Mathematics and Mathematical Literacy - Thutong

Mathematics(NSC)/Grade 12/P1 89 ExemplarMEMORANDUMGrade 12 Mathematics: Memorandum Paper 11.1.1 x = 9 11.1.2 x = 27 11.1.3 2 x − 1 = 0 1∴ x = 221.2 6 + 8 + 10 + 12 + 14 = 50 21.3 5S 5 = (1 + 5) = 1524S 4 = (1 + 4) = 102∴T 5 = 15 − 10 = 5 31.4 a = 64 and r = 1,5 3 6∴T 7 = 64( ) = 729 231.5 n2 = (1,087) ∴n = 2 8,3 log 1 , 087 =Thus during the 9 th year 31.6 2f ( x)= x ( x − 1) − 4( x − 1 ) = ( x − 1)( x − 2)( x + 2) Thus x = 1 or x = 2 or x = -2 41.7.1 x = 5 11.7.2 y- intercept is y = -0,2 11.7.3 x – 5 = -1 Thus x = 4 21.7.4 y = x – 5 OR y = -x + 5 21.8 x = 2y – 4 Thus y = (x + 4)/2 Thus f ( x)= x + 2 231.9 C 21.10 3f ( x)= x (may include a constant) 21.11 1 3Distance = × 60 + × 80 4= 15 + 60 = 75 km 32.1 t100 000 = 5 000(1,15) t4∴ 20(1,15)∴t = 21,43 Thus 21 hours and 26 minutes 4na 1 − rS8=1 − r2.2.1 ( )⎛ 110⎜1−2S8=⎝11 −2= 19,928⎞⎟⎠ ⎛ 1= 20⎜1−⎝ 28⎞⎟⎠ 32.2.2S∞−1011 −2⎛ 1 ⎞∴⎜⎟⎝ 2 ⎠S n⎛ 1 ⎞∴ 20⎜⎟⎝ 2 ⎠=∴n> 10,966⎛ 110 ⎜ ⎛ ⎞− 1 − ⎜ ⎟⎜⎝ ⎝ 2 ⎠−11 −2⎛ 120 20⎜⎛ ⎞= − 1 −⎜⎟⎜⎝ ⎝ 2 ⎠∴ n >< 0,01< 0,0005log 0,0005log 0,5⎞⎟⎟⎠∴ n = 112.3 From AP:b − a = (a −b) − b∴3b = 2an∴b = 2 3 a From GP:a − b 1a=a − b ∴ (a −b)² = a∴ (a − 2 3a)² = an∴( 1 3 a)² = ann⎞⎟⎟⎠ ∴ 1 9 a² − a = 0∴ a² − 9a = 0∴ a(a − 9) = 0∴a = 0 or a = 9∴ b = 2 3 × 9∴b = 6 62.4 3 ! + 4! + 5! = 3!(1 + 4 + 4 × 5)= 150 33.1.1 Net salary = 0,75× 8250 = R6187,50 13.1.2 Bond repayments:0,3× 6187,50 = R1856,25 13.1.3 0.135i =12n = 20 × 12 = 240 ⎛n⎞⎜1 − (1 + i)A = 1 856.25 ⎟⎝ i ⎠A = R 153 742,66 Thus you can afford the flat. 64Copyright reserved