How should an error-drill paper be used?

Cover the answers, work through every item, then write the cause of each slip beside it and retry the next day.

What is the most common index-law slip?

Multiplying the indices instead of adding them: 2^3 x 2^4 is 2^7.

Why check the roots of a log equation?

A logarithm is defined only for positive numbers, so each root must be tested in the original expression.

S4 Maths indices and logarithms paper 4: ten common errors taken apart

2026-11-10

Tutor Prep Guide · S4 Maths Indices and Logarithms

Ten items target the slips seen most often in the first three papers: adding versus multiplying indices, unchecked log roots, misread powers of ten and off-by-one digit counts.

Direct answers　Items 01 to 03 rebuild multiplying powers, zero and negative indices and fractional indices, 04 to 06 cover log sums, an exponential equation and algebraic simplification, 07 to 09 a log equation, scientific notation and digit counting, and 10 attacks the multiplied-index slip.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S4 Maths Indices and Logarithms
Level	S4

02　Questions (10 items)

FoundationWork out 2^3 x 2^4 and say how it relates to 2^(3+4).
FoundationWork out 5^0 + 5^(-1) as a fraction or a decimal.
FoundationWork out 25^(3/2) as a whole number.
IntermediateFind log2(32) + log2(1/8).
IntermediateSolve 3^(2x-1) = 81.
IntermediateSimplify (x^3 y^-2)^2 / (x^2 y^-3), leaving positive indices only.
ChallengeSolve log3(x+6) – log3(x) = 1.
ChallengeWrite 0.00000048 in scientific notation.
ChallengeHow many digits does 2^50 have? (Take log 2 = 0.3010)
Error redoError drill: a student wrote 2^3 x 2^4 = 2^12 = 4096. What is correct and where did it go wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	128	For one base the indices add: 3 + 4 = 7, so 2^7 = 128.
2	6/5 = 1.2	5^0 is 1 and 5^(-1) is 1/5, giving 6/5 = 1.2.
3	125	Take the square root first to get 5, then cube it: 125.
4	2	The two terms are 5 and -3, so the sum is 2.
5	x = 2.5	Since 81 = 3^4, we get 2x – 1 = 4 and so x = 2.5.
6	x^4 / y	The numerator is x^6 y^-4; subtracting the denominator indices gives x^4 y^-1, that is x^4 / y.
7	x = 3	Rewrite it as (x+6)/x = 3, giving x = 3, which lies in the domain x > 0.
8	4.8 x 10^-7	The point moves seven places to the right, so the index is -7.
9	16 digits	50 x 0.3010 = 15.05, and adding one to the integer part gives 16 digits.
10	128	The indices should add rather than multiply, so 2^7 = 128; 4096 is 2^12.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.