Binary Operations: JAMB Mathematics Questions, Answers & Notes

What Binary Operations covers in the JAMB Mathematics syllabus

A binary operation * combines two elements according to a given rule, e.g. a * b = a + b + 2. To evaluate, simply substitute the numbers into the rule and simplify — mind the order of operations. For a nested expression like 3 * (2 * 1), work out the bracket first. An operation is commutative if a * b = b * a for all values. The identity element e is the value that leaves any element unchanged: a * e = a — solve that equation to find e. To find an unknown, substitute what you know into the rule and solve the resulting equation.

For Binary Operations, JAMB expects you to be able to:

• Evaluate a binary operation defined by a rule
• Apply operations in sequence and solve for an unknown
• Recognise properties such as commutativity and the identity element

Key facts & revision notes: Binary Operations

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

• 5 * 2 = (5×2) − 5 = 10 − 5 = 5.
• 2 * 3 = 2 + 3 − (2×3) = 5 − 6 = −1.
• 3 * 4 = 3² + 4² = 9 + 16 = 25.
• 6 * 10 = (6 + 10)/2 = 16/2 = 8.
• 4 * 3 = 2(4) − 3 = 8 − 3 = 5.
• 2 * 5 = (2×5) + 2 + 5 = 10 + 7 = 17.
• First 2 * 1 = 2 + 2(1) = 4.
• Then 3 * 4 = 3 + 2(4) = 3 + 8 = 11.
• The identity e satisfies a * e = a: a + e − 3 = a, so e = 3.
• 3 * 2 = 3 − 2 + (3×2) = 1 + 6 = 7.
• 1 * 2 = (1 + 2)² = 3² = 9.
• 3 * 5 = 3² − 5 = 9 − 5 = 4.
• 2 + x + 2x = 8 → 2 + 3x = 8 → 3x = 6 → x = 2.
• When the order does not matter (a * b = b * a), the operation is commutative.
• 2 * 4 = 3(2) + 4 = 6 + 4 = 10.
• 3 * 0 = 3 + 0 + (3×0) = 3 + 0 + 0 = 3.
• 2 * 4 = 2/4 + 4/2 = 0.5 + 2 = 2.5.
• 5 * (−1) = 5 + (−1) + 1 = 5.
• 3(4) − 2(1) = 12 − 2 = 10.
• (3 × 4) − 3 − 4 = 12 − 7 = 5.
• 3 * 4 = 5; then 2 * 5 = 2 + 5 − 2 = 5.
• a * e = a needs a + e − 5 = a, so e = 5.
• 2(3) + 2(4) = 6 + 8 = 14.
• 3 + x + 3x = 15, so 4x = 12 and x = 3.

Worked examples

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

How Binary Operations is tested in JAMB Mathematics

Our Binary Operations bank holds 40 questions (17 easy, 16 medium, 7 hard). JAMB Mathematics typically returns to Binary Operations 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 Binary Operations 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 Binary Operations. 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 Binary Operations is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Binary Operations

The errors that cost marks on Binary Operations 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 Binary Operations actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Binary Operations part of the JAMB Mathematics syllabus?

Yes. Binary Operations is a recognised topic in the JAMB Mathematics syllabus, covering evaluate a binary operation defined by a rule. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Binary Operations questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Binary Operations 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 Binary Operations?

A binary operation * combines two elements according to a given rule, e.g. a * b = a + b + 2. To evaluate, simply substitute the numbers into the rule and simplify — mind the order of operations. For a nested expression like 3 * (2 * 1), work out the bracket first. An operation is commutative if a *…

How do I answer Binary Operations questions quickly in JAMB?

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

Are these JAMB Mathematics Binary Operations 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 Binary Operations questions free without signing up?

Right here — tap “Start Binary Operations 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.