SPM 2023 Add Maths Paper 1, Question 8Progressions

Solved on video in English and Bahasa Melayu · Form 4, Progressions · 5:51 video

The question

(a)

Listing out all terms of the sequence is not accepted. A cylindrical wooden block is cut into pieces for decoration. Diagram 7 shows the first three pieces that have been cut and the remaining part. The angles of the sectors increase by a constant amount for each subsequent piece. A total of n pieces can be cut from this block. The angle of sector of the 4th piece is 3 times the angle of sector of the smallest piece. The sum of the angles of the sectors for the first 4 pieces is 72°. Find (a) the angle of the sector, in degrees, for the smallest piece.

(b)

Using the same arithmetic progression of sector angles (smallest a = 9°, common difference d = 6°), and that the total of all n sector angles makes up the full circle, find (b) the value of n.

SPM 2023 Add Maths Paper 1, Question 8: the question as drawn in Eduly's video5:51

Part (a)

Step 1

The sector angles form an arithmetic progression with first term a (smallest piece) and common difference d.

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

Final answer

a = 9°

Where students lose marks

Watch out: 3d = 2a gives a = (3/2)d, not (2/3)d. Check the fraction before substituting into 4a + 6d = 72.

Part (b)

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

Final answer

n = 10

Where students lose marks

Watch out: show every step of solving the quadratic (factorise, state both roots), then reject n = −12 to justify n = 10.

Watch every step of this question solved on video (5:51), with the reason behind each step and a box that checks your own answer.

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