Mathematics · Oct / Nov 2020 · Paper 41 · Question 4

38.6 [3]

M2 for [2 ×] (8.5 + 0.05 + 10.7 + 0.05)

or M1 for 8.5 + 0.05 or 10.7 + 0.05

8.86 or 8.863… [2]

M1 for 9 h = sin 80 or better oe

∠CDF = 100 leading to ∠DCF = 40 Or ∠EDF = 80 leading to ∠DCF = 40 ‘two equal angles’ [2]

M1 Implied by 180-(100 + 40) = 40 or 80 – 40 A1 With no incorrect work seen

66.5 or 66.45 to 66.47… [3]

M2 for 0.5(3 + 12) × their (b)(i) or 12 × their (b)(i) – 0.5 × 9 × 9 × sin 100 oe

or B1 for DC = 9 or BC = 3

130 nfww or 129.6 to 129.8 [5]

B1 for ∠ACD = 21º or ∠CAD = 69º Method 1

M2 for cos 21 = 12 AC oe

or M1 for ∠ADC = 90 soi

M1 for π(their AC/2)2 OR Method 2 12 r

M2 for = oe sin 138 sin 21

or M1 for ∠COD = 138 soi

M1 for π ( their r ) 2 OR Method 3

M2 for cos 21 = 6 OC oe

or M1 for ∠CXO = 90 soi where X is the point where the perpendicular from O meets the chord CD

M1 for π ( their OC) 2

78.4 or 78.37 to 78.41 [3]

M2 for x × 2 × π × 9.5 + 2 × 9.5 = 4 × 8 oe 360 x × 2 × π × 9.5

or M1 for 360 After M0,

SC1 for 9.5x + 19 = 32 oe