SPM 2019, Paper 2

Question 3:Diagram 1 shows a sector POA with centre O.It is given that the length of arc PB is 2.56 cm. [Use π = 3.142]Calculate(a) ∠ POB in radians, [2 marks](b) the area, in cm2, of the shaded region. [4 marks]Solution:(a) s=rθ 2.56=10θ θ=0.256 radian (b) Area of OBP = 1 2 r 2 θ = 1 2 … Read more

Question 2:Express 2n + 2 – 2n + 1 + 2n – 1 in the form p(2n – 1), where p is a constant.Hence, solve the equation 8(2n + 2 – 2n + 1 + 2n – 1) = 5( 2 n 2 ). [6 marks]Solution: 2 n+2 − 2 n+1 + 2 n−1 =( … Read more

Question 1:Solve the simultaneous equations x + 2y = 1 and 3 x − 2 y =5. Give you answer correct to three decimal places. [5 marks]Solution: x+2y=1 x=1−2y ………… (1) 3 x − 2 y =5 ×  xy, 3y−2x=5xy ………… (2) Substitute (1) into (2): 3y−2( 1−2y )=5y( 1−2y ) 3y−2+4y=5y−10 y 2 10 y 2 +2y−2=0 5 y 2 +y−1=0 a=5, b=1, c=−1 y= … Read more