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

Solved on video in English · Form 4, Indices, Surds & Logarithms · 8:26 video

The question

(a)(i)

(Section B) 14 (a)(i) Simplify (4^(m+1) × 25²m)) / (5¹+4m) × 2²m)).

(a)(ii)

(a)(ii) Solve 5²x) − 125⁶−2x) = 0.

(b)(i)

(b) The area of a rectangular room is (3 + √3) cm² and the width of the room is (2 + √3) cm. Find (i) the length, in cm, of the room. Give your answer in surd form.

(b)(ii)

(b)(ii) Find the difference in length and width, in cm, of the room. Give your answer in surd form.

Selangor Trial 2025 Add Maths Paper 1, Question 14: the question as drawn in Eduly's video8:26

Part (a)(i)

Step 1

Write every base in prime form. 4^(m+1) = (2²)^(m+1) = 2²m+2). 25²m) = (5²)²m) = 5⁴m).

Why this step

Indices only combine when the bases match. Rewriting 4 as 2² and 25 as 5² leaves only bases 2 and 5, so the laws of indices can work.

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

Final answer

4/5

Where students lose marks

Watch out: write 4 as 2² and 25 as 5² first, bracket (1 + 4m) when subtracting, and write 5^(−1) as 1/5.

Part (a)(ii)

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

Final answer

x = 9/4

Where students lose marks

Watch out: write 125 as 5³ first, then multiply 3 by the whole bracket (6 − 2x), giving 18 − 6x.

Part (b)(i)

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

Final answer

Length = (3 − √3) cm

Where students lose marks

Watch out: use the conjugate (2 − √3), and expand carefully: (√3)² = 3, so the last term is −3. The denominator becomes 1.

Part (b)(ii)

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

Final answer

Difference = (1 − 2√3) cm

Where students lose marks

Watch out: the minus before (2 + √3) flips both signs, giving −2 − √3. Then −√3 − √3 = −2√3, not 0.

Watch every step of this question solved on video (8:26), with the reason behind each step and a box that checks your own answer.

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