GCSE Maths revision · Probability and statistics

Multi-step problems

Foundation and Higher

The idea

Longer questions join several topics together. Plan what you need to find, find each piece in order, and finish with a clear answer or decision.

Write down what the question finally asks for.
Work out each intermediate value and label it.
Finish with a sentence that answers the question, with units.

Watch out A comparison question needs a conclusion: say which is better and show the numbers that prove it.

See it worked

Worked exampleNon-calculator3 marks

The mean of four numbers is 10. Three of the numbers are 7, 9 and 12.

Work out the fourth number. You must show your working.

The four numbers add up to $4 \times 10 = 40$ .
$40 - (7 + 9 + 12) = 40 - 28 = 12$

Answer 12

Your turn

Question 1Non-calculator3 marks

A shop records delivery times, in days, for two couriers. Courier $A$ : 2, 3, 3, 4, 4. Courier $B$ : 1, 1, 2, 6, 6.

The shop wants the more reliable courier. Which should it choose? You must show how you get your answer.

Question 2Non-calculator5 marks

A garden centre sells 240 plants in one day. The ratio of shrubs to flowers sold is 1 : 3. Shrubs cost £10 each and flowers cost £5 each.

(a) Work out the number of shrubs sold.

(b) Work out the percentage of the day’s takings that came from shrubs.

Question 3Non-calculator5 marks

A bag contains only red and blue counters in the ratio $3 : 5$ . Four more red counters are added. Now the probability of taking a red counter is $\frac{1}{2}$ .

(a) Work out how many counters were in the bag at the start.

(b) Two counters are taken from the new bag without replacement. Work out the probability that both are red.

In past papers

12 official questions in 10 papers since 2017. The latest:

All GCSE Maths past papers

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