SPM 2021 Add Maths Paper 2, Question 2Indices, Surds & Logarithms

Solved on video in English and Bahasa Melayu · Form 4, Indices, Surds & Logarithms · 5:19 video

The question

(a)

(a) Is √0.25 a surd? Justify your answer.

(b)

(b)(i) Prove that log_a b = (log_c b) / (log_c a). (b)(ii) Hence, express log_3 h + log_9 k as a single logarithm in base 3.

Step 1

Evaluate √0.25 = √(1/4) = 1/2.

Why this step

Always simplify the number under the root first. √0.25 looks like a surd, but 0.25 is 1/4, a perfect square fraction.

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

Final answer

No. √0.25 = 1/2 = 0.5 is rational, so it is not a surd.

Where students lose marks

Watch out: simplify √0.25 to 1/2 first, then say a rational number is not a surd. Never answer "No" without a reason.

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

Final answer

(i) Proved; (ii) log_3 (h√k)

Where students lose marks

Watch out: (log_3 k)/(log_3 9) is not log_3 (k − 9). It equals (1/2) log_3 k, so 1/2 becomes a power of k.

Watch every step of this question solved on video (5:19), 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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