SPM 2024 Add Maths Paper 1, Question 15Quadratic Functions

Solved on video in English and Bahasa Melayu · Form 4, Quadratic Functions · 7:10 video

The question

(a)

(a) Diagram 12 shows a square and a rectangle. The square has side x metres. The rectangle has dimensions x metres by (2x + 10) metres. Given that the sum of the areas of the shapes is more than 8 m², using the table method, find the range of values of x.

(b)(i)

(b) A quadratic equation is given by x² + 3x = -4p, such that p is a constant. (i) Find the range of values of p if the equation has imaginary roots.

(b)(ii)

(b) Using the same equation x² + 3x = -4p, it is given that the equation has roots α and β. (ii) Form a quadratic equation with roots α - β + 1 and β - α + 1.

Part (a)

Step 1

Area of square = x². Area of rectangle = x(2x + 10) = 2x² + 10x.

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

Final answer

x > 2/3

Where students lose marks

Watch out: x is a side length, so it must be positive. Reject x < −4 and keep only x > 2/3.

Part (b)(i)

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

Final answer

p > 9/16

Where students lose marks

Watch out: imaginary roots need b² − 4ac < 0. Using ≥ 0 (real roots) wrongly gives p ≤ 9/16.

Part (b)(ii)

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

Final answer

x² − 2x + 16p − 8 = 0

Watch every step of this question solved on video (7:10), with the reason behind each step and a box that checks your own answer.

Start 7 days free Already a member? Watch it now

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

All questions in SPM 2024 Paper 1

Quadratic Functions: lessons and every past-year question

Baca dalam Bahasa Melayu

More Quadratic 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.