Skill: variation

Variation Practice

An endless supply of never-repeating variation problems: find the constant k for direct, inverse, and joint variation, predict new values, and identify the variation type.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

How to enter answers

Constants and values: plain numbers or fractions like 1/2.
Identify: type direct, inverse, joint, or neither.

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Direct

y = kx: ratio constant. Find k, then predict.

y = 20 at x = 4 → k = 5

Inverse

y = k/x: product constant. Bigger x, smaller y.

y = 8 at x = 3 → k = 24

Joint & identify

y = kxz plus “which variation is this?” checks.

y = 30 at x = 2, z = 3 → k = 5

3 Watch out for these

The mistakes students make most often on these problems.

1. y = kx for inverse

Wrong: inverse with y = 8, x = 3 → k = 8/3. Right: k = xy = 24.

2. Assuming direct

Wrong: fitting y = kx to inverse data. Right: test y/x and xy first.

3. Stopping at k

Wrong: answering k when asked for y. Right: k is the middle step — finish the prediction.

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