SPM 2022 Add Maths Paper 1, Question 2Indices, Surds & Logarithms

Solved on video in English and Bahasa Melayu · Form 4, Indices, Surds & Logarithms · 4:13 video

The question

(a)(i)

(a) Express p in terms of k for (i) x²k+p) = 1.

(a)(ii)

(a) Express p in terms of k for (ii) a^p = (k-th root of a)⁶, i.e. a^p = (a¹/k))⁶.

(b)

(b) Given that 3 + 3^y/3²(x+1)) = 84, express y in terms of x.

Step 1

Write 1 in index form with base x: 1 = x⁰.

Why this step

Indices can only be compared on the same base, so write 1 as x⁰. Treating 1 as x gives the common wrong answer p = 1 − 2k.

3 more steps, each with the reason for it, in the full solution

Final answer

p = −2k

Where students lose marks

Watch out: 1 = x⁰, so 2k + p = 0, not 1. Using 1 gives the wrong answer p = 1 − 2k.

4 more steps, each with the reason for it, in the full solution

Final answer

p = 6/k

Where students lose marks

Watch out: combine the root and the power by multiplying, 1/k × 6 = 6/k. Adding gives the wrong p = 1/k + 6.

5 more steps, each with the reason for it, in the full solution

Final answer

y = 2x + 6

Where students lose marks

Write the law a^m/a^n = a^(m−n) clearly when simplifying 3^y/3²(x+1)); do not skip the working.

Watch every step of this question solved on video (4:13), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.

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