You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
This capstone lesson consolidates every topic covered in the course: ratios, percentages, compound interest, growth and decay, compound measures (speed, density, pressure) and Higher-tier direct and inverse proportion. Each question is written in the style of an Edexcel GCSE Mathematics (1MA1) exam question, with mark allocations, mark-scheme-style solutions and examiner notes so you can see exactly how marks are awarded.
Use this lesson in one of two ways:
| Paper | Calculator | Duration | Marks | Typical ratio/proportion weighting |
|---|---|---|---|---|
| Paper 1 | No | 1 hour 30 minutes | 80 | 20–25% |
| Paper 2 | Yes | 1 hour 30 minutes | 80 | 20–25% |
| Paper 3 | Yes | 1 hour 30 minutes | 80 | 20–25% |
Across a full set of three papers, roughly 50–60 marks out of 240 come from ratio, proportion and rates of change. That is more than any other topic area, so fluency here is the highest-leverage thing you can do before the exam.
Every Edexcel mark is one of three types:
The examiner notes after each question show exactly which marks you earn at each step and the most common places candidates drop marks.
Anya, Ben and Chris share a sum of money in the ratio 2 : 3 : 7. Chris receives £85 more than Anya.
Work out how much Ben receives.
Examiner note. The most common error is using the total (2 + 3 + 7 = 12 parts) rather than the difference (5 parts) — candidates who do this typically work out "the money" as £85, assume it is the total and get £21.25 for Ben. Always re-read the question — the "£85 more" clue tells you to work with the difference between shares, not the sum. On a non-calculator paper, recognising that £85 ÷ 5 is an integer (£17) is a good check that you have interpreted the ratio correctly.
A sofa costs £540 including VAT at 20%.
Calculate the price of the sofa before VAT was added.
Examiner note. This is a classic reverse percentage trap. Weaker candidates calculate 20% of £540 (= £108) and subtract, giving £432 — which is wrong because the 20% VAT was added to the pre-VAT price, not to £540. The correct reasoning: £540 already includes the 20%, so £540 = 120% of the original. Divide by the multiplier (1.20) to reverse the increase. This skill — dividing by the multiplier to reverse a percentage change — appears in almost every Edexcel paper, often disguised inside a longer problem. A useful sense-check: after finding the pre-VAT price, add the VAT back on (450 + 90 = 540) and confirm you recover the given figure. If you get £432 and try to check (432 × 1.20 = 518.40), the mismatch signals the error. Reverse percentages also apply to sale prices ("reduced by 15%, now £68, find the original price"), depreciation ("a car worth £X now was worth 25% more a year ago") and inflation. The logic is always identical: identify what percentage of the original the given figure represents, then divide by the corresponding multiplier.
Raj invests £6,000 for 4 years.
(a) Calculate how much Option A is worth after 4 years. (2)
(b) Calculate how much Option B is worth after 4 years. (2)
(c) Which option gives Raj more money, and by how much? (1)
(a) Simple interest per year = 6,000 × 0.035 = £210. (M1)
Total interest over 4 years = 4 × 210 = £840. Value = 6,000 + 840 = £6,840. (A1)
(b) Multiplier = 1.032. Value = 6,000 × 1.032⁴. (M1)
1.032⁴ = 1.13446… (keep full calculator display).
6,000 × 1.13446… = £6,806.76 (to the nearest penny). (A1)
(c) Option A − Option B = 6,840 − 6,806.76 = £33.24.
Option A gives Raj more money, by £33.24. (B1)
Examiner note. Parts (a) and (b) together test the distinction between simple and compound interest — a standard Edexcel pairing. Part (c) is a comparison mark: you must state both which option wins and by how much. Examiners award this mark only for a complete statement; writing "Option A" alone loses the mark. The calculator-precision rule matters here — if you round 1.032⁴ to 1.13, you get £6,780, which differs from the mark-scheme answer by more than £20. Always store intermediate values in the calculator and only round at the very end.
A solid gold bar is a cuboid with dimensions 7.5 cm × 4 cm × 2 cm. The density of gold is 19.3 g/cm³.
