Mathematics Grade 9 P1 Eastern Cape November 2023 QP

O.R.TAMBO INLAND DISTRICT SENIOR PHASE GRADE 9 NOVEMBER 2023 MATHEMATICS PAPER 1 MARKS: 75 TIME : 2 hours This question paper consists of 10 pages including annexure .

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District INSTRUCTIONS AND INFORMATION TO THE LEARNER 1. You will be given 15 minutes reading time before you begin answering the paper. 2. Read the instructions for each question carefully. 3. Answer all the questions. 4. Number your work exactly as questions are numbered. 5. Clearly show ALL the calculations, diagrams and graphs you have used in determining your answers 6. You may use an approved scientific calculator (non-programmable and non-graphical). 7. Diagrams are NOT necessarily drawn to scale. 8. 9. 10. 2|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District QUESTION 1 1. In this question, 4 possible answers are given. Write only the correct letter for the correct answer next to the corresponding number. EXAMPLE: If the correct answer for 1.1 is A, write only answer as 1.1 A. 1.1 Which of the numbers below is a rational number? (1) A. 𝜋 B. 2, 3̇ C. √−16 3 D. √53 1.2 Sipho is a car salesperson. He earns a commission of 3% on the sale of a car that (1) values R220 000. The commission he earned is A. R660 000 B. R733 333 C. R6 600 D. 154 000 1.3 (23 )2 × (23 )−2 when simplified is (1) A. 210 B. 2−1 C. 1 D. 2 1.4 The general rule (𝑇𝑛 ) for −5; −1; 3; 7 is (1) A. 𝑇𝑛 = −4𝑛 − 9 B. 𝑇𝑛 = −4𝑛 − 9 C. 𝑇𝑛 = −4𝑛 + 9 D. 𝑇𝑛 = 4𝑛 − 9 1.5 (1) The number of dots in the next hexagonal prism will be A. 19 B. 24 C. 25 D. 28 3|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District 1.6 16𝑥 2 𝑦 − 12𝑥𝑦 (1) = 4𝑥𝑦 A. 4𝑥 2 𝑦 − 3 B. 4𝑥 2 𝑦 − 3𝑥𝑦 C. 4𝑥 3 𝑦 2 − 3𝑥 2 𝑦 2 D. 4𝑥 − 3 1.7 If 𝑝 = 4; 𝑞 = 6 𝑎𝑛𝑑 𝑟 = 5, then the value of 2𝑝 + 𝑞𝑟 = (1) A. 17 B. 19 C. 38 D. 46 1.8 When (𝑥 − 1)(𝑥 + 2) = 0, 𝑡ℎ𝑒𝑛 𝑥 = (1) A. −1 𝑜𝑟 0 B. 1 𝑜𝑟 − 2 C. 1 D. −2 1.9 The gradient for the graph drawn below is (1) A. −2 B. 2 C. −1 D. 1 4|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District 1.10 The graph of a straight line defined by 𝑦 = 2𝑥 + 4 is (1) [10] QUESTION 2 2.1 2.1.1 Use prime factorization to find the HCF of 360 and 780. (2) 2.1.2 Study the table below which shows the relationship between the period of (1) time in minutes at which Zelha and Nalo collect apples in the orchard. Then answer the question that follow. Period of time in minutes 1 2 3 8 10 Zelha 12 24 36 96 120 Nalo 15 30 45 120 150 Is the relationship shown in the table a direct or indirect proportion? Give a reason for your answer. 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? 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. 2.2 In the pattern, 2 ; 5 ; 10 ; 17 2.2.1 Explain how can you extend the pattern in words? (1) 2.2.2 Hence, determine the 10𝑡ℎ term (2) 5|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District 2.3 Read the geometric pattern below to answer the questions that follow 2.3.1 Draw figure 5 (1) 2.3.2 Find the general rule in the form 𝑇𝑛 = (2) 2.3.3 In the table below, Figure 1 2 3 4 5 q number Number of 7 12 17 22 p 62 dots (i) How many dots represented by letter p in the table? (1) (ii) Use the general rule: 𝑇𝑛 to find the figure number that has 62 dots. (2) 2.4 Determine the value of 216÷ 27 in an exponential form. (2) 2.5 Simplify (2𝑑2 𝑒)2 (3) 2.5.1 (4𝑑 −3 𝑒 −2 )−1 15𝑥 × 3𝑥+1 × 25𝑥 (3) 2.5.2 9𝑥+1 × 125𝑥 3 2.5.3 √(20𝑥 − 15𝑥)3 (2) 2.5.4 −2(𝑥 + 1)(𝑥 + 2) + 2(𝑥 + 2)2 (4) 𝑦 2 −1 (3) 2.5.5 × (2𝑦 − 4 𝑦 2 −𝑦−2 2.6 Factorize fully 2.6.1 𝑥 2 + 5𝑥 + 6 (2) 2.6.2 3𝑥 2 − 9 (3) 6|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District 2.7 Mrs G has 12 children. Each child needs 36 crayons. How many crayons must (2) she buy? 2.8 If 𝑦 = 2𝑥 2 + 4𝑥 + 3, determine the value of y when 𝑥 = −2. (3) 2.9 Solve for 𝑥 1 (3) 2.9.1 22𝑥−2 = 64 2𝑥 13 (4) 2.9.2 +1= 5 5 [52] QUESTION 3 3.1 Read the flow diagram below and answer the questions that follow 3.1.1 Complete the rule in 3.1.1 (1) 3.1.2 What an output value represented by 3.1.2? (2) 3.1.3 What is an input value represented by 3.1.3? (2) 7|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District 3.2 Read the graph of 𝑦 = −2𝑥 − 4 drawn below and answer the questions that follow. 3.2.1 On the same Cartesian plane above which is attached at the end of the (2) question paper. Take it off, attach it on your answer sheet and then draw the graph of 𝑦 = −2𝑥 + 4. Indicate the graph drawn. 3.2.2 What are the intercepts of the graph you have drawn? (2) 3.2.3 How are the gradients of the two graphs? Give a reason for your answer. (2) 8|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District 3.3 Study the straight line graphs drawn below and answer the questions that follow. 3.3.1 Write down the equation of graph AB. (1) 3.3.2 Write down the equation of graph CD. (1) [13] END GOOD LUCK - ENJOY THE FESTIVE SEASON. 9|Page

November 2023 Mathematics Grade 9 paper 1 O.R.T.I.District NAME:_________________________________ QUESTION 3.2 ANNEXURE 10 | P a g e