grade 09 test memo 2025

. H I. S SCHOOL MATHEMATICS MARCH 2025 GRADE 9 1 HOUR TEST 50 MARKS MARKING GUIDELINE 1|Page

This marking guideline consists of 5 pages QUESTION SOLUTIONS MARK ALLOCATION 1 1.1 D An irrational number  (1) 1.2. C 864  (1) 1.3 D 315 km  (1) 1.4 D −34  (1) 1.5 B 𝑎9  (1) 1.6 C 23  (1) 6 marks QUESTION SOLUTIONS MARK 2 ALLOCATION 2.1.1 Rational Rational  (1) 2.1.2 Irrational Irrational  (1) 2.1.3 Rational Rational  (1) 2.2 2.2.1 135 = 3 x 3 x 3 x 5 135 = 3 x 3 x 3 x 5  (1) 2.2.2 225 = 3 x 3 x 5 x 5 225 = 3 x 3 x 5 x 5  (1) 2.2.3 315 = 3 x 3 x 5 x 7 315 = 3 x 3 x 5 x 7  (1) 2|Page

2.2.4 135 = 3 x 3 x 3 x 5 HCF =45  (1) 225 = 3 x 3 x 5x 5 315 = 3 x 3 x 5x 7 ∴ HCF = 3 x 3 x 5 = 45 TOTAL 7 marks QUESTION SOLUTIONS MARK 3 ALLOCATION 3.1 5 5 = 3 × 12  = × 12 (2) 3 = 20  OR = 20 OR 3 12 3 ∶ 5 = 12 ∶ 𝑥 = 𝑥  5 3 12 𝑥 = 20 = 5 𝑥 3𝑥 = 60 ∴ 𝑥 = 20 3.2 3 kg of potatoes cost R24 Cost per unit (R8)  (2) 𝑅56 3|Page

24 1kg will cost 3 OR = R8 ∴ 7𝑘𝑔 𝑤𝑖𝑙𝑙 𝑐𝑜𝑠𝑡 7 × 𝑅8 = 𝑅56 OR 7 × 24 𝐶𝑜𝑠𝑡 𝑜𝑓 3𝑘𝑔 = 3 7 ×24 Simplifying:  = 𝑅56 3 𝑅56  3.3 Distance travelled by car = 100 km/h x 6 Distance travelled by (4) h car 600 km  = 600 km Distance travelled by air = 1200 km – Distance travelled by 600 km air = 600 km 600 km  𝑑 𝑡= 𝑠 600 𝑘𝑚 600 𝑘𝑚 𝑡 = 300 𝑘𝑚/ℎ Substitution 300 𝑘𝑚/ℎ ∴ 𝑡 = 2 ℎ𝑜𝑢𝑟𝑠  She travelled 2 hours by air. Answer 2 hours  8 TOTAL marks QUESTION SOLUTIONS MARK 4 ALLOCATION 4.1 𝐴 = 𝑃( 1 + 𝑖)𝑛 Substitution  (3) 4|Page

= 20 000( 1 + 0,12)10 Simplifying  = 20 000( 1,12)10 𝑅62 116,96 = 𝑅62 116,96 4.2 He first 500 km are free. 350 km (3) ∴ 850 – 500 = 350 km 5 x 175 + 2 x 350 Total cost = 5 x 175 + 2 x 350 R1 575  = R1 575 8 marks 6 TOTAL marks QUESTION SOLUTIONS MARK 5 ALLOCATION 5.1.1 −6 + 4 − 23 NB: Learners must = −2 − 23 show the calculations: (2) Allocate 1 mark if only answer written. = −25 −2 − 23 OR −25 −29 + 4 OR = −25 −29 + 4 −25 5.1.2 11 − [−3 + 2 − (−1)] 11 − (−1 + 1)  (2) = 11 − (−1 + 1) = 11 + 0  5|Page

= 11 − 0 = 11 = 11 OR OR = 11 − (−3 + 2 + 1) 11 − (−3 + 2 + 1)  = 11 − 0 11 − 0  = 11 11 5.1.3 4 × (−28) Answer (1) = −112 −112 5.1.4 √6 − 2  √ √36 − √4 (3) √ 4  = √6 − 2 2 = √ 4 =2 TOTAL 8 marks QUESTION SOLUTIONS MARK 6 ALLOCATION 6.1.1 𝑥4 × 𝑥7 𝑥 11  = 𝑥 11 (1) 6.1.2 (4𝑥)0 (1) 6|Page

1 =1 6.1.3 3𝑎−2 𝑏 × 24𝑏−1 𝑎−1 72 (4) 9𝑎−4 𝑏 −3 𝑎−2+(−1)−(−4) = 3 ×24 𝑎−2+(−1)−(−4) 𝑏1+(−1)−(−3) 𝑏1+(−1)−(−3) 9 8𝑎𝑏3  72 𝑎𝑏3 = 9 = 8𝑎𝑏3 6.1.4 2𝑛+2 2𝑛+2−𝑛+1 2𝑛−1 23 or 8  2𝑛+2−𝑛+1 23 =8 TOTAL 8 marks QUESTION SOLUTIONS MARK 7 ALLOCATION 7.1 5; 7; 9; 11; ......... 7|Page

7.1.1 13; 15 13  (2) 15  7.1.2 𝑇𝑛 = 2𝑛 + 3 2𝑛  (2) +3  7.1.3 𝑇100 = 2(100) + 3 2(100)  (2) = 203 203  TOTAL 6 marks GRAND TOTAL 50 Marks 8|Page