Mathematics Grade 9 Paper 1 GEC Test 2023 Memo (English)

Downloaded from hlayiso.com GEC PILOT STUDY MARKING GUIDELINE 2023 MATHEMATICS PAPER1 GRADE 9 SECTION A  One mark per answer.  There are no half marks. No. Expected answer Clarification 1. B Irrational  2. B 108  12 = 2 × 2 × 3 18 = 2 × 3 × 3 27 = 3 × 3 × 3 2 × 2 × 3 × 3 × 3 = 108 3. A 2  Numerators 3 8 = 23 12 = 22 × 3 HCF= 2 × 2 = 4 Denominators 30 = 2 × 3 × 5 36 = 22 × 32 HCF = 2 × 3 = 6 4 2 HCF = = 6 3 4. C  Grade 9 Mathematics P1 Marking Guideline 1

Downloaded from hlayiso.com No. Expected answer Clarification 5. A 103,13 km/h  𝑑 𝑠= 𝑡 𝑑 120 = 2,75 𝑑 = 120 × 2,75 𝑑 = 330 km 330 𝑠= 3,2 𝑠 = 103,13 km/h 6. D R1 339,42  𝐴 = 𝑃(1 + 𝑖)𝑛 12 2 𝐴 = 𝑅5 265 (1 + ) 100 𝐴 = 𝑅5 265(1 + 0,12)2 𝐴 = 𝑅5 265(1,12)2 𝐴 = 𝑅5 265(1,2544) 𝐴 = 𝑅6 604,42 𝐶𝐼 = 𝑅6 604,42 − 𝑅5 265 𝐶𝐼 = 𝑅1 339,42 7. C −7 × (11 × 4)  8. B 8  3(4) − 2(2) = 12 − 4 =8 9. D 1  2 and − 2 10. C 14  2( − 3) − (5) − 4(6 ÷ 8) 5−6 3 −6 − 5 − 4 ( ) = 4 −1 −14 = −1 = 14 11. A 1  3 √49 − 23 + √216 ÷ 3 =7−8+6÷3 =7−8+2 =1 12. C 1  3 +5 −4 + 5 5 √ √−64 =√ 2 4 +3 2 16 + 9 1 =√ 25 1 = 5 13. A 𝑎5 𝑐  𝑎3 × 𝑎2 𝑐 = 𝑎5 𝑐 Grade 9 Mathematics P1 Marking Guideline 2

Downloaded from hlayiso.com No. Expected answer Clarification 14. C 2𝑥+2  4𝑥+1 2𝑥 (22 )𝑥+1 = 2𝑥 2𝑥+2 2 = 2𝑥 2𝑥+2−𝑥 = 2 = 2𝑥+2 15. B 𝑏+𝑎  𝑎−1 + 𝑏 −1 𝑎𝑏 1 1 = + 𝑎 𝑏 𝑏+𝑎 = 𝑎𝑏 16. B 1  (2 )3 × (23 )−2 2 = 26 × 2−6 = 20 =1 17. A 8𝑥 3  𝑥 −3 𝑦 −3 − ( ) 𝑦3 −2𝑥 −2 3 −2𝑥 −2 = ( −3 ) 𝑥 𝑦 3 −2𝑥 3 =( 2 ) 𝑥 𝑦 2𝑥 3 = (− ) 𝑦 8𝑥 3 = − 3 𝑦 18. D 7  3(𝑥 + 𝑦)0 (𝑥 −1 𝑦)3 + 5𝑦 −1 − −3 4 𝑦 𝑦 𝑥 𝑦 −3 3 3×1 1 𝑥 𝑦 = + 5 × − −3 4 𝑦 𝑦 𝑥 𝑦 3 5 1 = + − 𝑦 𝑦 𝑦 7 = 𝑦 19. B 35  3 + 5 ; 8 + 7 ; 15 + 9 ; 24 + 11 = 35 OR Perfect squares −1 22 − 1 = 3 32 − 1 = 8 42 − 1 = 15 20. C 83  3 + 6 + 10 + 15 + 21 + 28 = 83 Grade 9 Mathematics P1 Marking Guideline 3

Downloaded from hlayiso.com No. Expected answer Clarification 21. A A constant ratio of three was  used. 22. C 𝑇𝑛 = −2𝑛 + 7  1; 3; 5; 7; … are not consecutive term positions 5; 𝑎; 1; 𝑏; −3; 𝑐; … 𝑎−5=1−𝑎 2𝑎 = 6 2𝑎 6 = 2 2 𝑎=3 5; 3; 1; … are consecutive terms 3−5=1−3 𝑑 = −2 𝑇1 = −2(1) + ___ = 5 𝑇2 = −2(2) + ___ = 3 𝑇3 = −2(3) + ___ = 1 𝑇𝑛 = −2𝑛 + 7 23. A 3𝑥 3 and 3𝑥(𝑥 2 )  24. D −8 and 6th  (−2𝑥 2 )3 = (−2)3 (𝑥 2 )3 = −8𝑥 6 Coefficient is −8 and degree is 6th 25. C 𝑥 + 3𝑥 2 + 2 − 4𝑥  26. A −4𝑥 3 − 2𝑥 2 + 𝑥  −𝑥(4𝑥 2 + 2𝑥 − 1) = −4𝑥 3 − 2𝑥 2 + 𝑥 27. A 3𝑥 2 − 10𝑥 + 1  4𝑥 + 2 3𝑥(𝑥 − 4) + 2 4𝑥 2 = 3𝑥(𝑥 − 4) + 2 + 2 = 3𝑥 2 − 12𝑥 + 2𝑥 + 1 = 3𝑥 2 − 10𝑥 + 1 OR 2 × 3𝑥(𝑥 − 4) + 4𝑥 + 2 = 2 6𝑥 2 − 24𝑥 + 4𝑥 + 2 = 2 2 6𝑥 20𝑥 2 = − + 2 2 2 2 = 3𝑥 − 10𝑥 + 1 Grade 9 Mathematics P1 Marking Guideline 4

Downloaded from hlayiso.com No. Expected answer Clarification 28. A 𝑥  3 √0,125𝑥 3 2 3 1 = √ 𝑥3 8 3 1 = √ 3 𝑥3 2 1 1 3 = ( 3 𝑥3) 2 1 1 3 1 = ( 3 ) (𝑥 3 )3 2 1 = 𝑥 2 𝑥 = 2 29. C 17𝑥  1 2𝑥 2 + −1 (𝑥 + 3)(2𝑥 − ) 3 3 𝑥 3 = 2𝑥 2 − + 6𝑥 − 3 3 𝑥 + 18𝑥 = 2𝑥 2 − −1 3 17𝑥 = 2𝑥 2 + −1 3 30. D 16  1 2 −8 (− ) + 10(2) − 2 2 1 = −8 ( ) + 20 − 2 4 = −2 + 20 − 2 = 16 31. A (2𝑥 − 3)(2𝑥 + 3)  32. B (𝑥 − 8)(𝑥 + 3)  33. A 6(𝑦 − 3)(𝑦 + 1)  34. B 𝑥+2  2𝑥 2 − 2𝑥 − 12 2𝑥 − 6 2(𝑥 2 − 𝑥 − 6) = 2(𝑥 − 3) 2(𝑥 + 2)(𝑥 − 3) = 2(𝑥 − 3) =𝑥+2 Grade 9 Mathematics P1 Marking Guideline 5

Downloaded from hlayiso.com No. Expected answer Clarification 35. A 𝑥+𝑦+1  (𝑥 + 𝑦)2 − 1 𝑥+𝑦−1 (𝑥 + 𝑦 − 1)(𝑥 + 𝑦 + 1) = 𝑥+𝑦−1 =𝑥+𝑦+1 36. A 2  37. B 2  2𝑝 4 = 2 2 𝑝=2 38. D 𝑥 = 0 or 𝑥 = 1  39. D 𝑏 = 3 or 𝑏 = −2  40. B 2𝑥 − 8 = 18  41. C 4  𝑦 = 16 − 12 𝑦=4 42. C −2  3𝑚 = 9−1 3𝑚 = (32 )−1 3𝑚 = 3−2 𝑚 = −2 43. D 𝑝 = 17 and 𝑡 = 6  𝑦 = 𝑥2 + 1 𝑝 = (−4)2 + 1 𝑝 = 16 + 1 𝑝 = 17 and 𝑦 = 𝑥2 + 1 37 = 𝑡 2 + 1 𝑡 2 = 36 𝑡 = ±6 ∴𝑡=6 44. D 𝑥 = −6 or 𝑥 = 1  𝑥 2 + 3𝑥 + 2𝑥 − 6 = 0 𝑥 2 + 5𝑥 − 6 = 0 (𝑥 + 6)(𝑥 − 1) = 0 𝑥 = −6 or 𝑥 = 1 Grade 9 Mathematics P1 Marking Guideline 6

Downloaded from hlayiso.com No. Expected answer Clarification 45. B 𝑎 = 0 or 𝑎 = 4  1 1 ( 𝑎 − 1) ( 𝑎 − 1) = 1 2 2 1 2 𝑎 −𝑎+1=1 4 1 2 𝑎 −𝑎 =0 4 𝑎2 − 4𝑎 = 0 𝑎(𝑎 − 4) = 0 𝑎 = 0 or 𝑎 − 4 = 0 𝑎 = 0 or 𝑎 = 4 OR 1 𝑎 − 1 = ±1 2 1 1 2 𝑎 − 1 = 1 or 2 𝑎 − 1 = −1 1 1 2 𝑎 = 2 or 2 𝑎=0 𝑎 = 4 or 𝑎=0 46. B 2m  𝐴 = (𝑥 − 18)(𝑥) 40 = 𝑥 2 − 18𝑥 0 = 𝑥 2 − 18𝑥 − 40 0 = (𝑥 − 20)(𝑥 + 2) 𝑥 = 20 or 𝑥 = −2 ∴ 𝑥 = 20 breadth = 20 − 18 breadth = 2 m 47. A 𝑏 = 33  𝑦 = 4𝑥 − 3 𝑏 = 4(9) − 3 𝑏 = 33 48. C  𝒙 −2 0 2 𝒚 −8 −2 4 49. B 𝑚 = (𝑛 + 1)2  𝑚 = (𝐸𝑣𝑒𝑛 + 1)2 𝑚 = (𝑂𝑑𝑑)2 𝑚 = 𝑂𝑑𝑑 50. D 1  1 𝑦 =− 𝑥+1 𝑚=− 2 2 𝑦-intercept at (0; 1) and 𝑐 = 1 1 𝑦 =− 𝑥+1 2 51. D 𝑉 = 4𝑡 + 6  Common difference = 4 𝑉 = 4𝑡 + 𝑐 By inspection: 𝑉 = 4𝑡 + 6 Grade 9 Mathematics P1 Marking Guideline 7

Downloaded from hlayiso.com No. Expected answer Clarification 52. A  𝑐 = 40𝑡 + 500 𝑦-intercept = R500 and the gradient = 40 53. B (0; −5)  54. D 1  𝑦 = 2𝑥 − 2 2𝑥 − 2 = 0 2𝑥 = 2 𝑥=1 55. C 3  − 4 56. B  𝒙 −4 −2 2 𝒚 −1 −2 −4 57. C  Constant difference of 8 𝒙 1 2 3 4 𝒚 12 20 28 36 58. D −2𝑥 + 𝑦 − 2 = 0  −2𝑥 + 𝑦 − 2 = 0 𝑦 = 2𝑥 + 2 59. B (−1; −3)  𝑦 = 2𝑥 − 1 −3 = 2(−1) − 1 −3 = −3 60. A 𝑦 = −3𝑥 + 5  𝑚𝐴𝐵 = 𝑚𝐶𝐷 …Parallel lines 𝑦 = −3𝑥 + 𝑐 ∴ 2 = −3(1) + 𝑐 𝑐=5 Section A total 60 Grade 9 Mathematics P1 Marking Guideline 8

