Kuala Lumpur Trial 2025 Add Maths Paper 1, Question 2Functions

Solved on video in English · Form 4, Functions · 6:39 video

The question

(a)(i)

Given that f(x) = 2x − 5 and g(x) = x² + 2.

(a)(i) Find g(5).

(a)(ii)

(a)(ii) Find f⁻¹(x).

(a)(iii)

(a)(iii) Find fg(x).

(b)(i)

Diagram 1 shows the curve of the function g(x) = (x − 2)² + 3 for the domain 0 ≤ x ≤ m.

(b)(i) State the value of p.

(b)(ii)

(b)(ii) Calculate the value of m.

(b)(iii)

(b)(iii) Hence, state the range for the function g(x).

Kuala Lumpur Trial 2025 Add Maths Paper 1, Question 2: the question as drawn in Eduly's video6:39

Part (a)(i)

Step 1

Substitute x = 5 into g(x) = x² + 2 (the substitution of 5 as the object must be shown).

Why this step

The mark is for showing (5)² + 2, not just 27. Write the substitution line every time, even if you can do it in your head.

1 more step, with the reason for it, in the full solution

Final answer

g(5) = 27

Where students lose marks

Watch out: write the substitution (5)² + 2 before the answer 27. The mark needs to see it.

Part (a)(ii)

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

Final answer

f⁻¹(x) = (x + 5)/2

Where students lose marks

Watch out: f⁻¹(x) is not the reciprocal 1/f(x). Solve for x carefully, adding 5 before dividing by 2.

Part (a)(iii)

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

Final answer

fg(x) = 2x² − 1

Where students lose marks

Watch out: fg(x) means f(g(x)), not gf(x). Multiply the whole bracket (x² + 2) by 2.

Part (b)(i)

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

Final answer

p = 3

Where students lose marks

Watch out: p is the minimum value 3, not the y-intercept 7 read off the graph.

Part (b)(ii)

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

Final answer

m = 5

Where students lose marks

Watch out: reject m − 2 = −3 (m = −1), it is outside the domain. Also subtract 3 before square-rooting.

Part (b)(iii)

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

Final answer

3 ≤ g(x) ≤ 12

Where students lose marks

Watch out: the range is the g(x) values, not the domain, and use ≤ because 3 and 12 are both reached.

Watch every step of this question solved on video (6:39), with the reason behind each step and a box that checks your own answer.

Start 7 days freeAlready a member? Watch it now

No card. Every past-year question on video, in English and BM.

All questions in Kuala Lumpur Trial 2025 Paper 1

Functions: lessons and every past-year question

More Functions questions

Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.