x and y are both positive, and y is inversely proportional to x. Which statement describes the graph of y against x?

A curve falling from left to right that gets closer to both axes without ever touching them

A straight line with a negative gradient

A curve falling from left to right that gets closer to both axes without ever touching them

A straight line through the origin

A curve through the origin that gets steeper as x increases

Is direct and inverse proportion on the Foundation paper as well?

Partly. Spec reference R10 is common content, so Foundation candidates solve direct and inverse proportion problems, usually by finding the value of one unit and scaling. The algebraic side is where the tiers separate: R13 asks Foundation candidates to interpret an equation such as y = (k)/(x), while Higher candidates have to construct it themselves, including the versions with x^2 and x^3.

Do you get the proportion formula on the Edexcel formulae sheet?

No. The Exam Aid sheet issued with 1MA1 papers for the 2025 to 2027 windows carries the quadratic formula, the sine and cosine rules, the area of a triangle, Pythagoras, the trapezium, prism and circle formulae and compound interest. The cone and sphere formulae are not on it either; those are printed inside the question that needs them. Nothing about proportion appears anywhere, so you need to know that direct proportion is y = kx, that inverse proportion is y = (k)/(x), and that a square or a cube named in the sentence attaches to the x.

How many marks is a proportion question worth on Edexcel Higher?

The three-part version is usually 5 marks: about 3 for setting up the equation and finding the constant, then 1 each for using the formula forwards and backwards. A graph-matching or table question is 1 or 2 marks on its own. Each paper is 80 marks, so it is a small block, but a reliable one once the first line is right.

What does an inverse proportion graph look like?

For positive values it is a curve falling from left to right that flattens off, getting closer to both axes without ever touching them. It is not a straight line with a negative gradient, which is the option Edexcel includes to catch exactly that idea. Direct proportion gives the straight line through the origin, and y = kx^2 gives a curve that also starts at the origin but gets steeper as x grows.

Direct and Inverse Proportion - Edexcel GCSE Higher Maths

Typically 3-5 marks per paper, usually one question split into parts · Spec 1MA1

Proportion at Higher tier is two jobs wearing one name. The first is the reasoning students already have from earlier years: 5 litres of paint covers 40 square metres, so work out what one litre does and scale up. The second is the algebraic treatment, and that is where Edexcel's 1MA1 Higher tier goes past Foundation. Spec reference R13 asks Foundation candidates to interpret equations that describe direct and inverse proportion; the Higher wording adds the word construct, so you are expected to write $y = kx$ , $y = kx^2$ , $y = kx^3$ or $y = \frac{k}{x^2}$ yourself from a sentence of English. R10 covers the problem solving around it and R14 covers the graphs.

The usual Edexcel shape is a two-line stem and three parts: part (a) gives you one pair of values and asks for a formula, part (b) uses the formula forwards, part (c) uses it backwards. That comes to about 5 marks and sits in the second half of the paper. It can appear on any of the three papers. Paper 1 is non-calculator, so there the numbers are picked to make $k$ a whole number or a simple fraction; on Papers 2 and 3 the constant is often a decimal and the setting does more of the work, with light intensity, magnetic force, stopping distance or the time a job takes. The graph version is a matching question, four sketches with letters, and you say which one goes with $y = \frac{k}{x}$ .

Everything turns on the first line you write. Three failures account for most of the lost marks: reading past the word inversely and starting from $y = kx$ , reading past the word square and using $x$ where the sentence said $x^2$ , and mixing the two notations into $y \propto \frac{k}{x}$ , which states nothing and cannot be substituted into. Write the relationship as an equation with $k$ , substitute the given pair, then write the formula out again with the number in place of $k$ . A candidate who gets $k = 80$ and never writes $y = \frac{80}{x^2}$ has dropped the accuracy mark in part (a) and left the other two parts with nothing to use.

Worked example

y

is inversely proportional to the square of

x

. When

x = 4

y = 5

. (a) Find a formula for

y

in terms of

x

. (b) Work out the value of

y

when

x = 10

. (c) Work out the positive value of

x

when

y = 20

[5 marks]

Inversely proportional to the square of $x$ means $y = \frac{k}{x^2}$ .
M1: a correct relationship with a constant $k$ ; the square must be on the $x$ , not on the whole fraction
Substitute $x = 4$ and $y = 5$ : $5 = \frac{k}{16}$ , so $k = 80$ .
M1: substituting the given pair and solving for $k$
Write the formula out in full: $y = \frac{80}{x^2}$ .
A1: the answer to (a) is the formula, not the value of $k$ on its own
(b) When $x = 10$ : $y = \frac{80}{100} = 0.8$ .
B1: follow through from their formula
(c) When $y = 20$ : $20 = \frac{80}{x^2}$ , so $x^2 = 4$ and $x = 2$ .
B1: multiply up first, then square root; $x = 4$ here is the sign of a missed root

Practice questions

These are original questions in Edexcel 1MA1 Higher style. The opening ones use the unitary method the way a Foundation paper would set it, the middle of the set is about writing the equation with $k$ and using it in both directions, and the last third moves into the inverse square contexts that turn up late in a Higher paper. Where a question asks for a formula, type it as an expression such as 50/x^2, and any equivalent form is accepted.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [3 marks]

The cost of a length of rope is directly proportional to its length. A 12 metre length costs £8.40. Work out the cost of a 20 metre length of the same rope, in pounds.

