12 short questions across all six content areas, designed as a lesson starter or a daily warm-up.

⏱️ Ten-minute starters — Foundation

Maths · GCSE Foundation · 12 questions · ~10 min

MathsUKwww.geekhero.co.uk

Twelve short questions, two from each of the six content areas: number, algebra, ratio, geometry, probability and statistics. Nothing here needs more than a minute, and nothing needs a calculator. It is built as a lesson starter — print it, hand it out, take ten minutes, mark it together — and it works just as well as a daily warm-up at home in the fortnight before a mock. The value is in the spread rather than the depth: a student who has spent a week on algebra can find out in ten minutes what a week away from statistics has cost. Generate a new sheet whenever you want a fresh twelve on the same pattern.

1.The marks scored by four pupils in a quiz were 8, 8, 8, 8. Work out the mean, the median and the mode of these marks.
(a)mean = 2, median = 8, mode = 8
(b)mean = 8, median = 8, mode = 4
(c)mean = 8, median = 8, mode = 8
(d)mean = 32, median = 8, mode = 8
2.A printer's ink cartridge level, I millilitres, is plotted against the number of pages printed, p, and the points lie on a straight line. The line passes through (0, 24) and (300, 9). The printer has now printed 300 pages. Work out how many more pages it can print before the cartridge is empty.
(a)480 pages
(b)0.45 pages
(c)180 pages
(d)9 pages
3.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
4.A laptop is bought for £600. Its value decreases by 20% after 1 year. Work out the value of the laptop after 1 year.
(a)£120.00
(b)£580.00
(c)£480.00
(d)£720.00
5.The mean of the four numbers 10, 15, 20 and x is 18. Work out the value of x.
(a)27
(b)72
(c)45
(d)18
6.There are 400 students at a school. 25% of them have a brother, 40% have a sister and 15% have both a brother and a sister. Work out how many of the students have neither a brother nor a sister.
(a)140 students
(b)300 students
(c)200 students
(d)260 students
7.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.
(a)72.3 cm
(b)26.2 cm
(c)36.2 cm
(d)46.2 cm
8.Priya and Ben each want to estimate the probability that a coin lands on heads. Priya flips the coin 50 times and works out her relative frequency. Ben flips the same coin 500 times and works out his relative frequency. Whose relative frequency is more likely to be close to the true probability? Give a reason for your answer.
(a)Ben, because a larger sample is closer to the theory
(b)Neither, because every flip is a separate random event
(c)Ben, because 500 flips must give exactly 250 heads
(d)Priya, because a small sample is less affected by luck
9.Work out how many seconds there are in 3 minutes and 20 seconds.
(a)200 seconds
(b)320 seconds
(c)180 seconds
(d)23 seconds
10.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?
(a)A formula, relating two quantities
(b)An identity, true for all values of x
(c)An expression, with x terms and numbers
(d)An equation, true for one value of x
11.Solve x² + 7x = 0.
(a)x = 0 or x = 7
(b)x = 0 or x = −14
(c)x = 0 or x = −7
(d)x = −7
12.The probability that Leo wakes up before his alarm is 0.35. The probability that his younger sister wakes up before her alarm, independently of Leo, is 0.28. Work out the probability that neither of them wakes up before their alarm.
(a)0.098
(b)0.63
(c)0.532
(d)0.468

What is on this worksheet?

The sheet holds 12 questions drawn from the MathsUK bank — the content areas covered: Number, Algebra, Ratio, proportion and rates of change, Geometry and measures, Probability, Statistics. It is pitched at GCSE Foundation and takes about 10 minutes to work through in full. It works as a class handout, a homework, or a warm-up before a test.

How to use the sheet well

Print it or open it on screen — both work. Printing is A4; the screen view fits phones and tablets.
Do all 12 questions before checking — about 10 minutes is the guide, but there is no time pressure.
Check the answers — press “Show answers” or print the answer page separately.
Redo the questions you got wrong — twice as effective as doing 12 fresh ones.
“New questions” — builds a fresh sheet on the same statements, so you can practise again without repeats.

Why this sheet helps

MathsUK worksheets use questions graded by difficulty and a fair spread of correct-answer positions (the answer is not always (a)) — so the student really has to think about each question rather than guess a pattern. Every question is tagged to a DfE content statement and checked before it enters the bank. The answers come with a step-by-step explanation, not just a value — so a wrong answer becomes a lesson.

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