2.1 = = 2 (3) 2.2.1 + ( = + = = 6 Converting decimals to fractions Squaring Simplifying/adding answer /antwoord (3) 2.2.2 = = 1 Converting decimals to fractions Simplifying/adding Determining the square roots answer /antwoord (3) 2.3 3 = 6 x 2 3 = 12 = 4 3 = 6 x 2 = 4 workers /werkers (2) 2.4.1 2 100 + 300 + 1 450 + 370 + 600+ 655 +1 350 = R6825 answer /antwoord (1) 2.4.2 8 900 – 6 825 = R2 075 answer /antwoord (1) 2.4.3 A = P(1 + = 5 000(1 + 0.085 x 3) = 5 000(1,255) = R6 275 6 275 – 5 000 = R1 275 formula /formule substitution/ substitusie answer /antwoord (1) (1) (1) 2.4.4 A = P(1 + n = 15 000(1 + 0,12)2 = R 9 600(1.12)2 = R18 816 18 816 – 15 000 = R3 816 formula / formule substitution/substitusie answer /antwoord answer /antwoord (1) (1) (1) (1) TOTAL / TOTAAL 16marks / punte
QUESTION 3 VRAAG 3 SOLUTIONS OPLOSSING MARK ALLOCATION PUNTE TOEKENNING 3.1.1 : = answer /antwoord (1) 3.1.2 - multiplying answer /antwoord (3) 3.1.3 = 2 = 14 substitution /substitusie answer /antwoord (2) 3.2.1 = 33y3 Simplifying answer /antwoord (1) (1) (1) 3.2.2 = = 2 answer /antwoord (1) (1) 3.3.1 (1) (1) 3.3.2 = 2 (1) (1) (1) TOTAL / TOTAAL 16 marks / punte QUESTION 4 VRAAG 4 SOLUTIONS OPLOSSING MARK ALLOCATION PUNTE TOEKENNING 4.1.1 (1) (1)
answer /antwoord 4.1.2 7 answer /antwoord (1) (1) (1) 4.2 …(3) (3) into (2) y=1 into (1) (1) (1) (1) (1) TOTAL /TOTAAL 9 marks / punte QUESTION 5 VRAAG 5 SOLUTIONS OPLOSSING MARK ALLOCATION PUNTE TOEKENNING 5.1 3 and 5 7 and 9 11 and 13 (1) (1) (1) 5.2 Add 2 sticks to the previous pattern Tel 2 stokkies by die vorige patroon answer /antwoord (1) 5.3 Tn = 2n + 1 answer /antwoord (2) 5.4 T17 = 2(17) + 1 substitution/substitusie (1)
= 35 answer /antwoord (1) TOTAL / TOTAAL 8 marks / punte QUESTION 6 VRAAG 6 SOLUTIONS OPLOSSING MARK ALLOCATION PUNTE TOEKENNING 6.1 ANNEXURE B / BYLAAG B Plot co-ordinates Stip koördinate (2) 6.2 = -1 answer /antwoord (1) (1) 6.3 answer /antwoord (2) TOTAL /TOTAAL 6 marks / punte QUESTION 7 VRAAG 7 SOLUTIONS OPLOSSING MARK ALLOCATION PUNTE TOEKENNING 7.1 In ABD and ACD AD = AD = AB = CD ABD ≡ ACD Common Both = 90° Given H; 90°, S (1) (1) (1) (1) 7.2 In ABE and DCE = = 1 = 2 ABD ACD Alt < AB || CD Alt < AB || CD Vert opp <’s A; A; A (1) (1) (1) (1) TOTAL / TOTAAL 8 marks / punte QUESTION 8 VRAAG 8 SOLUTIONS OPLOSSING MARK ALLOCATION PUNTE TOEKENNING 8.1.1 ext. < of / buite < van ∆ (1)
Reason / rede answer /antwoord (1) (1) 8.1.2 = 180°- (58° + 𝑥) sum int<∆/som binne<∆ = 93° Reason/ rede answer /antwoord (1) (1) 8.1.3 𝑧 = 𝑥= 29° alt. < / verw. < reason / rede answer /antwoord (1) (1) 8.2 = (10m)2 – (8m)2 Pythagoras = 100m2 – 64m2 = m2 = 6 m A = l x b = 6 x 8 = 48 m2 6 x 8 answer /antwoord (1) (1) (1) 8.3.1 Triangular prism answer /antwoord (1) 8.3.2 Pythagoras = 29,44mm SA = + 3( = 2[ x 34 x 29,44] + 3(170 x 34) = 1000,96 + 17340 = 18340,96 mm2 substitution / substitusie 1000,96 + 17340 answer /antwoord (1) (1) (1) TOTAL / TOTAAL 14 marks / punte QUESTION 9 VRAAG 9 SOLUTIONS OPLOSSING MARK ALLOCATION PUNTE TOEKENNING 9.1 See annexure C / bylaag C image / refleksie (2) 9.2.1 See annexure C / bylaag C image / refleksie (3) 9.2.2 6 (units) answer / antwoord (1) TOTAL / TOTAAL 6 marks / punte QUESTION 10 SOLUTIONS MARK ALLOCATION
