is divided. If national income fell, a bigger share could still be a smaller amount [1]. A judgement needs mean income or each quintile’s income in real terms, then a conclusion that the poorest probably gain relatively but the gain in absolute terms is not shown [1]. [8] Examiner insight: Strong evaluation names what the data cannot show, here the level of income, and uses the figures already calculated.

11. (a) Mean = 636 / 10 = 63.6 [1] Median = (52 + 56) / 2 = 54 [1]. (b) New sum = 648, mean = 64.8; median still (52 + 56) / 2 = 54 [1]. (c) 1.2 / 63.6 = +1.89% (2 d.p.) [1]. (d) n + 1 = 11, so positions 2.75 and 8.25 [1]. Before: Q1 = 44 + 0.75 × 4 = 47, Q3 = 66 + 0.25 × 14 = 69.5, IQR = 22.5 [1]. After: Q1 = 48, Q3 = 69.5, IQR = 21.5 [1]. (e) The lowest pay rose 20% and the ratio of highest to lowest pay fell from 3.5 to 2.92 [1]. The median and upper quartile did not move, and the IQR fell by only 1, so the middle and top are unchanged [1]. Inequality at the bottom narrowed modestly. The data say nothing about jobs or hours lost, so the gain applies only to those still employed [1]. [10] Examiner insight: Compare more than one measure. A single figure, such as the mean rising, cannot show whether the spread changed.

Where marks are usually lost

• Dividing by the final figure rather than the starting figure when finding a percentage change.
• Mixing up percentage points and per cent.
• Adding successive growth rates instead of multiplying multipliers.
• Taking the percentage off the tax-inclusive price in a reverse percentage.
• Reading a median from data that are not in order.
• Dividing a frequency-table total by the number of rows rather than the number of items.
• Leaving out the position rule for a quantile, or ignoring interpolation.
• Quoting ratios the wrong way round.
• Stopping at the number without saying what it shows about the economy.

Next steps

• Re-read the study guide and the revision notes.
• Check the OxfordAQA Economics hub and the printable checklist.
• Take the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

OxfordAQA International AS and A-level Economics (9640), specification version 1.2, section 3.5 Quantitative skills (QS1, QS2 and QS3). First teaching September 2020; first International AS exams May/June 2021; first International A-level exams May/June 2022. Published by OxfordAQA.