Your answer (fractions like 1/2 are fine)
Question 2 Exam pace [2 marks]

$y$ is inversely proportional to $x$ . When $x = 3$ , $y = 8$ . Find the value of $k$ in $y = \frac{k}{x}$ .

Your answer (fractions like 1/2 are fine)
Question 3 Exam pace [3 marks]

$y$ is directly proportional to $x$ . When $x = 8$ , $y = 20$ . Write a formula for $y$ in terms of $x$ .

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 4 Exam pace [1 mark]

$x$ and $y$ are both positive, and $y$ is inversely proportional to $x$ . Which statement describes the graph of $y$ against $x$ ?

Answer options for question 4
A straight line with a negative gradient A curve falling from left to right that gets closer to both axes without ever touching them A straight line through the origin A curve through the origin that gets steeper as $x$ increases
Question 5 Exam pace [4 marks]

$y$ is directly proportional to the square of $x$ . When $x = 2$ , $y = 20$ . (a) Find the value of $k$ in $y = kx^2$ . (b) Work out the value of $y$ when $x = 5$ .

k = y when x = 5 =
Question 6 Stretch [2 marks]

$y$ is directly proportional to the cube of $x$ . The value of $x$ is doubled. The value of $y$ is multiplied by $n$ . Find the value of $n$ .

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Reading past the word inversely and starting from $y = kx$ . Given $y = 15$ when $x = 4$ , that produces $k = 3.75$ and an answer of 30 when $x = 8$ , where the inverse relationship gives 7.5.

Underline inversely before you write anything, then put $y = \frac{k}{x}$ on the first line. Sense-check at the end: in inverse proportion a larger $x$ has to give a smaller $y$ , so an answer that has gone up in both columns is wrong.
Ignoring the word square, so $y$ proportional to the square of $x$ is set up as $y = kx$ . With $y = 45$ at $x = 3$ that gives $k = 15$ instead of $k = 5$ , and every value calculated afterwards is wrong.

Write the power into the equation before any numbers go in: $y = kx^2$ , then substitute. The square belongs to $x$ alone, so $x = 3$ gives $9k$ , not $(3k)^2$ .
Putting the proportion symbol and the constant in the same statement, as in $y \propto \frac{k}{x}$ . It is not an equation, so no pair of values can be substituted into it, and the method mark for a correct relationship goes.

Pick one: $y \propto \frac{1}{x}$ records the relationship, $y = \frac{k}{x}$ is the thing you can work with. Move to the equals sign as soon as you have read the sentence, and never carry the symbol into the working.
Finding $k$ and stopping. Part (a) asks for a formula, so a script that ends at $k = 80$ collects the method marks and loses the accuracy mark, and part (b) then has nothing to follow through from.

Write the formula again with the number where $k$ was: $y = \frac{80}{x^2}$ . Box that line, because the rest of the question is marked against it.
Forgetting the square root when working backwards from $y = \frac{k}{x^2}$ . Reaching $x^2 = 36$ and writing $x = 36$ , or halving it to 18.

Split the rearrangement into two written lines: multiply up to get $x^2 = \frac{k}{y}$ , then take the square root on the next line. Where $x$ is a length or a distance, only the positive root is an answer.

Frequently asked questions

Is direct and inverse proportion on the Foundation paper as well?: Partly. Spec reference R10 is common content, so Foundation candidates solve direct and inverse proportion problems, usually by finding the value of one unit and scaling. The algebraic side is where the tiers separate: R13 asks Foundation candidates to interpret an equation such as $y = \frac{k}{x}$ , while Higher candidates have to construct it themselves, including the versions with $x^2$ and $x^3$ .
Do you get the proportion formula on the Edexcel formulae sheet?: No. The Exam Aid sheet issued with 1MA1 papers for the 2025 to 2027 windows carries the quadratic formula, the sine and cosine rules, the area of a triangle, Pythagoras, the trapezium, prism and circle formulae and compound interest. The cone and sphere formulae are not on it either; those are printed inside the question that needs them. Nothing about proportion appears anywhere, so you need to know that direct proportion is $y = kx$ , that inverse proportion is $y = \frac{k}{x}$ , and that a square or a cube named in the sentence attaches to the $x$ .
How many marks is a proportion question worth on Edexcel Higher?: The three-part version is usually 5 marks: about 3 for setting up the equation and finding the constant, then 1 each for using the formula forwards and backwards. A graph-matching or table question is 1 or 2 marks on its own. Each paper is 80 marks, so it is a small block, but a reliable one once the first line is right.
What does an inverse proportion graph look like?: For positive values it is a curve falling from left to right that flattens off, getting closer to both axes without ever touching them. It is not a straight line with a negative gradient, which is the option Edexcel includes to catch exactly that idea. Direct proportion gives the straight line through the origin, and $y = kx^2$ gives a curve that also starts at the origin but gets steeper as $x$ grows.

Direct and Inverse Proportion - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics