GR 10 MATHS – EXAM MEMOS M - The Answer

1 Grade 10 MATHS Exam MEMOS : Paper 1. M. GR 10 MATHS EXAM MEMOS . 2. i i i 2 x NATIONAL EXEMPLAR PAPER 1 Let x = 0,245 3S. = R. x = 0,245 245 .. % 3 S) 2 x = 3 SR. % 1 000) 1 000 x = 245, 245 245 .. 3 SR. 2 2 2) x =. (m - 2n)(m - 6mn - n ) - : 999 x = 245 2. 9 S2 R2. 245 Square : x = . 3. = m - 6m n - mn 2 2. x = 4. 999. 2 2 3. - 2m n + 12 mn + 2n 3 2 2 3 .. x can be expressed as a where = m - 8m n + 11 mn + 2n b 6q + 7p = 3 .. a & b Z. 2q + p = 5 .. x3 + 1 4x 2 - 3x - 1. % 3: .. x - x +1. 2. - 4x + 1 x is a rational number 6q + 3p = 15.

2 - : 4p = - 12. (x + 1)( x 2 - x + 1) - (4x + 1)(x - 1). = p = -3 . ( x 2 - x + 1) (4x + 1). = (x + 1) - (x - 1) : 2q - 3 = 5. x2 - 4x = 21. = x+1 - x+1 2 2q = 8. x - 4 x - 21 = 0. = 2 q = 4 . (x + 3)(x - 7) = 0. x+3 = 0 or x-7 = 0. 2. 6 x - 7x - 20 2 5 x = -3 x = 7 . EXAM MEMOS : PAPER 1. 3 4. = (2x - 5)(3x + 4) st The 1 3 terms : 5. 2 3(3) + 1 ; 2(3) ; 3(3) - 7. a + a - 2ab - 2b 3x 4 = 96. = a(a + 1) - 2b(a + 1) 5 10 ; 6 ; 2 . = (a + 1)(a - 2b) . 3) x 4 = 32. (x ). 4 4. 5. 4. 5 = ( 25 ) 5 The difference is - 4.

3 In Tn = an + b : a = - 4. 49 < 51 < 64 .. 51 lies between 49 and 64 x = 24. & T0 = b = 14 .. the st term before the 7< 51 < 8 .. taking the square root x = 16 1 term Tn = - 4n + 14 . 51 lies between 7 and 8 . M1 Copyright The Answer Grade 10 Exam MEMOS : Paper 1. The amount of interest (a) n(L or S) = 3 + 4 + 14 = 21. M n ? if Tn < - 31. - 4n + 14 < - 31 = The total amount paid over the 18 months P(L or S) =. 21.. 40. - 4n < - 45 the loan amount 2 (- 4) n > 11. 1 = R6 046,88 R5 399 (b) n(R and S) = 14.

4 Where R is the set 4 14 of all right-handed th = R647,88 P(R and S) =. The 12 term 40 people 7. = . 28,35 g is worth $978,34 = R978,34 % 8,79 20. The even numbers : 6 ; 12 ; 18 .. th = R8 599,61. The 13 even number = 13 % 6 = 78 . 1 g is worth R8 599,61. th 28,35 y OR : The 13 even number 1 kg is worth R 8 599,61 % 1 000 .. 1 kg = 1 000 g th = the 26 term of the pattern 28,35. = 26 % 3. l R303 337,16 . = 78. f 1. y =1. A B OR : A and B . O x 4,25 30 1 -3 -2. P = 4 500 ; i = = 0,0425 ; n = = 2 ; A?

5 A OR : not A . 100 12 2 Note : n 2,5 We can only know A = P(1 + i ) = 4 500(1 + 0,0425) = R4 993,47 Set B that the graphs -4 intersect once Question The loan amount = R5 999 - R600 = R5 399 Of the 40 learners, 7 are left-handed has been done ! 40 - 7 = 33 are right-handed The accumulated amount, A = P(1 + i n) 3. f: y =. Of the 18 learners who play soccer, x +1. 1. EXAM MEMOS : PAPER 1. where P = 5 399; i = 8% = 0,08; n = 1 years; A ? 4 are left-handed y-intercept (x = 0) : none 2. 14 learners who play soccer are right-handed x-intercept (y = 0) : 3x + 1 = 0.

6 A = 5 399 1 + (0,08) 3 . 2 () The number of learners who are right-handed and DON'T play soccer . 3. = R6 046,88 x = -1. = 33 - 14 = 19 . x = -3. 6 046,88. The monthly amount to be paid =. 18. n(Class) = 40 g : y = - 2x - 4. = R335,94 y-intercept (x = 0) : y = - 4. L S. 7-4. 4. 18 - 4 x-intercept (y = 0) : - 2x - 4 = 0. = 3 = 14. - 2x = 4. 19. x = -2. Copyright The Answer M2. Grade 10 Exam MEMOS : Paper 1. Asymptotes : y = 1 g y h The graph of h y x-intercept of g : (- 2; 0). M. f & x = 0 (the y-axis) & x-intercept of h : (2; 0) O x is obtained by 2.

7 (- 2; 0) (2; 0) flipping f .. -f(x). O x Domain of f : x 0; x R y-intercept of g : (0; - 4) then, shifting down -2. 2.. (- ; 0) (0; ) & y-intercept of h : (0; - 4) 2 units .. -2. (0; - 4). The range of h : y 0 h 3. f (x) = g(x) . x + 1 = - 2x - 4 Notice : The reflected points have 2. the same y-coordinate, OR : ( - ; 0 ] . % x) 3 + x = - 2x - 4x but the x-coordinates 2. 2x + 5x + 3 = 0 are opposite in sign. OR : h(x) = - 1 x 2 - 2 - 2 y 2 . (2x + 3)(x + 1) = 0 1 2 O x h(x) = - x +2-2. 2x + 3 = 0 or x+1 = 0 2.

8 2x = - 3 x = -1 C(- 2; 0) .. symmetrical about the y-axis 1 2. h(x) = - x 2 h x = -3 . 2. The equation of f : y = a(x + 2)(x - 2) .. roots The range of h : y 0 . Note : These are the x-coordinates of the 2 -2 & 2. y = a( x - 4). points of intersection of f and g : 5 q = - 4 .. range y > - 4 y = - 4 is an asymptote -- 1 1 ; -1 - 2). Subst. B - 3; 5 : = a (- 3) 2 - 4 . 2 2 2 y g Equation of g : 5. = a(5) x f 2 y = b -4; b>0. -1 g( x) < 3 1. 5) a = O x 2 A(2; 0). - 1 - 2x - 4 < 3 .. g(x) = -2x - 4 Substitute A(2; 0) : -2.

9 2 y = -4. 1 2 0 = b -4 -4. The equation of f : y = (x - 4). add 4 : 3 - 2x < 7 When one divides by 2 2. b = 4. 1 2. (- 2) : - 3. x > - 7 a negative number, .. the direction of the y = x -2 b = 2 .. b -2 b > 0. 2 2 2. 'inequality' changes. EXAM MEMOS : PAPER 1. 7 3 Equation of g : means therefore - < x - .. the inequality has been The y-intercept of f is (0; - 2) x means because 2 2 rewritten with the y = 2 -4 . smaller value on the left The range of f : y - 2 OR : [ - 2; ) . 1. - 3 < x - 11 1 1. OR : - 3 ; - 1.]

10 2 2 2 2 . ( means excluding ; ] means including Graphs are easier than you thought ! The Answer Series offers excellent material in several subjects for Gr 10 - 12. k( x) = 2 g( x) = 2(- 2x - 4) = - 4x - 8. See our website The equation of k : y = - 4x - 8. The y-intercept of k : (0; - 8) .. substitute x=0. M3 Copyright The Answer Grade 10 Exam MEMOS : Paper 2. x < 4 500 M . - 3 + (- 1) 3 + (- 8) . M. 2 500 ;.. NATIONAL EXEMPLAR PAPER 2 2 2 . 5. The sum of .. M - 2 ; - . 2 The mean, the products of the frequency 2.)