IGCSE Mathematics Paper 2 (Extended) — non-calculator

⚠ If you missed marks here: averaging the two percentages gives 47.5% and is wrong, because there is more of the weaker alloy — 60 kg against 40 kg — so the answer must be pulled below the halfway point. A percentage of one quantity cannot be added to a percentage of a different quantity. Turn both into real kilograms of copper first, then divide by the real total mass.

⚠ If you missed marks here: dividing the whole $153 by 1.2 gives $127.50 and is the standard error — it quietly taxes the labour, which the question says is untaxed. Strip out every untaxed item before you reverse the percentage. And 108 ÷ 1.2 is a division, not "take off 20%": taking 20% off 108 gives 86.40, which does not grow back to 108.

⚠ If you missed marks here: the tax is 20% of the parts, not 20% of the whole bill — 20% of 153 is $30.60, which would leave the arithmetic not adding up. If your three figures do not sum back to the total on the bill, one of them is wrong.

⚠ If you missed marks here: the two tests are out of different totals, which is exactly why raw scores cannot be compared — 45 is a bigger number than 33 and yet it is the weaker result. Without a calculator, 33 ÷ 40 is easiest as 33 ÷ 4 = 8.25 then × 10, or as ¼ of 33 × 10.

⚠ If you missed marks here: the difference between two percentages is measured in percentage points, not in per cent. Saying "7.5% better" means something different and is wrong here: as a percentage increase from 75 it would be 7.5 ÷ 75 = 10%. Cambridge accepts 7.5 either way in this part, but the distinction is worth having — it changes the answer whenever a question asks for a percentage increase.

⚠ If you missed marks here: subtracting 21:48 from 06:15 straight down the page gives a negative answer, and "15 h 33" comes from doing it the wrong way round (21:48 − 06:15). When a time crosses midnight, split it at midnight and add the two pieces, or add 24 hours to the finishing time before you subtract. Never column-subtract: 15 − 48 is not 33 on a clock.

⚠ If you missed marks here: two base-60 traps again. Taking 45 minutes off 8 h 27 needs a borrow, so it is 7 h 42 — not 8 h 18 and not 7 h 82. Then 5 × 42 = 210 minutes, which is 3 h 30, not "2 h 10". Minutes only convert to hours in sixties. If you find yourself writing a minutes figure of 60 or more, convert it before you go any further.

⚠ If you missed marks here: writing 01:35 is the error to avoid — that is twenty-five to two in the morning. In the 24-hour clock a pm time has 12 added to the hours (1 pm is 13:00, 11 pm is 23:00), an am time keeps its hours, and the two exceptions are 12 midnight, which is 00:00, and 12 noon, which is 12:00. Take both times from the S2 row and nowhere else.

⚠ If you missed marks here: S4 is the one that decides this question and it is the one most likely to be wrong, because it finishes after midnight — 12.25 am is 00:25 on the next day, so it is 1 h 45 min, not a negative answer and not 10 h 15. And you cannot tell which crossing is slowest by looking at the table; all four have to be worked out. Convert every time to the 24-hour clock first, then subtract, and treat a crossing that passes midnight by splitting it there.

⚠ If you missed marks here: treating this as simple interest gives 408 ÷ 2 = 204 a year and r = 4.08%, which is close enough to look right and is wrong — with compound interest the second year earns more than the first, so the rate must be below the simple-interest answer. Two years of compound interest multiply by k ², so finding k means taking a square root; on a non-calculator paper that root is always exact, and here 1.0816 comes from 104² = 10816. If you cannot spot the root, try 4% and 5% and check.

⚠ If you missed marks here: answering £204 means you halved the total interest of £408, which is what simple interest would do. Under compound interest the second year earns interest on £5200, not on £5000, so it must be more than the first year’s £200. A second-year figure smaller than the first year’s is always a signal that something has gone wrong.

⚠ If you missed marks here: the trap is answering $75 by adding 25% to the cost. Read which number the percentage is of: almost every profit question on this course measures profit against the cost, and this one deliberately measures it against the selling price, so the 100% you are working towards is the selling price and not the $60. Check your answer by computing the profit as a fraction of the price you found — with $75 you would get 15 ÷ 75 = 20%, not 25%.

⚠ If you missed marks here: the phrase that decides this question is what is left. A quarter of his income would be $600, but he spends a quarter of the $1560 that survives the rent, which is $390. Percentages and fractions in a chain each apply to whatever is left at that moment, not to the original amount — unless the question says otherwise. Adding your three figures back to $2400 catches this instantly.

⚠ If you missed marks here: divide by the income, $2400, and not by the $1560 that was left after the rent — that would give 75%, which is the fraction of the remainder he saves, a different quantity. The question names the total it wants the percentage taken of; underline it before dividing.