Mathematics Grade 9 Gauteng November 2016 Memo

Downloaded from hlayiso.com testpapers.co.za GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION NOVEMBER 2016 GRADE 9 MATHEMATICS MEMORANDUM 9 pages 1

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS SECTION A QUESTION 1 1.1 C  1.2 A  1.3 B  1.4 A  1.5 C  1.6 D  1.7 A  1.8 B  1.9 B  1.10 B  [10] SECTION B QUESTION 2 2.1 2.1.1 P  A(1  i)n  (3)  15000 (1  0,08)1  = R16200  2.1.2 P  A(1  i)n   15000 (1  0,08)5  (3) = R22039 ,92115  R22039 ,92  2

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 2.2 3  64  (3) 2  4  9   5 (2) 2.3 3 1 1 :1 : 4 2 3 3 3 1 : :  4 2 3 9 : 18 : 4  (2) 2.4 16,5l xl =  100 km 1284 km 100 x = 21186  x = 211,86  (2) [12] QUESTION 3 3.1 3.1.1 3 Balls  (1) 3.1.2 Figure 1 4 5 Number of balls 5 14 17 (2) 3.1.3 Yes.  Difference is 3 Tn  3n  2  3(n  1)  5  3n  3  5  3n  2  (3) 3.2 (2 x  1) 2  4 x 2  1 LHS  (2 x  1)(2 x  1)  4 x 2  4 x  1 Not correct / 4 x 2  1  4 x 2  4 x  1  (2) [8] 3

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 QUESTION 4 4.1  2(2 x 2  3x  5)  (4 x 2  3)  4 x 2  6 x  10  4 x 2  3   8x 2  6 x  7  (3) 4.2 4.2.1 b3 2ab  (4b   12) 12 6 b4 ab4     b3  3 36 (3) 4.2.2 4 x 3  2 x(3 x 2 ) 2x3 4 x3  6 x3   2 x3  2 x3   2 x3  1  (3) 4.3 x( a  y )  ( y  a )  x( a  y )  ( a  y )   (a  y)( x  1)  (2) 4.4 4.4.1 2( x  2)  ( x  3)  5 2 x  4  x  3  5  x  7  5 x  2  (4) 4.4.2 2x 2x 1   2 x 1 1 x x 1 2x 2x 1    x 1 x 1 ( x  1)( x  1) 2 x( x  1)  2 x( x  1)  1 2x2  2x   2 x2  2 x   1  4x  1 1 x  4 (5) 4

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 4.4.3 10 x  0,0001 10 x  104  x  4  (2) 4.5 Let the first number be 2 x , then the second is 2x  2 and third 2 x  4  2 x  2 x  2  2 x  4  78  6 x  6  78 6 x  78  6 6 x 72  6 6 x  12   the numbers are 24 , 26 and 28  (5) [27] QUESTION 5 5.1 y  2 x  1  (2) 5.2 y2  y1 y 3 m OR m     x2  x1 x 2 30 m  20 3   2 (2) 5.3 The equation y  1  2( x  2) defines a straight line graph. 5.3.1 y-intercept  3 (1) 5.3.2 y  1  2( x  2) 0  1  2( x  2)  0  1  2x  4 3  2x  3 (3) x  2 5

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 5.3.3 y  1  2( x  2)  (1 (1 mark for each intercept) (2) 5.4 5.4.1 p.  Increasing graph OR when x increases, y also increases OR x and y are directly proportional  (2) 5.4.2 y  x   5  (2) [14] QUESTION 6 6.1 a = 550  [corresponding angles of parallel lines]  (4) b = 550  [opposite angles of a parallelogram]  6.2 AB = BE [given]  AB = DC  [opposite sides of a parallelogram ] DC=BE  [both = AB]  (4) 6.3 6.3.1 In ΔDCB and ΔAED D̂1  Â  [alternate angles; DC // AE]  B̂  D̂2  [alternate angles; BC // DE ]   Ĉ  Ê  [interior angles of a triangle]   ΔDCB /// ΔAED [AAA] (6) 6

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 6.3.2 AD ED   DB CB AD 7,5 cm   5,2 cm 3 cm AD = 13 cm  AB = 13 cm – 5,2 cm = 7,8 cm  (4) 6.4 SꞋ S  (1 mark for each vertex of the image) (3) [21] QUESTION 7 7.1 7.1.1 Find the length of BC. BC 2  AB 2  AC 2 = (3 m)2 + (4 m)2 ✓ = 9 m2 + 6 m2 ✓ = 25 m2 ✓ BC = 5 m ✓ (4) 7

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 7.1.2 5m 5m 4m 7m 3m 3m (1) 1 7.1.3 Surface Area = (5 m × 7 m) + (4 m × 7 m) + 2(  4  3 ) + (3 m × 7 m)  2 = 35 m  28 m  12 m  21 m  2 2 2 2 = 96 m2  (3) 7.2 160 m  x  480 000 m2  160 xm  48 0000 m2 48 0000 m 2 x 160 m x  3 000 m  Length needed = 2(160 m  3 000 m)  = 6 320 m  (4) 7.3 7.3.1 V  300 cm  500 cm  700 cm   105 000 000 cm3  (2) 105 000 000 cm 3 7.3.2 Amount of water =  1 000 = 105 000 l  (2) [16] 8

Downloaded from hlayiso.com MEMORANDUM MATHEMATICS GRADE 9 QUESTION 8 8.1.1 4 , 8 , 12 , 12 , 16 , 16 , 16 , 24 , 24 , 32 , 32 , 36 , 48 , 48  16  24 Median =  2 = 20  (3) 8.1.2 16  (1) 8.1.3 Range = 48 – 4 = 44  (1) 8.2 8.2.1 Both homework and sports  2 hours each OR 4 hours altogether  (2) 8.2.2 Watching TV  1 hour  (2) 3 1 8.3 8.3.1 P(B) = =  (2) 6 2 5 8.3.2 P(Not W) =  (1) 6 [12] TOTAL: 120 9