MRSM Trial 2025 Add Maths Paper 1, Question 6Functions

Solved on video in English · Form 4, Functions · 4:18 video

The question

(a)

Given the function h : x → |3 − 4x|, find the values of x such that h(x) = 1.

(b)

A runner burns calories according to the function g(t) = 8t − 10, such that g(t) is the total calories burned after running for t minutes. After the run, the body continues to burn calories during the recovery period according to the function f(c) = 0.25c, such that c is the total calories burned during the run. Using the concept of composite functions, express the function for calories burned during the recovery period in terms of t.

(c)

Given the function f⁻¹ : x → (x + 5)/3 and 6f⁻¹(a) = f(1), find the value of a.

MRSM Trial 2025 Add Maths Paper 1, Question 6: the question as drawn in Eduly's video4:18

Part (a)

Step 1

|3 − 4x| = 1 gives two cases: 3 − 4x = 1 or 3 − 4x = −1.

Why this step

1 and −1 both have modulus 1, so the bracket can be either one. Solving only 3 − 4x = 1 misses a value of x.

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

Final answer

x = 1/2 or x = 1

Where students lose marks

Watch out: solve both 3 − 4x = 1 and 3 − 4x = −1, not just the positive case.

Part (b)

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

Final answer

fg(t) = 2t − 5/2

Where students lose marks

Watch out: we need fg(t), so g goes first. gf(t) gets no marks. Multiply 0.25 by both terms in the bracket.

Part (c)

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

Final answer

a = −6

Where students lose marks

Watch out: invert f⁻¹ carefully to get f(x) = 3x − 5, and put a into f⁻¹, not f.

Watch every step of this question solved on video (4:18), with the reason behind each step and a box that checks your own answer.

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