SPM 2021 Add Maths Paper 1, Question 5Quadratic Functions

Solved on video in English and Bahasa Melayu · Form 4, Quadratic Functions · 5:24 video

The question

(a)

It is given that f(x) = x² + 3x − 4. Find the range of values of x such that f(x) > 0.

(b)(i)

The equation px + q − f(x) = 0, where p and q are constants and f(x) = x² + 3x − 4, has roots α and β. State α + β and αβ in terms of p and/or q.

(b)(ii)

The roots of the quadratic equation x² + rx + r = 10 are 2/α and 2/β, where r is a constant, and α, β are the roots from part (b)(i) (so α + β = p − 3 and αβ = −q − 4). Express p in terms of q.

SPM 2021 Add Maths Paper 1, Question 5: the question as drawn in Eduly's video

5:24

Part (a)

Step 1

Set up the inequality: x² + 3x − 4 > 0.

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

Final answer

x < −4 or x > 1

Where students lose marks

Watch out: show your method, a graph sketch, number line or table, not just the final range, or you lose method marks.

Part (b)(i)

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

Final answer

α + β = p − 3, αβ = −q − 4

Where students lose marks

Watch out: sum of roots is −b/a, so keep the negative sign. Writing 3 − p instead of p − 3 loses the mark.

Part (b)(ii)

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

Final answer

p = 5q + 21

Where students lose marks

Watch out: equate the sum of 2/α and 2/β with −r and their product with r − 10, then keep every sign when substituting.

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SPM 2021 Add Maths Paper 1, Question 5Quadratic Functions

The question

Part (a)

Part (b)(i)

Part (b)(ii)

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