SPM 2023 Add Maths Paper 1, Question 7Differentiation

Solved on video in English and Bahasa Melayu · Form 5, Differentiation · 7:01 video

The question

(a)

Diagram 6 shows a curve y = −2x² + 3x + p and a tangent y = −x + c to the curve. Express p in terms of c.

(b)

Find the range of values of x for (x + 1)(−3x − 3) < x − 1 by using the table method.

(c)

It is given that p and 2p are the roots of the quadratic equation 2x² + 6x + 4p² = 0. Find the quadratic equation with roots (p − 1) and (p + 1).

Step 1

Differentiation method (preferred): dy/dx of the curve = −4x + 3.

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

Final answer

p = c − 2

Where students lose marks

Watch out: set dy/dx equal to the tangent's gradient, −1, not 0, and make sure no x is left in your answer for p.

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

Final answer

x < −2 or x > −1/3

Where students lose marks

Watch out: the question says table method. A correct range from a graph sketch can still lose marks, so draw the sign table.

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

Final answer

x² + 2x = 0

Where students lose marks

Watch out: write the new equation as x² − (sum)x + (product) = 0, including the '= 0', and take care with the signs.

Watch every step of this question solved on video (7:01), with the reason behind each step and a box that checks your own answer.

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