MYP Maths: Direct & Inverse Proportion — Frequently Asked Questions

Direct proportion means two quantities increase or decrease together at a constant rate — double one, double the other. Inverse proportion means one quantity increases as the other decreases, keeping their product constant. In MYP 4-5 this falls under the Number and Algebra strands, formalised as y = kx (direct) and y = k/x (inverse).

Check what happens to the ratio and the product of the two values. If dividing one by the other always gives the same constant (y/x = k), it's direct proportion. If multiplying them always gives the same constant (xy = k), it's inverse proportion. A quick table of values is the fastest way to test this under exam conditions.

Direct proportion produces a straight line through the origin — the steeper the line, the larger the constant k. Inverse proportion produces a curve called a reciprocal graph, or hyperbola, that gets closer to both axes without ever touching them. Spotting a straight line through (0,0) versus a curved asymptote is the fastest visual check in an exam.

Direct proportion shows up wherever cost or quantity scales evenly — fuel priced per litre, currency conversion, or recipe ingredients for more guests. Inverse proportion appears when one thing speeds up as another slows down — more workers on a job means fewer hours needed, or a faster average speed means less time for the same journey.

The formula for direct proportion is y = kx, where k is the constant of proportionality and never changes for a given relationship. Find k by dividing any known y value by its matching x value. Once you know k, substitute it back in to predict any other pair of values in that same relationship.

The formula for inverse proportion is y = k/x, which can also be written as xy = k. Here k stays constant even though x and y move in opposite directions — as one doubles, the other halves. Find k by multiplying any matching x and y pair given in the question.

Solving a direct proportion problem means finding the constant k first, then using it to answer the actual question. Write y = kx, substitute the given values to solve for k, then substitute k back in with the new value to find the unknown. Examiners consistently reward this three-step working, even on a two-mark question.

Solving an inverse proportion problem starts the same way — find k — but you use xy = k instead of y = kx. Substitute the known pair to get k, then substitute the new value into y = k/x to find the missing quantity. Always sanity-check: if x has increased, y should have decreased.

Proportion questions in MYP 4-5 are usually assessed under Criterion A (Knowing and understanding) for correct formula use and calculation, and Criterion D (Applying mathematics in real-life contexts) when the scenario involves recipes, maps or exchange rates. Criterion B can also apply if you're asked to generalise a pattern from a table of values.

The most common mistake is mixing up which formula to use — applying y = kx to a problem that's actually inverse, usually because the student skipped a quick table check. The second most common slip is forgetting units in real-life context questions marked against Criterion D, where a labelled, sensible final answer is expected.

Direct and inverse proportion is the foundation for power and exponential functions in IB DP Mathematics: Analysis & Approaches and Applications & Interpretation. According to the IB, both current guides have been examined since 2021, and proportional reasoning underpins variation problems in DP Physics too, like the inverse-square law for gravitational and electric fields.

Proportion itself isn't conceptually hard — most MYP 4-5 students grasp the idea within a lesson. Where it gets tricky is multi-step problems combining proportion with percentages or algebraic manipulation, and worded questions that never explicitly say 'directly' or 'inversely'. Practising past-style questions until spotting the relationship becomes automatic usually fixes this within a few sessions.

The best practice uses everyday numbers rather than a textbook — comparing supermarket prices per 100g, working out fuel cost for a journey, or scaling a recipe for more guests. Ask your child to say out loud whether the relationship is direct or inverse before touching a formula; that habit is exactly what MYP examiners check for.