GCSE Maths · Ratio, proportion & rates of change

Proportion

Direct and inverse proportion, including finding and using the constant in y = kx and y = k/x.

199 GCSE-style practice questions

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Proportion, explained point by point

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  1. Recognise direct and inverse proportion from tables, graphs and descriptions

    Direct proportion: double one, the other doubles - the graph is a straight line through the origin. Inverse proportion: double one, the other HALVES, like speed and journey time - the graph is a curve that never touches the axes. Check a table by testing whether yx stays constant (direct) or x × y does (inverse).

  2. Solve proportion problems using the unitary method - recipes, prices, scaling

    Go down to one unit, then up to what you need. If 6 cakes need 270 g of flour, one cake needs 45 g, so 10 cakes need 450 g. For inverse problems flip the logic: 4 builders take 6 days, so 1 builder takes 24 days, and 8 builders take 3.

  3. Interpret graphs of quantities in direct or inverse proportion

    A straight line through the origin says "directly proportional", and its gradient is the constant - the unit price, the exchange rate. A reciprocal-shaped curve says "inversely proportional". A straight line that misses the origin is NOT direct proportion, however straight it looks.

  4. Set up and use proportion equations like y = kx and y = k/x, including squares and cubesHigher only

    Translate the sentence into an equation with a constant k: "y is proportional to x²" means y = kx². Use the given pair of values to find k, then answer the question. If y = 48 when x = 4, then k = 3, so y = 3x² and x = 5 gives y = 75.

Practice

Try a Proportion question

A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.

y is directly proportional to x. When x = 4, y = 18. Find the value of y when x = 10.

  1. 45
  2. 24
  3. 40
  4. 32
Show the answer and the working

Answer: 45

Find k = y ÷ x, then use y = kx for the new value of x.

  1. Direct proportion means y = kx.
  2. Find k: k = 18 ÷ 4 = 4.5.
  3. Use x = 10: y = 4.5 × 10 = 45.

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