Mathematics Grade 11 Paper 1 North West June 2017 Memo

GRADE 11 MATHEMATICS P1 MEMORANDUM JUNE 2017 MARKS: 100 This memorandum consists of 9 pages.. Copyright reserved Please turn over

Mathetics/P1 2 June/2017 NSC QUESTION 1 1.1.1 2x2 – 7x = 0 factors x(2x – 7) = 0 x = 0 x = 0 or x = x = (3) 1.1.2. 2x (x – 3) = 1 2x2 – 6x – 1 = 0 2x2 – 6x – 1 = 0  formula sub. into correct formula answer (4) x = 3,16 or x = – 0,16 1.1.3   squaring Square both sides, 1+ x = x2 – 10x + 25 standard form x2 – 11 x + 24 = 0 factors (x – 8 )( x – 3 ) = 0 answer x = 8 or x = 3 N/A (5) 1.1.4  x2 + 3x = k Let x2 + 3x = k std form in k factors k2 – 26k – 56 = 0 vales of k Copyright reserved Please turn over

Mathetics/P1 3 June/2017 NSC ( k – 28 )(k + 2 ) = 0  2 eqs. in x k = 28 or k = – 2  4 values of x (7) x2 + 3x = 28 or x2 + 3x = – 2 x2 + 3x– 28 = 0 or x2 + 3x + 2 = 0 (x +7) (x – 3) = 0 or (x + 2)(x + 1) = 0 x = –7 or x =3 or x = – 2 or x = – 1 ( x – 3)( 2 – x) > 0 1.1.5 ( x + 3)( 2 – x) > 0 end values ( x + 3)( x – 2) < 0 - notation (3) -3 2 – 3 < x < 2 1.1.6  factors   x = 16 (4) N/A x = 16 1.2 x2 – 2xy – 3y2 and 3x + y – 2 = 0  y = 2 – 3x y = 2 – 3x x2 – 2x(2 – 3x) – 3(2 – 3x )2 = 0 sub. of y x2 – 4x + 6x2 – 3(4 – 12x + 9x2 ) = 0 x2 – 4x + 6x2 – 12+ 36x – 27x2 ) = 0 –20 x2 + 32x –12 = 0 std form 5 x2 – 8x + 3 = 0 Copyright reserved Please turn over

Mathetics/P1 4 June/2017 NSC (5x – 3) (x – 1) = 0 factors or x = 1   x = 1 or y = 2 – 3 (1) y values (7) y = y = –1 1.3.1  sub of k in When k = 5, = 0 Roots are real and equal equal and real (2) 1.3.2 For non-real roots,  25 – 5k < 0 k>5 k>5 (2) QUESTION 2 Copyright reserved Please turn over

Mathetics/P1 5 June/2017 NSC 2.1.1 = taking common factor outside = ans (2) = 3 2.1.2 =  = 6x – 2x = 4x ans (2) 2.1.3 Convert base into prime = numbers removing the bracket = apply the law = = answer (4) = Copyright reserved Please turn over

Mathetics/P1 6 June/2017 NSC 2.2.1  taking common factor outside answer (3) 2.2.2   x = –1 answer (3) QUESTION 3 3.1 2 6 12 20 4 6 8 2 2 T5 = 30  T5 = 30 T6 = 42 T6 = 42 (2) 3.2 2a = 2 ; 3a + b = 4; a+b+c = 2 3a + b = 4; a= 1 3(1) + b = 4 1 +1 + c = 2 a+b+c = 2 b =1 c =0 value of a Value of b Tn = n2 + n value of c (5) QUESTION 4 4.1.1 i m ( i eff = 1 + m ) -1  formula correct sub. into formula = = 0.087747961... answer (3) Copyright reserved Please turn over

Mathetics/P1 7 June/2017 NSC Rate = 8,77% 4.1.2 formula sub. into the formula = R 18273,54 answer (3) 4.2 formula = 150000(1- 0,124)5 sub. into the formula = R77376,98 answer (3) 4.3 i  equation  x(3,52612449) = 20000 x(3,52612449) = 20000 answer (4) x = R5671,95 QUESTION 5 5.1 x = -2 or x = 6  OA = 2 OA = 2 and OB = 6  OB = 6 (2) 5.2 = -24  x =0 y = -24 (2) C(0; -24) 5.3 Axis of symmetry is x = 1 x=1 = -30  TP(1 ; -30) TP(1 ; -30) Copyright reserved Please turn over

Mathetics/P1 8 June/2017 NSC Range is y ans (3) 5.4 Notation end values (2) 5.5 c = - 24 c = -24 Passing through (6 ;0) sub. of (6;0) m= 4  m= 4 (3) 5.6 T.P of h(x) is ( 1 ; 30)  x value y value (2) QUESTION 6 6.1.1 Asymptotes are x = 3 and y = - 2 x = 3 y = -2 6.1.2 making y = 0 x –intercepts: 2(x -3) = 2  x =4 2x = 8 x = 4  making x = 0 y-intercepts y = (4) = 6.1.3 x-int y-int  shape Copyright reserved Please turn over

Mathetics/P1 9 June/2017 NSC 6.1.4 Domain is answer (1) 6.1.5 y = (x – 3) – 2  m= 1 = x – 5 c = -5 (2) 6.2 q = –1 value of q Passing through (0; -2) Sub. of (0;-2) a = -1  value of a sub. of -3 = b-1 b = value of b (5) Copyright reserved Please turn over