Gr9 MATH (ENG) June 2022 Question Paper_hlayiso.com_.pdf

Downloaded from hlayiso.com PROVINCIAL EXAMINATION JUNE 2022 GRADE 9 MATHEMATICS TIME: 1½ hours MARKS: 75 11 pages NAME OF LEARNER: GRADE: P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 GRADE 9 INSTRUCTIONS AND INFORMATION 1. This question paper consists of 7 questions. 2. Answer ALL questions. 3. A non-programmable calculator may be used, unless otherwise stated. 4. Clearly show all calculations, diagrams, and graphs that you have used in determining your answers. Answers only will not necessarily be awarded full marks. 5. If necessary, round-off your answers to 2 decimal places, unless otherwise stated. 6. Diagrams are not necessarily drawn to scale. 7. Answer QUESTION 1 in Section A by circling the letter next to the correct answer. 8. Answer QUESTIONS 2 to 7 in Section B in the spaces provided on this question paper. 9. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 GRADE 9 SECTION A QUESTION 1 Answer the following questions by choosing the correct answer. Circle the letter next to the correct answer. 1.1 Complete: (2𝑥 + 𝑦)0 A 2𝑥 + 𝑦 B 𝑥+𝑦 C 1 (1) D 0 1.2 Written below are two statements about a number pattern: • The first term of a sequence is 8. • The constant difference of the sequence is 2. Which of the following sequences agrees with the above statements? A 8; 6; 4; 2; … B 8; 4; 2; 1; … C 8; 16; 32; 64; … D 8; 10; 12; 14; … (1) 1.3 Given the expression: 𝑚3 + 3𝑚2 + 5𝑚 + 2, the coefficient of 𝑚 is … A 1 B 2 C 3 D 5 (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 GRADE 9 1.4 Determine the value of 3 − (−5 + 2) + 3. A 13 B 9 C 7 D 3 (1) 𝑡 1.5 For which value of 𝑡 is undefined? 2𝑡−2 A 1 B 2 C −1 D −2 (1) [5] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 GRADE 9 SECTION B QUESTION 2 2.1 The following table shows multiples and factors of 30, 75 and 100. Factors Number Multiples 1, 2, 3, 5, 6, 10, 15, 30 30 30, 60, 90, 120, 150, 180, 210, 240, 270, 300… 1, 3, 5, 15, 25, 75 75 75, 150, 225, 300, 375, 450, 525, 600, 675, 750… 1, 2, 4, 5, 10, 20, 25, 50, 100 100, 200, 300, 400, 500, 600, 700, 100 800, 900, 1 000 … 2.1.1 Write down the HCF of 30 and 75. (1) 2.1.2 Write down the LCM of 75 and 100. (1) 2.2 The 3 15 is between which two consecutive whole numbers? (2) 2.3 Is the 3 15 rational or irrational? (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 GRADE 9 2.4 Determine which ONE of the four tables given below represents direct proportion. Justify your answer. Table A Table B 𝒙 4 8 12 16 𝒙 30 50 100 120 2 2 𝒚 5 15 20 25 𝒚 6 4 2 1 3 3 Table C Table D 𝒙 3 5 8 12 𝒙 1 2 3 4 𝒚 12 20 32 48 𝒚 10 7 5 2 (3) 2.5 It takes Sandile 6 hours to fill 1 tank with water, working alone. Jacob needs 12 hours to fill the same tank with water, working alone. If Sandile and Jacob work together to fill the tank, how long would it take? Give your answer in hours. (4) [12] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 GRADE 9 QUESTION 3 3.1 Which type of numbers in the number system are defined by the following? “Numbers that extend the natural and whole number systems by including the operation 𝑎 − 𝑏, where 𝑎 < 𝑏. ” (1) 3.2 The following statements are incorrect. Write down the correct version of each statement. No. Incorrect Statement Correct Statement 3 3.2.1 √−64 = −8 3.2.2 −4 − (−6) = −10 3.2.3 √−9 = ±3 3.2.4 (−5)2 = −25 (4) 3.3 Calculate the following. 3.3.1 (5)(−2)2 − 15 ÷ 3 (3) 3.3.2 2 − (−4) − 2(1 − 4) 1−4 (3) [11] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 8 GRADE 9 QUESTION 4 4.1 The exponential form of 25 is written as 52. What does the exponent tell us? (1) 4.2 Represent the following statement in exponential form: “7 to the fifth power”. (1) 4.3 Rewrite the following expressions with positive exponents. Leave your answer in the simplest exponential form. 4.3.1 3𝑥 −2 (1) 4.3.2 2 5−2 (1) 4.4 Simplify the following fully: 4.4.1 (−5𝑤𝑧)2 (−2𝑤 2 𝑧) 50𝑤 −1 𝑧 (4) 4.4.2 81𝑥+1 . 52𝑥−2 34𝑥 . 25𝑥 (5) [13] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 9 GRADE 9 QUESTION 5 5.1 Examine the first three diagrams in the sequence of diagrams given below. 1st Diagram 2nd Diagram 3rd Diagram 5.1.1 Complete the table by determining the number of points of intersection in the next two diagrams. Position of diagram 1 2 3 4 5 Number of points of intersection 3 12 27 (2) 5.1.2 Describe the relationship between the position of the diagram and the number of points in each intersection in your own words. (2) 5.2 Numbers are arranged in the following pattern. If the pattern is extended, what will be the fifth number in the 100th row? Row 1 21 22 23 24 25 26 Row 2 27 28 29 30 31 32 Row 3 33 34 35 36 37 38 (3) [7] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 10 GRADE 9 QUESTION 6 6.1 What is an algebraic expression containing two terms called? (1) 6.2 What are 𝑥 and 𝑦 in the expression 2𝑦 4 − 3𝑥 2 𝑦 2 + 5𝑥 3 referred to as? (1) 6.3 Simplify the following fully: 6.3.1 √9𝑥 4 𝑦 2 (1) 6.3.2 (𝑥 + 5)(𝑥 − 3) (3) 6.3.3 25𝑧 2 − 9 5𝑧 + 3 (3) 6.4 Factorise fully: 6.4.1 3𝑥(𝑞 − 𝑟) − 2(𝑞 − 𝑟) (1) 6.4.2 2𝑥 3 − 10𝑥 2 − 28𝑥 (3) [13] P.T.O.

Downloaded from hlayiso.com QUESTION 7 7.1 Describe 3(𝑥 − 5) = 16, in words. (1) 7.2 Translate the following statement into a mathematical equation. The sum of half a number and 4 are doubled, thereafter decreased by 1 to give an answer of 13. (1) 7.3 Solve for 𝑥: 7.3.1 0,3𝑥 − 2,1 = 0,7 − 0,4𝑥 (2) 1 7.3.2 9𝑥+1 = 27 (3) 7.3.3 5𝑥 − 7 7𝑥 − 10 − =1 3 5 (3) 7.4 The square of a number added to twice the number equals three. Determine the possible values of the number. (4) [14] TOTAL: 75 END