Melaka Trial 2025 Add Maths Paper 2, Question 1Indices, Surds & Logarithms

Solved on video in English · Form 4, Indices, Surds & Logarithms · 6:09 video

The question

(a)

Rationalise the denominator and simplify:

(5 + √3) / √3

(b)

Solve the equation:

(k/169)¹/2) × √k = 6

(c)

Without using a calculator, solve the equation:

log₄[log₃(5 − 2x)] = log₁₆ 4

Step 1

Multiply numerator and denominator by √3 to rationalise: (5 + √3)/√3 × √3/√3.

Why this step

Multiplying top and bottom by √3 is just multiplying by 1, so the value is unchanged, and √3 × √3 = 3 clears the surd below.

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

Final answer

1 + (5/3)√3

Where students lose marks

Watch out: multiply BOTH terms of the numerator by √3, then split 3/3 into 1 so the answer is fully simplified.

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

Final answer

k = 78

Where students lose marks

Watch out: √169 = 13, not 169, and show k¹/2) × k¹/2) = k by adding the indices, since that step earns the mark.

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

Final answer

x = −2

Where students lose marks

Watch out: simplify log₁₆ 4 to 1/2 first, then raise each base to its power: 4¹/2) = 2, and 3² = 9.

Watch every step of this question solved on video (6:09), with the reason behind each step and a box that checks your own answer.

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