Mathematics Grade 9 Paper 1 Eastern Cape November 2023 Memo

O.R.TAMBO INLAND DISTRICT SENIOR PHASE GRADE 9 NOVEMBER 2023 MATHEMATICS PAPER 1 MARKING GUIDELINE MARKS: 75 This marking guideline consists of 5 pages. .

November 2023 Mathematics Grade 9 Paper 1 Marking guideline O.R.T.I.District QUES SOLUTION Total No. QUESTION 1 1.1 B ✓ (1) 1.2 C✓ (1) 1.3 C✓ (1) 1.4 D✓ (1) 1.5 C✓ (1) 1.6 D✓ (1) 1.7 C✓ (1) 1.8 B✓ (1) 1.9 D✓ (1) 1.10 B✓ (1) [10] QUESTION 2 2.1 2.1.1 (2) 2.1.2 Direct. As the time goes up, the number of apples collected increases. ✓ (1) 2.1.3 Phiko takes a bus to school. The school is 9 km from his home. If the bus (3) travels at an average speed of 40km/h, how many minutes does he take to get to school? 𝑑 𝑡=𝑠✓ 9𝑘𝑚 = 40𝑘𝑚/ℎ = 0,225/ℎ × 60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 ✓ 𝑡 = 13,5 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 ✓ 2.1.4 Liya invests R15 000 in his savings account at 16% per annum compound (3) interest. Calculate how much interest there will be in his savings account after 3 years 𝑟 𝑛 𝐴 = 𝑃 (1 + 100) ✓ 𝑟 3 = 15 000 (1 + ) 100 = 15 000(1,56) 𝐴 = 23 413,44 ✓ 𝑖 = 23 413,44 − 15 000 𝑖 = 8 413,44 ✓ 2.2 2.2.1 1×1+1=2 (1) 2×2+1=5 Square the position of a number and add 1. ✓ 2|Page

November 2023 Mathematics Grade 9 Paper 1 Marking guideline O.R.T.I.District 2.2.2 10 × 10 + 1✓ = 101 ✓ (2) 2.3 2.3.1 (1) 2.3.2 5×1+2=7 (2) 5 × 2 + 2 = 12 5 × 3 + 2 = 17 ∴ 𝑇𝑛 = 5𝑛✓ + 2 ✓ 2.3.3 (i) 5 × 5 + 2 = 27 (2) (ii) 5𝑛 + 2 = 62 ✓ 5𝑛 = 60 𝑛 = 12 ✓ 2.4 Determine the value of 216÷ 27 in an exponential form. (2) = 23 × 33 ÷ 33 ✓ = 23 × 33−3 = 23 × 1 ∴ 216 ÷ 27 = 23 ✓ 2.5 (2𝑑2 𝑒)2 (3) 2.5.1 (4𝑑 −3 𝑒 −2 )−1 ✓ 4𝑑4 𝑒 2 = 𝑑 × 𝑒0 4𝑑3 𝑒 2 ✓ =𝑑 ✓ 15𝑥 × 3𝑥+1 × 25𝑥 (3) 2.5.2 9𝑥+1 × 125𝑥 3𝑥 ×5𝑥 ×3𝑥+1 ×52𝑥 ✓ = 32𝑥+2 ×53𝑥 ✓ = 3𝑥+𝑥+1 × 5𝑥+2𝑥 ÷ 32𝑥+2 × 53𝑥 = 3−1 × 50 1 = 3−1 𝑜𝑟 3 ✓ 2.5.3 3 √(20𝑥 − 15𝑥)3 or = 20𝑥 − 15𝑥 ✓ (2) 3 = √5𝑥 3 ✓ = 5𝑥 ✓ = 5𝑥 ✓ 3|Page

November 2023 Mathematics Grade 9 Paper 1 Marking guideline O.R.T.I.District 2.5.4 −2(𝑥 + 1)(𝑥 + 2) + 2(𝑥 + 2)2 (4) = −2(𝑥 2 + 3𝑥 + 2)✓ + 2(𝑥 2 + 4𝑥 + 4) ✓ = −2𝑥 2 − 6𝑥 − 4 + 2𝑥 2 + 8𝑥 + 8 = 2𝑥✓ + 4✓ 2.5.5 (3) 2.6 2.6.1 𝑥 2 + 5𝑥 + 6 (2) = (𝑥 − 3)✓(𝑥 − 2) ✓ 2.6.2 3𝑥 2 − 27 (3) = 3(𝑥 2 − 9) ✓ = 3(𝑥 − 3)✓(𝑥 + 3) ✓ 2.7 Mrs G has 12 children. Each child needs 36 crayons. How many crayons must she (2) buy? 36 × 12✓ = 432 Mrs G must buy 432 crayons. ✓ 2.8 If 𝑦 = 2𝑥 2 + 4𝑥 + 3, determine the value of y when 𝑥 = −2. (3) 𝑦 = 2(−2)2 + 4(−2) + 3 𝑦 = 8−8+3 ✓✓ 1 mark : 8 and 1 mark: −8 𝑦=3 ✓ 2.9 1 (3) 2.9.1 22𝑥−2 = 64 22𝑥−2 = 64−1 22𝑥−2 = 2−6 ✓ 2𝑥 − 2 = −6 2𝑥 = −4 ✓ ∴𝑥 = −2 ✓ 2𝑥 13 (4) 2.9.2 +1= 5 5 2𝑥+5 13 = 5 ✓ 5 5(2𝑥 + 5) = 5 × 13 ✓ 10𝑥 + 25 = 65 ✓ 10 𝑥 = 40 ∴ 𝑥 =4 ✓ [52] 4|Page

November 2023 Mathematics Grade 9 Paper 1 Marking guideline O.R.T.I.District QUESTION 3 3.1 3.1.1 +4 ✓ (1) 3.1.2 4 ✓ ✓ (2) 3.1.3 −5 ✓ ✓ (2) 3.2 3.2.1 (2) 3.2.2 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑖𝑠 (2 ; 0) ✓ (2) 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑖𝑠 (0 ; 4) ✓ 3.2.3 The gradients are parallel ✓because they are equidistant from each other. ✓ (2) 3.3 3.3.1 Graph AB is 𝑦 = 𝑥 ✓ (1) 3.3.2 Graph CD is 𝑥 = −2 ✓ (1) [13] END 5|Page