Downloaded from hlayiso.com SECTION B  Do not penalise the learner for the same mistake twice.  There are no half marks. MARKING CODES M Method mark A Accuracy mark CA Consistent Accuracy mark No. Expected answer Clarification Mark 61. 𝑦 = 3𝑥 − 5 𝐌 General term: 1 mark 3 Substitution: 1 mark 46 = 3𝑞 − 5 𝐌 Answer: 1 mark 51 𝑞= 3 Accept 𝑥 = 17 𝑞 = 17 CA Answer only full marks 62. −5𝑦 3 (6𝑦 − 1) − 3𝑦 2 (5 − 10𝑦 2 ) Simplification:1 mark 3 5𝑦 2 (𝑦−3) 5𝑦 2 :1 mark 5𝑦 2 −30𝑦 4 + 5𝑦 3 − 15𝑦 2 +30𝑦 4 Answer:1 mark = 𝐌 5𝑦 2 5𝑦 3 − 15𝑦 2 = 5𝑦 2 5𝑦 2 (𝑦 − 3) = 𝐌 5𝑦 2 = 𝑦 − 3CA OR 𝑦 2 (6𝑦 − 1) 3𝑦 2 (5 − 10𝑦 2 ) − Simplification:1 mark −𝑦 5𝑦 2 −6𝑦 2 + 𝑦 − 3 + 6𝑦 2 :1 mark 6𝑦 3 − 𝑦 2 15𝑦 2 − 30𝑦 4 Answer:1 mark = − 𝐌 −𝑦 5𝑦 2 6𝑦 3 𝑦 2 15𝑦 2 30𝑦 4 = − − + −𝑦 −𝑦 5𝑦 2 5𝑦 2 = −6𝑦 2 + 𝑦 − 3 + 6𝑦 2 M = 𝑦 − 3 CA Grade 9 Mathematics P1 Marking Guideline 9

Downloaded from hlayiso.com No. Expected answer Clarification Mark 63. Let 𝑥 be the mass of the car Equation: 1 mark 4 𝑥 Simplification: 1 mark 900 + 120 + = 𝑥 𝐌 𝑥 = 1275 kg: 1 mark 5 Answer: 1 mark 4500 + 600 + 𝑥 = 5𝑥 𝐌 4𝑥 = 5100 𝑥 = 1275 kg CA 𝑥 ∴ The car’s engine = 5 = 255 kg CA OR Let 𝑥 be the mass of the car Equation: 1 mark 𝑥 Simplification: 1 mark 900 + 120 + = 𝑥 𝐌 𝑥 = 1275 kg: 1 mark 5 4 Answer: 1 mark 900 + 120 = 𝑥 𝐌 5 4𝑥 = 5100 𝑥 = 1275 kg CA 𝑥 ∴ The car’s engine = 5 = 255 kg CA 64.     64.1 On graph A Correct plotting of any 2 points:1 mark (3) Correct 𝑦-intercept:1 mark Shape of graph: 1 mark 64.2 On graph A Correct drawing of graph: 1 mark (1) Grade 9 Mathematics P1 Marking Guideline 10

Downloaded from hlayiso.com No. Expected answer Clarification Mark 64.3 Distance between 𝑥- intercepts = 6 Answer: 1 mark (1) units CA Section B total 15 Grade 9 Mathematics P1 Marking Guideline 11