Variation: JAMB Mathematics Questions, Answers & Notes

What Variation covers in the JAMB Mathematics syllabus

Variation describes how quantities change together. Direct: y = kx (y grows as x grows). Inverse: y = k/x (y shrinks as x grows). Joint: y = kxy or y = k·(product of variables). Partial: y = c + kx (a fixed part plus a variable part). The steps are always the same: write the relation with the constant k, use the given values to find k, then use k to answer the question. Watch for 'square' or 'cube' — 'y varies as the square of x' means y = kx².

For Variation, JAMB expects you to be able to:

• Set up and solve direct and inverse variation problems
• Handle joint and partial variation
• Find the constant of variation and apply it to word problems

Key facts & revision notes: Variation

These are the recurring points our Variation questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• Direct variation: y = kx.
• Inverse variation: y = k/x.
• P = kQ, so k = P/Q = 20/4 = 5.
• Inversely as the square of x means y = k/x².
• Joint variation: m = knp.
• So 24 = k(2)(3) = 6k, giving k = 4.
• In direct variation y = kx, doubling x doubles y.
• Then 20 = 4x, giving x = 5.
• In y = k/x, doubling x halves y.
• V = kr³; 16 = k(2³) = 8k, so k = 2.
• C = kd; 4000 = 50k so k = 80.
• Then C = 80 × 80 = ₦6400.
• a = k/b; 5 = k/3 so k = 15.
• Joint variation means one quantity varies as the product of two others: z = kxy.
• Partial variation combines a constant and a variable part: y = c + kx.
• y = kx²; 18 = k(9) so k = 2.
• y = k/x, so k = yx = 10 × 2 = 20.
• Directly as m and inversely as d²: F = km/d².
• t = k/n; 10 = k/6 so k = 60.
• Subtract the equations: (11 − 7) = k(3 − 1), so 4 = 2k, giving k = 2.
• z = kx/y; 6 = k(12)/4 = 3k, so k = 2.
• k = 15/5 = 3, so y = 3 × 8 = 24.
• k = 8 × 3 = 24, so y = 24/6 = 4.
• Direct variation with √x is y ∝ √x.

Worked examples

Three Variation questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Variation is tested in JAMB Mathematics

Our Variation bank holds 40 questions (12 easy, 21 medium, 7 hard). JAMB Mathematics typically returns to Variation year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Variation questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Variation. If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Variation is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Variation

The errors that cost marks on Variation are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Variation actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Variation part of the JAMB Mathematics syllabus?

Yes. Variation is a recognised topic in the JAMB Mathematics syllabus, covering set up and solve direct and inverse variation problems. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Variation questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Variation questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Variation?

Variation describes how quantities change together. Direct: y = kx (y grows as x grows). Inverse: y = k/x (y shrinks as x grows). Joint: y = kxy or y = k·(product of variables). Partial: y = c + kx (a fixed part plus a variable part). The steps are always the same: write the relation with the consta…

How do I answer Variation questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Variation. Practising timed Variation questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Variation questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Variation questions free without signing up?

Right here — tap “Start Variation practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.