MRSM Trial 2025 Add Maths Paper 1, Question 14Indices, Surds & Logarithms

Solved on video in English · Form 4, Indices, Surds & Logarithms · 6:14 video

The question

(a)(i)

Given ln(e¹/a)) = b, express a in terms of b.

(a)(ii)

Given that ln(x² + 6x + 9) = 2y, express x in terms of y.

(b)

It is given that the side length of a square is √x cm. If the length of each side of the square is increased by 6 cm, the area becomes 9 times greater.

(i) Show that 2x − 3√x − 9 = 0. (ii) Hence, find the value of x.

MRSM Trial 2025 Add Maths Paper 1, Question 14: the question as drawn in Eduly's video6:14

Part (a)(i)

Step 1

Use ln(eᵏ) = k, so ln(e¹/a)) = 1/a.

Why this step

ln and e are opposites, so ln(eᵏ) just gives back the power k. This is the key idea behind both log parts.

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

Final answer

a = 1/b

Where students lose marks

Watch out: simplify ln(e¹/a)) to 1/a first, and remember 1/a = b gives a = 1/b, not a = b.

Part (a)(ii)

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

Final answer

x = eʸ − 3

Where students lose marks

Watch out: recognise (x + 3)², change ln(x + 3) = y to x + 3 = eʸ, then subtract 3 (not add).

Part (b)

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

Final answer

(i) Shown; (ii) x = 9

Where students lose marks

Watch out: don't miss the 12√x term when expanding (√x + 6)², and reject u = −3/2 because √x cannot be negative.

Watch every step of this question solved on video (6:14), with the reason behind each step and a box that checks your own answer.

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