VRAAG 10 OPLOSSING PUNTE TOEKENNING 10.1.1 55218 = 30,67 55218 answer / antwoord (2) 10.1.2 26 answer / antwoord (1) 10.1.3 = 31 answer / antwoord (1) (1) 10.1.4 42 – 18 = 24 42 – 18 answer / antwoord (1) 10.2.1 GG GP GB PG PP PB BG BP BB GG,GP,GB PG, PP, PB BG, BP, BB (1) (1) (1) 10.2.2 9 answer / antwoord (1) 10.2.3 answer / antwoord (1) 10.2.4 answer / antwoord (1) 10.2.5 = answer / antwoord (1) TOTAL / TOTAAL 12 marks / punte MATHEMATICS 2014 WISKUNDE EXAMINATION GRADE 9 NOVEMBER EKSAMEN GRAAD 9 ANNEXURE A / BYLAAG A SECTION A / AFDELING A QUESTION 1 / VRAAG 1 Answer sheet for Multiple Choice Antwoordblad Meervoudige Keuse 1 A B C D 2 A B C D 3 A B C D
ANNEXURE C / BYLAAG C: QUESTION 9.1 and 9.2.1 / VRAAG 9.1 en 9.2.1 𝑦 9 B’ 8 7 6 B” 5 C’ B 4 3 C” C 2 A” 1 A A’ 𝑥 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -7 -8 -9 (1)
1.9 The number is equal to: A 1 2 2 1.10 Sipho memorized 5 out of 7 songs for a music competition. What percent of the songs did he memorize? 0,71% 140% 1,4% 71% 2 [20] SECTION B QUESTION 2 2.1 Simplify: 3 2.2 2.2.1 2.2.2 2.3 2.4 Calculate the following with a calculator: 4,85 10-4 2 10-5 3,1 104 + 0,061 107 A car travelling at an average speed of 150 km/h covers a certain distance in 3 hours. How long will it take the car to travel the same distance at a speed of 120 km/h? A = P(1 + ) A = P(1 + n A = P(1 - n Study the lounge suite advert below: 2 2 3
QUESTION 1 SOLUTIONS MARK ALLOCATION 1.1 D Correct answer 2 marks 1.2 C Correct answer 2 marks 1.3 B - - -1 Correct answer 2 marks 1.4 A 18 = 2.3.3 24 = 2.3 2.2 32 = 2 2.2.2.2 HCF: 2 Correct answer 2 marks 1.5 A Correct answer 2 marks 1.6 C 2; 2; 3; 3; 4; 5; 5; 6; 7; 7; 7; 8; 8; 9; 10 Correct answer 2 marks 1.7 D Correct answer 2 marks 1.8 D Correct answer 2 marks 1.9 A Correct answer 2 marks 1.10 D 71% Correct answer 2 marks TOTAL 20 marks QUESTION 2 SOLUTIONS MARK ALLOCATION 2.1 = = = 1 1 mark = 1 mark 1 mark 2.2.1 9,7 10-9 Correct answer 2 marks 2.2.2 6,41 105 Correct answer 2 marks
= = 1 mark 1 mark 3.3.2 = 1 mark 1 mark TOTAL 14 marks QUESTION 4 SOLUTIONS MARK ALLOCATION 4.1 1 mark Correct answer 1 mark 4.2 1 mark 1 mark Correct answer 1 mark 4.3 OR or 1 mark 1 mark 4.4 1 mark Correct answer 1 mark TOTAL 9 marks QUESTION 5 SOLUTIONS MARK ALLOCATION 5.1 17 1 mark 21 1 mark 5.2 Add 4 sticks to the previous pattern Correct answer 1 mark 5.3 Tn = 4n + 1 Correct answer 2 marks 5.4 T20 = 4(20) + 1 = 81 Correct answer 2 marks TOTAL 7 marks QUESTION 6 SOLUTIONS MARK ALLOCATION 6.1 MAB = = -1 Correct answer 1 mark 6.2 Correct answer 2 marks 6.3 If If Any other method can be used for 2 marks 1 mark 1 mark Graph 1 mark
See annexure B for graph 6.4 M() Estimation accepted (0,5; 2,5) Correct answer 1 mark TOTAL 7 marks QUESTION 7 SOLUTIONS MARK ALLOCATION 7.1.1 + 62° + 42° = 180° = 76° interior angles of triangle 76° 1 mark Reason 1 mark 7.1.2 Angles are equal 1 mark 7.1.3 PQR /// TMS 10 1 mark 10 1 mark 1 mark 1 mark 7.2 In ABD and CBD is: AB = CB given given BD = BD common ABD CBD SAS AB = CB 1 mark 1 mark BD = BD 1 mark SAS 1 mark TOTAL 10 marks QUESTION 8 SOLUTIONS MARK ALLOCATION 8.1.1 = 63° angles opposite equal sides 63° + 63° exterior angles of triangle 126° OR = 63° angles opposite equal sides BC + + 63°= 180° interior angles of BC + = 180° angles on straight line = 126° = 63° 1 mark Reason 1 mark 126° 1 mark Reason 1 mark 8.1.2 = 63° alternate angles, DA//BC = 63° 1 mark alternate angles, DA//BC 1 mark 8.2 AC 1 mark 8.3.1 Triangular prism Correct answer 1 mark 8.3.2 PQ² = QS² - PS² Pythagoras = (12 cm)² - (6 cm)² = 144 cm² - 36 cm² = 108 cm² PQ = cm OR 6 cm Substitution 1 mark 108 cm² 1 mark Correct answer 1 mark 8.3.3 V = = (12 cm)(10,4 cm)(40 cm) = 2496 cm³ Substitution 1 mark Correct answer 1 mark