Gold is sold at £48 per gram.
Calculate the value of the gold bar. Give your answer to the nearest £100.
Examiner note. A three-stage compound-measure problem: (1) volume of a cuboid, (2) density formula in the form mass = density × volume, (3) unit price × mass. Candidates routinely lose the first M1 by miscalculating the volume, but the more common error is writing the density formula the wrong way round — starting with density = mass × volume or dividing when they should multiply. The density triangle (ρ at the top, m and V below) is a reliable way to avoid this: cover what you want to find, read off the correct operation. The final rounding ("to the nearest £100") is worth an A1 on its own — write "£55,600", not "£55,584".
The number of bees in a colony is modelled by the formula
B = 20,000 × 0.92ⁿ
where B is the number of bees after n complete years.
(a) Write down the initial number of bees. (1)
(b) Find the number of bees after 6 years, correct to the nearest 100. (2)
(c) Describe what the value 0.92 represents in the context of the question. (2)
(a) When n = 0, B = 20,000 × 0.92⁰ = 20,000 × 1 = 20,000 bees. (B1)
(b) B = 20,000 × 0.92⁶ = 20,000 × 0.60634… = 12,126.77… (M1)
To the nearest 100 = 12,100 bees. (A1)
(c) 0.92 = 1 − 0.08, so it represents a decrease of 8% per year — each year the number of bees is 92% of the previous year's number. (B1 for "decrease/decay", B1 for "8%").
Examiner note. Edexcel's growth-and-decay questions on the Higher tier almost always include an interpretation mark like part (c). The key moves are (i) subtracting from 1 to see that 0.92 is a decrease multiplier and (ii) converting that to a percentage. Candidates who simply state "the rate" or "the multiplier" score zero on this mark — the mark scheme specifically requires students to communicate both the direction (decrease/decay) and the size (8%) of the yearly change. Writing "it decays by 8% each year" scores the full 2 marks in one sentence.
y is directly proportional to the square of x.
When x = 4, y = 48.
(a) Find an equation linking y and x. (3)
(b) Find the value of x when y = 300. Give your answer to 3 significant figures. (2)
(a) y∝x2, so y=kx2 for some constant k. (M1 for writing the equation with k)
Substitute x = 4, y = 48: 48 = k × 16. (M1)
k = 48 ÷ 16 = 3, so y=3x2. (A1)
(b) 300 = 3x² → x² = 100 → x = 100. (M1)
x = 10.0 (3 s.f.). (A1)
Strictly, x² = 100 has two solutions: x = 10 and x = −10. Unless the question specifies that x is positive (for example by context: length, mass, time), both answers should be stated. In this case the mark scheme accepts x = 10.0 (or x = ±10.0) as the final answer.
Examiner note. This is a four-step recipe that appears on every Higher-tier paper: (1) write the proportion with a k, (2) substitute to find k, (3) write the equation, (4) use the equation to answer the question. Candidates who jump straight from "x = 4, y = 48" to a numerical answer without writing the y=kx2 line lose both M1 marks. Compare carefully with inverse proportion (Question 7) — the structure looks similar, but k is placed differently. On a calculator paper, take care with the square root step: if x² = 100, the calculator's √ button gives only the positive root, so you must add the ± symbol yourself if the context allows negative values.
Priya drives from Bristol to Cardiff, a distance of 45 miles, at an average speed of 60 mph. She then drives from Cardiff to Swansea, a distance of 40 miles, at an average speed of 50 mph.
(a) Show that the total journey time is 1 hour 33 minutes (to the nearest minute). (3)
(b) Hence work out her average speed over the whole journey, to 1 decimal place. (2)
(a) Time for leg 1 = distance ÷ speed = 45 ÷ 60 = 0.75 hours = 45 minutes. (M1)
Time for leg 2 = 40 ÷ 50 = 0.8 hours = 48 minutes. (M1)
Total time = 45 + 48 = 93 minutes = 1 hour 33 minutes as required. (A1 — conclusion stated)
(b) Total distance = 45 + 40 = 85 miles. Total time = 93 ÷ 60 = 1.55 hours. (M1)
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.