Mathematics Grade 10 IEB Paper 1 November 2012 Memo

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Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 EXEMPLAR 2012 MEMORANDUM MARKS: 100 This memorandum consists of 7 pages. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 2 DBE/2012 NSC – Grade 10 – Memorandum QUESTION 1 1.1.1 (m − 2n )(m 2 − 6mn − n 2 )  expansion = m 3 − 6m 2 n − mn 2 − 2m 2 n + 12mn 2 + 2n 3  m3 ; + 2n3 3 2 2 3 = m − 8m n + 11mn + 2n  − 8m 2 n + 11mn 2 (3) 1.1.2 x +13 2 4 x − 3x − 1 x2 − x +1 − 4x + 1 (  ( x + 1) x 2 − x + 1 )  (4 x + 1)(x − 1) ( x + 1) ( x 2 − x + 1) ( 4 x + 1)( x − 1) = − x2 − x + 1 4x +1  x + 1 − ( x − 1) = x + 1 − ( x − 1) answer =2 (5) 1.2.1 6 x 2 − 7 x − 20  (3 x + 4 ) = (3 x + 4 )(2 x − 5)  (2 x − 5) (2) 1.2.2 2 a + a − 2ab − 2b grouping = a (a + 1) − 2b(a + 1)  (1 + a) = (a + 1)(a − 2b)  (a − 2b ) (3) 1.3 Since 7 = 49 and 8 = 64 and 2 2 49 < 51 < 64 ,  49 < 51 < 64 7 < 51 < 8  answer (2) i.e. 51 lies between 7 and 8 1.4 Let x = 0,2 4 5  introduce variable Then 1000 x = 245,2 4 5  1000 x = 245,2 4 5 i.e. 999 x = 245  999 x = 245 245 i.e. x= 245 x= 999 999 Therefore x is a rational number. (4) [19] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 3 DBE/2012 NSC – Grade 10 – Memorandum QUESTION 2 2.1.1 x 2 − 4 x = 21 x 2 − 4 x − 21 = 0  standard form (x + 3)(x − 7 ) = 0  factors x+3= 0 or x−7 = 0  answers x = −3 x=7 (3) 2.1.2 5 96 = 3 x 4 5  32 = x 4 5  x = (32 ) 5 4 32 = x 4 x = (32 ) 5 4 ( ) 4 = 25 5 = 24 = 16  answer (3) 2.1.3 2 x R=  Multiply by 3S and 3S divide by 2 3RS  Squaring both sides = x 2 9R 2 S 2 (2) x= 4 2.2 6q + 7 p = 3......................Equation 1 2q + p = 5......................Equation 2 6q + 7 p = 3......................Equation 1 14q + 7 p = 35....................multiply Equation 2 with 7 ........Equation 3  14q + 7 p = 35 Equation 3 – Equation 1:  8q = 32 8q = 32 q = 4 q=4  substitution 2(4 ) + p = 5  p = −3 p = −3 (5) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 4 DBE/2012 NSC – Grade 10 – Memorandum QUESTION 3 3.1.1 10 ; 6 ; 2  10 6 2 (3) 3.1.2 d=–4 –4n  14 T n = – 4n + 14 (2) 3.1.3 − 4n + 14 < −31  − 4n + 14 < −31 − 4n < −45  n >11,25  answer n > 11,25 (3) n = 12 3.2 Tn = 6n Tn = 3n  6n T13 = 6(13) OR T26 = 3( 26)  substitution of 13  answer = 78 = 78 (3) OR  3n  substitution of 26  answer (3) [11] QUESTION 4 4.1 A = P(1 + i ) n n = 2.5 2.5  4.25  substitution = 45001 +   100  answer (3) = R 4993.47 4.2.1 Loan amount = R5 999 – R600 y=0 = R5 399 Total amount owed = 5 399[1+(0,08)(1,5)] 5 399 = R6 046,88 n = 1,5 Substitution 6046.88 Monthly instalment = R6 046,88 18 = R335,94  ÷ 18 R335,94 (6) 4.2.2 R6 046,88 - R5 399  answer = R647,88 (1) 4.3 1 kg = 1 000 g conversion 1000 division = 35,27336861… ounces multiplication 28,35 35,27336861… x 978,34 x 8,79 answer = R303 337,16 (4) [14] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 5 DBE/2012 NSC – Grade 10 – Memorandum QUESTION 5 5.1.1 A ∩ B OR A and B  answer (1) / 5.1.2 A OR not A  answer (1) 5.2 B  answer (1) 5.3.1 19 learners are right-handed and do not play soccer.  answer (1) 5.3.2  15 4 S L 2  19 14 3 (4) 4 19 5.3.3 (a) 14 + 4 + 3  15 + 4 + 2 P(L OR S) =  40 40  answer 21 = (3) 40 5.3.3 (b) 14 15 P(R AND S) =  40 40 7  answer = 20 (2) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 6 DBE/2012 NSC – Grade 10 – Memorandum QUESTION 6 y 6.1 8 7 shape of f 6 5 f  x-int of f g 4 3  x-intercept of g 2 1  y-intercept of g x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 (4) f -5 -6 -7 6.2 x = 0 and  answer y=1  answer (2) 6.3 (−∞ ; 0) ∪ (0 ; ∞)  values  notation (2) 6.4 3 + 1 = −2 x − 4 x 3  + 1 = −2 x − 4 3 x = −2 x − 5 x 3 = −2 x 2 − 5 x 2 x 2 + 5x + 3 = 0  standard form  factors (2 x + 3)( x + 1) = 0 3 x = − or x = −1  answers 2 (5) 6.5 − 1 ≤ −2 x − 4 < 3  3 ≤ −2 x < 7 − 1 ≤ −2 x − 4 < 3  3 ≤ −2 x < 7 − 1,5 ≥ x > −3,5 − 3,5 < x ≤ −1,5 OR x ∈ (−3,5 ; − 1,5]  answer (3) 6.6 k ( x) = 2(−2 x − 4)  equation of k(x) = −4 x − 8  answer (2) y-intercept: (0 ; – 8) 6.7 x-intercept: (2 ; 0)  x-intercept y-intercept: (0 ; – 4)  y-intercept (2) [20] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 7 DBE/2012 NSC – Grade 10 – Memorandum QUESTION 7 7.1 C(– 2 ; 0)  answer (1) 7.2 f ( x) = ax 2 + q ( f ( x) = a x 2 − 4 ) (  f ( x ) = a x 2 − 16 ) 2 2,5 = a ((−3) − 4) 2,5 = 5a  substitution of (– 5 ; 2,25) 1 a= 2  answer 1 ( f ( x) = x 2 − 4 2 ) (3) 7.3 Range of f: [−2 ; ∞)  answer (1) 7.4 Range of h: (−∞ ; 0]  notation  critical values (2) 7.5 g ( x= ) bx − 4  g ( x= ) b −4 x = b2 − 4 0  substitution 4 = b2 b=2 g ( x= ) 2x − 4  answer (3) [10] TOTAL: 100 Copyright reserved Powered by TCPDF (www.tcpdf.org)