Direct and inverse proportion Cambridge IGCSE Mathematics revision
Not started
Learn it
In plain words
Buy twice as many apples and you pay twice as much: that's direct proportion. Put twice as many people on a job and it takes half the time: that's inverse proportion. Both turn into a simple formula with one number, k, to find.
Three things to know
- y is directly proportional to x: y = kx. Double x and y doubles. It could also be to x²: y = kx².
- y is inversely proportional to x: y = k/x. Double x and y halves.
- Method: write the formula with k, use the pair of values you're given to find k, then use the formula.
Worked example
y is inversely proportional to x, and y = 6 when x = 4. Find y when x = 8.
- Write y = k/x. Put in the values: 6 = k/4, so k = 24.
- The formula is y = 24/x.
- When x = 8, y = 24/8 = 3.
Tips and tricks
- Always find k first. Never try to jump straight to the answer.
- Read the question carefully: proportional to x, to x squared, or to the square root of x?
It lands in your notebook with its questions as flashcards.
Direct and inverse proportion: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
y = kx, and y = 12 when x = 3. What is k?
12 ÷ 3.
y is directly proportional to x. If x doubles, what happens to y?
y = kx.
y is inversely proportional to x. If x doubles, what happens to y?
y = k/x.
y is proportional to x². If x is multiplied by 3, y is multiplied by what?
3² = 9.
y = 20/x. What is y when x = 4?
20 ÷ 4.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 9 marks. Write your answers on paper, then check them.
Direct and inverse proportion
Cambridge IGCSE Mathematics 0580 · 9 marks · papermunch.org
Name ______________________________ Date ______________
y is directly proportional to x, and y = 15 when x = 5. Find y when x = 8.[3]
Show answerHide answer
24. k = 3.
y is directly proportional to x², and y = 12 when x = 2. Find y when x = 5.[3]
Show answerHide answer
75. k = 3; 3 × 25.
y is inversely proportional to x, and y = 10 when x = 2. Find x when y = 4.[3]
Show answerHide answer
5. k = 20; x = 20 ÷ 4.
Answers: Direct and inverse proportion
- 1. 24. k = 3.
- 2. 75. k = 3; 3 × 25.
- 3. 5. k = 20; x = 20 ÷ 4.