Indices, Logarithms and Surds: JAMB Mathematics Questions, Answers & Notes

What Indices, Logarithms and Surds covers in the JAMB Mathematics syllabus

Laws of indices: multiply powers of the same base by adding indices (aᵐ × aⁿ = aᵐ⁺ⁿ), divide by subtracting (aᵐ ÷ aⁿ = aᵐ⁻ⁿ), and raise a power to a power by multiplying ((aᵐ)ⁿ = aᵐⁿ). a⁰ = 1 for any non-zero a, and a⁻ⁿ = 1/aⁿ. A fractional index a^(m/n) means the n-th root raised to the m-th power. Logarithms are the inverse of indices: if aˣ = b then logₐb = x. The log laws mirror the index laws: log(mn) = log m + log n, log(m/n) = log m − log n, and log(mᵏ) = k log m. Surds are irrational roots; simplify by extracting perfect-square factors, and rationalise a denominator by multiplying top and bottom by a suitable surd.

For Indices, Logarithms and Surds, JAMB expects you to be able to:

• Apply the laws of indices to simplify expressions and solve index equations
• Convert between index and logarithm form and use the laws of logarithms
• Simplify surds and rationalise simple denominators

Key facts & revision notes: Indices, Logarithms and Surds

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

• When multiplying powers of the same base, add the indices: 3⁴ × 3² = 3⁴⁺² = 3⁶.
• When dividing powers of the same base, subtract the indices: 5⁷ ÷ 5³ = 5⁷⁻³ = 5⁴.
• A power raised to a power: multiply the indices.
• Any non-zero number raised to the power 0 equals 1, so 7⁰ = 1.
• A negative index means the reciprocal: 2⁻³ = 1/2³ = 1/8.
• An index of 1/2 means the square root: 16^(1/2) = √16 = 4.
• 27^(2/3) = (27^(1/3))² = (∛27)² = 3² = 9.
• Express 32 as a power of 2: 32 = 2⁵, so 2ˣ = 2⁵, giving x = 5.
• 81 = 3⁴, so 3^(x+1) = 3⁴, meaning x + 1 = 4, hence x = 3.
• Add indices when multiplying, subtract when dividing: (x⁵⁺³) ÷ x² = x⁸ ÷ x² = x⁶.
• log₁₀100 asks: 10 to what power gives 100?
• Since 10² = 100, log₁₀100 = 2.
• log₂8 asks: 2 to what power gives 8?
• Since 6 = 2 × 3, log 6 = log(2 × 3) = log 2 + log 3 (product rule of logarithms).
• The quotient rule: log 20 − log 4 = log(20/4) = log 5.
• The power rule in reverse: 3 log 2 = log 2³ = log 8.
• log₁₀ x = 3 means x = 10³ = 1000.
• √50 = √(25 × 2) = √25 × √2 = 5√2.
• √12 = 2√3 and √27 = 3√3, so √12 + √27 = 2√3 + 3√3 = 5√3.
• Multiply numerator and denominator by √3: (1 × √3)/(√3 × √3) = √3/3.
• This is a difference of two squares: (√5)² − (√2)² = 5 − 2 = 3.
• 2⁵ × 2³ = 2⁸ = 256 (add the indices).
• 6⁹ ÷ 6⁶ = 6³ = 216 (subtract the indices).
• (3²)³ = 3⁶ = 729 (multiply the indices).

Worked examples

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

How Indices, Logarithms and Surds is tested in JAMB Mathematics

Our Indices, Logarithms and Surds bank holds 40 questions (17 easy, 19 medium, 4 hard). JAMB Mathematics typically returns to Indices, Logarithms and Surds 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 Indices, Logarithms and Surds 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 Indices, Logarithms and Surds. 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 Indices, Logarithms and Surds is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Indices, Logarithms and Surds

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

Frequently asked questions

Is Indices, Logarithms and Surds part of the JAMB Mathematics syllabus?

Yes. Indices, Logarithms and Surds is a recognised topic in the JAMB Mathematics syllabus, covering apply the laws of indices to simplify expressions and solve index equations. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Indices, Logarithms and Surds questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Indices, Logarithms and Surds 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 Indices, Logarithms and Surds?

Laws of indices: multiply powers of the same base by adding indices (aᵐ × aⁿ = aᵐ⁺ⁿ), divide by subtracting (aᵐ ÷ aⁿ = aᵐ⁻ⁿ), and raise a power to a power by multiplying ((aᵐ)ⁿ = aᵐⁿ). a⁰ = 1 for any non-zero a, and a⁻ⁿ = 1/aⁿ. A fractional index a^(m/n) means the n-th root raised to the m-th power.…

How do I answer Indices, Logarithms and Surds questions quickly in JAMB?

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

Are these JAMB Mathematics Indices, Logarithms and Surds 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 Indices, Logarithms and Surds questions free without signing up?

Right here — tap “Start Indices, Logarithms and Surds 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.