SPM 2021 Add Maths Paper 1, Question 14Indices, Surds & Logarithms

Solved on video in English and Bahasa Melayu · Form 4, Indices, Surds & Logarithms · 6:01 video

The question

(a)

Diagram 9 shows a right-angled triangle with vertical side (2^(x+1)) cm, horizontal side √(2^x) cm, and hypotenuse 3√2 cm. Find the value of x.

(b)

Diagram 10 shows a trapezium with parallel sides √7 cm (top) and 5 cm (bottom) and perpendicular height t cm. Given that the area of the trapezium is 9(√7 − 1) cm², express t in the form p + q√7, where p and q are constants.

SPM 2021 Add Maths Paper 1, Question 14: the question as drawn in Eduly's video6:01

Part (a)

Step 1

By Pythagoras' theorem: (2^(x+1))² + (√(2^x))² = (3√2)².

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

Final answer

x = 1

Where students lose marks

Watch out: never add exponents across a sum like 2²x+2) + 2^x. Let y = 2^x and solve the quadratic instead.

Part (b)

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

Final answer

t = −12 + 6√7 (p = −12, q = 6)

Where students lose marks

Watch out: write out every term of the expansion before simplifying. Skipping the term-by-term multiplication loses marks.

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