Mathematics and Mathematical Literacy - Thutong

Mathematics(NCS)/Grade 12/ P2 92 ExemplarMEMORANDUMGrade12 Mathematics: Memorandum Paper 21.11.2.1 4cos θ - 7sin θ = -8 (× 7)4sin θ + 7cos θ = 1 (× -4)A(0;1)B(-2;-3)EFC(8;2)D(d;6)28cos θ − 49sin θ = -56-28cos θ − 16sin θ = -4∴ -65sin θ = -60 ∴ sin = θ 6065 ∴ θ = 67,38° or 180° − 67,38° = 112,62°∴ θ = 112,62°OR2 2OA = 4 + 7 = 65 1.1.11.1.21.1.31.1.4M BC = 2 - (-3)8 -(-2) = 5 10 = 1 2 2M AD = 1 2 (lines parallel)AD: y = 1 2 x + cSub in (0;1)1 = cAD: y = 1 2 x + 1Sub(d;6): 6 = 1 2 d + 1d = 10 4M BC = 1 2∴ M AE = -2( lines ⊥ )A = (0;1) which is the y-intercept of AE.AE: y = -2x + 1⎛ 0 + 8 1+2 ⎞F = ⎜ ; ⎟⎝ 2 2 ⎠= (4;1 1 2 ) 22OA' =AA' =2 2( − 8) + 1 = 65 2 2(4 −− ( 8)) + (7−1)= 180 = 6 5 Using the cos rule:(6 5 )² = ( 65 )² + ( 65 )² − 2.65 65 .cos θ 180 = 130(1 − cos θ)∴ 180130 − 1 = − cos θ∴ cos θ = − 513 ∴ θ = 112,62°61.2.2 B' = (8cos 112,62° − 14sin 112,62°; 8sin112,62° + 14cos 112,62) = (-16;2) 41.3.1 Tanx = -0,3421∴x = − 18,89° 21.3.2 Sinx = 0,500∴x = 30° 21.4 y = 4sin5x 21.5.1 < 39minutes 21.5.2 16% × 590 runners = 94 runners(can accept answers in the range of 94 to106 runners) 31.5.328 44 57 72 112Copyright reserved