Question showcase
Stop 2 of 4
These are real published questions, rendered live from the bank with freshly generated numbers — not screenshots. Every one is playable: press Try it live on any card to answer it and see the marking.
Wrong answers are anticipated at authoring time, one written response each, so a student is told which mistake they made rather than just that they were wrong. These are per-question — 650+ of them coded across the bank.
Four coded wrong answers. Drop the sign on the second bracket and it says so; forget the middle terms entirely and it says that instead.
Expand and simplify (x + 4)(x − 2)
x^2+2x-8 — the power typed with a ^ instead of a superscriptx2+2x-8 — the power typed without a ^ at allAdding the two shorter sides instead of squaring them is the classic Pythagoras error — and it gets its own response.
Find the length of the side marked ?. Give your answer in cm.
Expressions, fractions, ratios, coordinates, sets and index notation are each graded on their own terms. This half is NOT authored per question: accepting an uncancelled fraction, or the brackets of a factorisation in either order, is the grader's job and applies to every question of that type. The strips below are live verdicts from it, not claims.
Graded as an expression, not as a string — so the order the student writes the brackets in is their business, not the marker’s.
Factorise x² − 36
(x − 6)(x + 6) — the two brackets the other way roundIndex notation. Superscripts and carets are the same answer; writing the multiplication out longhand is not, because that is not what was asked for.
Write 18 as a product of its prime factors. Give your answer using index notation.
2 × 3^2 — the power typed with a ^ instead of a superscript2 × 3 × 3 — the multiplication written out longhand2 × 32 — the power typed without a ^ at allGeometry is drawn, not described. The diagram is generated from the same parameters as the question, so every re-roll produces a correctly labelled figure.
The triangle is redrawn for whichever angle and side are generated — and the answer is marked to the accuracy the question asked for.
Not drawn accurately
In the right-angled triangle, the hypotenuse is 11 cm and the angle shown is 65°.
Work out the length of the side marked x. Give your answer to 2 decimal places.
9.9712 cm — the full calculator value, not rounded9.98 cm — one out in the last decimal placeA cyclic quadrilateral with the angles marked algebraically — the figure carries the information the question needs.
Not drawn accurately
ABCD is a cyclic quadrilateral. Angle A = (2x + 31)° and angle C = (3x + 19)°.
Work out the size of the larger of angles A and C.
Exam-style (a)/(b)/(c) built on one piece of information, each part carrying its own marks and its own skill — so a student who reads the graph correctly but slips on the final total is credited for what they got right.
One velocity–time graph, three parts, 2 + 2 + 3 marks. Part (c) depends on (a) and (b) but is graded on its own.
The velocity–time graph shows a car accelerating from rest, travelling at a constant velocity, then decelerating back to rest.
Use the graph to answer the questions.
(a) Work out the distance travelled while the car is accelerating (from 0 to 2 s).
(b) Work out the distance travelled while the car is at a constant velocity (from 2 s to 7 s).
(c) Work out the TOTAL distance travelled by the car.
Without replacement, three fraction answers — each part attributed to tree diagrams separately.
A bag contains 4 red and 5 blue counters. A counter is taken at random and NOT replaced. A second counter is then taken.
(a) Given that the first counter is red, write down the probability that the second counter is also red.
(b) Work out the probability that BOTH counters are red.
(c) Work out the probability that AT LEAST ONE of the two counters is red.
6/16 — the same fraction, not cancelled down0.375 — written as a decimalReflections, enlargements, plotting lines, completing histograms — marked on the placement, not on a typed answer. This is the part of the paper most online practice quietly skips.
Tap the grid to place the reflected triangle. Marked per vertex, with feedback for reflecting in the wrong line. The mirror line moves with the parameters.
On the grid, reflect the shaded triangle in the mirror line x = 5.
Place the corners of the reflected triangle.
A histogram with unequal class widths — the student draws the bars and the widths are part of the mark.
The table shows the times taken by 85 runners to finish a race.
| Time, t (minutes) | Frequency |
|---|---|
| 0 < t ≤ 10 | 15 |
| 10 < t ≤ 20 | 20 |
| 20 < t ≤ 40 | 30 |
| 40 < t ≤ 60 | 20 |
Draw a histogram for this data.
Draw each bar with two taps: one top corner, then its other edge.
Frequency trees, Venn diagrams and two-way tables with several labelled blanks, graded independently and banded the way a real mark scheme bands them.
A frequency tree with several blanks. Each is graded independently, and later branches follow through from earlier ones.
52 students were asked how they travel to school.
21 students walk; the rest come by bus.
6 of the walkers were late. 13 of the bus students were late.
Complete the frequency tree by writing down the values of A, B and C.
Venn diagram regions, filled in against the SVG rather than typed as a list.
31 students each study French, Spanish, both or neither.
12 study French. 14 study Spanish. 1 study both.
Complete the Venn diagram by writing down the values of A, B and C.
Questions that need two independent skills in one answer. These are marked positive-only: getting one right proves synthesis, getting it wrong routes to revision rather than penalising either underlying skill.
Ratio and coordinates in one answer — neither is a prerequisite of the other, so the question genuinely tests putting them together.
A is the point (3, -4).
B is the point (15, 8).
P lies on the straight line AB so that AP : PB = 1 : 2.
Work out the coordinates of P.
7, 0 — typed without the bracketsx = 7, y = 0 — written as x = …, y = …Rationalising a surd inside an area problem. Higher tier, five stars.
A rectangle has area (19 + 11√3) cm² and width (2 + √3) cm.
Work out the length of the rectangle.
Give your answer in the form p + q√3, where p and q are integers.
You mark the paper; this turns the marks into the next lesson — the questions the class dropped, per-student feedback, and a starter sheet. Free, no account.