UK GCSE · GCSE Mathematics (Higher Tier)

Ratio, Proportion, Probability and Statistics

13 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 13 questions

  1. is inversely proportional to the square of . When , . Find the value of when .
  2. A bag contains 5 red counters and 3 blue counters. Two counters are taken at random from the bag without replacement. Find the probability that both counters are the same colour.
  3. The mean of five numbers is 18. When a sixth number is added, the mean becomes 20. What is the sixth number?
  4. In a survey of 100 students, 60 study French, 45 study Spanish, and 20 study both. A student is selected at random. Given that the student studies French, what is the probability that they also study…
  5. The price of an antique increased by in year 1, and then decreased by in year 2. What was the overall percentage change across the two years?
  6. There are sweets in a bag. 6 of the sweets are orange and the rest are yellow. Hannah takes a random sweet and eats it. She then takes another sweet and eats it. The probability that Hannah eats t…
  7. £84 is shared between three people in the ratio 2 : 3 : 7. How much does the person with the smallest share receive?
  8. £2000 is invested at 3% compound interest per year. How much is it worth after 4 years, to the nearest penny?
  9. A bag contains 4 red and 6 blue counters. Two counters are taken at random without replacement. What is the probability that they are the same colour?
  10. is directly proportional to . When , . What is when ?
  11. A histogram has a bar for the class . The frequency density is 3.2. What is the frequency of this class?
  12. A car is worth £12000 and loses 15% of its value each year. What is it worth after 3 years?
  13. It takes 6 workers 10 days to build a wall. All workers work at the same rate. How many days would 4 workers take?

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