Circular Measures Archives - SPM Additional Mathematics

1.5.3 Circular Measure SPM Practice (Paper 2 Question 11 – 15)

January 15, 2026August 3, 2022 by

Question 11 (SPM 2018 – 7 marks):Mathematics Society of SMK Mulia organized a competition to design a logo for the society.Diagram 3 shows the circular logo designed by Adrian. The three blue coloured regions are congruent. It is given that the perimeter of the blue coloured region is 20π cm.[Use π = 3.142]Find(a) the radius, … Read more

1.5.2 Circular Measure SPM Practice (Paper 2 Question 6 – 10)

January 11, 2026August 2, 2022 by

Question 6: In the diagram above, AXB is an arc of a circle centre O and radius 10 cm with ∠AOB = 0.82 radian. AYB is an arc of a circle centre P and radius 5 cm with ∠APB = θ. Calculate: (a) the length of the chord AB, (b) the value of θ in … Read more

1.5.1 Circular Measure SPM Practice (Paper 2 Question 1 – 5)

January 11, 2026August 1, 2022 by

Question 1: Diagram shows a circle, centre O and radius 8 cm inscribed in a sector SPT of a circle at centre P. The straight lines, SP and TP, are tangents to the circle at point Q and point R, respectively. [Use p= 3.142] Calculate (a) the length, in cm, of the arc ST, (b) … Read more

1.4.2 Circular Measure Short Questions (Paper 1 Question 11 – 20)

January 18, 2026July 2, 2022 by

Question 11 (SPM 2019):Diagram 4 shows a rhombus OACB inscribed in sector AOB with centre O and radius r cm.Given the area of sector AOB is 18 cm2, express (a) α in terms of r, (b) the perimeter, in cm, of the shaded region in terms of r.[3 marks] Answer:(a)$$ \begin{aligned} &\text { Area of sector } … Read more

1.4.1 Circular Measure SPM Practice (Paper 1 Question 1 – 10)

January 15, 2026July 1, 2022 by

Question 1: The figure shows the sector OCB of radius 13 cm at the centre O. The length of the arc CB = 5.2 cm. Find (a) the angle in radians, (b) the perimeter of the shaded region. Solution: (a) s = r θ 5.2 = 13 ( ∠ C O B ) ∠ C O … Read more

1.3 Area of a Sector of a Circle

January 11, 2026May 10, 2022 by

1.3 Area of a Sector of a Circle (A) Area of a Sector of a Circle 1. If a circle divided into two sectors of different sizes, the smaller sector is known as the minor sector while the larger sector is known as the major sector. 2. If AOB is the area of a sector … Read more

1.2 Length of an Arc of a Circle

January 11, 2026May 3, 2022 by

(A) Formulae for Length and Area of a Circle r = radius, A= area, s = arc length, q = angle, l = length of chord (B) Length of an Arc of a Circle Example 1: An arc, AB, of a circle of radius 5 cm subtends an angle of 1.5 radians at the centre. … Read more

1.1 Radians

January 11, 2026May 1, 2022 by

8.1 Radians (A) Terminology: (B) Convert degrees to radians: (C) Convert radians to degrees: