Mathematics Grade 10 IEB Paper 1 November 2015 Question Paper

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Downloaded from hlayiso.com NOVEMBER EXAMINATIONS 2015 MATHEMATICS PAPER 1: GRADE 10 Examiner: Marks: 100 Moderators: Time: 2 hours SESSION: 1 Date: 13 November 2015 Name of Learner: __________________________________ Grade: ___________ Name of Teacher: (Please circle) For Examiner’s use only: SECTION A SECTION B Question 1 2 3 4 5 6 7 8 9 Total Cognitive 1/2 1/2 2 2 2 2 3 3/4 3/4 Levels Actual Mark Possible 9 8 8 9 6 13 20 17 10 100 Mark Marker’s Signature Read the following instructions carefully: 1. This examination paper consists of 13 pages and 9 questions. Please check that your paper is complete. 2. Read the questions carefully. Take note of the mark allocation and the wording of the questions. 3. Answer ALL the questions on the question paper in the spaces provided. 4. Only non-programmable, non-graphical calculators are permitted. 5. ALL CALCULATIONS AND WORKING DETAILS MUST BE SHOWN. 6. It is in your own interest to write legibly and to present your work neatly. 7. Unless otherwise stated, round off to ONE decimal place, where necessary. 8. Note that the diagrams and sketches are NOT drawn to scale. Grade 10 Mathematics Paper 1 – November 2015 Page 1 of 13

Downloaded from hlayiso.com SECTION A QUESTION ONE: [9 marks] Simplify the following fully: 1.1 (2𝑎 − 1)(𝑎 − 3) (2) 1.2 1 3 (2) − 𝑥−1 𝑥+1 1.3 52𝑥−1 . 25𝑥+1 . 5 (3) 252𝑥 1.4 3𝑥 + 3𝑥+2 (2) 3𝑥−1 Grade 10 Mathematics Paper 1 – November 2015 Page 2 of 13

Downloaded from hlayiso.com QUESTION TWO: [8 marks] Factorise the following fully. 2.1 𝑚2 − 2𝑚 + 1 (2) 2.2 3𝑥 2 − 3 (2) 2.3 𝑎𝑥 2 − 𝑥 2 − 4𝑎𝑦 2 + 4𝑦 2 (2) 2.4 Express this number line in interval notation: (2) QUESTION THREE: [8 marks] Grade 10 Mathematics Paper 1 – November 2015 Page 3 of 13

Downloaded from hlayiso.com 3.1 Solve these equations for 𝑥: 3.1.1 𝑥 13 = 8 (2) 3.1.2 2𝑥 − 3 2𝑥 (3) − 3𝑥 = 3 6 3.2 Solve for 𝑥 and 𝑦: 𝑥 + 2𝑦 = 1 and 2𝑥 + 3𝑦 = 6 (3) QUESTION FOUR: [9 marks] 4.1 On the set of axes below sketch the graphs of 𝑓 and 𝑔 where: Grade 10 Mathematics Paper 1 – November 2015 Page 4 of 13

Downloaded from hlayiso.com 𝑓(𝑥) = 𝑥 2 − 9 and 𝑔(𝑥) = 3𝑥 − 9 (5) Show all intercepts with the axes clearly. 4.2 Write down the range of 𝑓. (1) 4.3 For what values of 𝑥 is 𝑓(𝑥) > 𝑔(𝑥)? (2) 4.4 If 𝑓 is moved up 5 units, what is the equation of the new function? (1) QUESTION FIVE: [6 marks] 5.1 Harry buys a fridge from Nakro which is priced at R12 700. He takes out a loan with PNB Bank for the full amount. The interest on the loan is 12,3% per annum, simple interest, Grade 10 Mathematics Paper 1 – November 2015 Page 5 of 13

Downloaded from hlayiso.com and he pays off the loan over three years. How much are his monthly repayments, correct to the nearest cent? (3) 5.2 Louis invested a sum of money in November 2010. In November 2015 the amount in the account was R 162 108. If the interest was 6,2% per annum, compounded annually, how much, accurate to the nearest rand, did Louis invest in November 2010? (3) QUESTION SIX: [13 marks] Simplify all fractions fully. 6.1 There are six red tokens and four yellow tokens in a bag. 6.1.1 One token is chosen. What is the probability that a red token is chosen? (1) Grade 10 Mathematics Paper 1 – November 2015 Page 6 of 13

Downloaded from hlayiso.com 6.1.2 Two tokens are removed, one after the other, without replacement. What is the probability that they are both red? (Space for a tree diagram has been provided) (2) 6.1.3 Two tokens are removed, one after the other, with replacement. What is the probability that they are different colours? (Space for a tree diagram has been provided) (3) 6.2 Among a group of 20 boys, 11 play rugby, 8 play hockey and 3 play both sports. 6.2.1 Complete the Venn Diagram to represent the above information, and use the diagram to find the number of boys who play neither sport. (4) Grade 10 Mathematics Paper 1 – November 2015 Page 7 of 13

Downloaded from hlayiso.com 6.2.2 A boy is chosen at random. What is the probability that he plays hockey? (1) 6.2.3 A boy is chosen at random. What is the probability that he plays hockey, but not rugby? (2) SECTION B QUESTION SEVEN: [20 marks] 7.1 Solve for 𝑥 ∶ 𝑎𝑥 − 𝑏 = 𝑥 (3) Grade 10 Mathematics Paper 1 – November 2015 Page 8 of 13

Downloaded from hlayiso.com 7.2 Solve for 𝑥: 5𝑥 2 + 3 = 8𝑥 (4) 1 7.3 Simplify this expression fully : 𝑝−1 −𝑡 −1 (3) 7.4 𝑦2 13𝑦 (3) Factorise this expression fully: − 2 + 18 2 7.5 Simplify as far as possible: (4) 1 2𝑥 1 + 2 + 𝑥+1 𝑥 −1 1−𝑥 Grade 10 Mathematics Paper 1 – November 2015 Page 9 of 13

Downloaded from hlayiso.com 2 7.6 Solve for 𝑥 : 2. 9𝑥 = 81 (3) QUESTION EIGHT: [17 marks] Grade 10 Mathematics Paper 1 – November 2015 Page 10 of 13

Downloaded from hlayiso.com 8.1 In the diagram there are two functions: 𝑎 𝑝(𝑥) = 𝑥 + 𝑏 and 𝑞(𝑥) = 𝑚. 2𝑥 + 𝑡 𝑝 and 𝑞 have the same horizontal asymptote and meet at 𝐴(2; −1) 𝑞 crosses the 𝑦-axis at 𝑆. 8.1.1 Write down the range of 𝑝. (1) 8.1.2 Write down the range of 𝑞. (1) 8.1.3 Find the values of 𝑎 and 𝑏. (3) 8.1.4 Find the values of 𝑚 and 𝑡. (4) 8.2 In the diagram two functions are shown: 𝑓(𝑥) = 16 − 𝑥 2 and 𝑔(𝑥) = 𝑥 + 4. Grade 10 Mathematics Paper 1 – November 2015 Page 11 of 13

Downloaded from hlayiso.com The lines 𝐸𝐴𝐵 and 𝐶𝐷 are perpendicular to the 𝑥-axis. 8.2.1 If 𝑂𝐸 is 2 units, calculate the lengths of 𝐴𝐸 and 𝐵𝐸, and hence find 𝐴𝐵. (4) 8.2.2 If 𝐶𝐷 is 7 units, calculate the length of 𝑂𝐶. (4) QUESTION NINE: [10 marks] Grade 10 Mathematics Paper 1 – November 2015 Page 12 of 13

Downloaded from hlayiso.com 9.1 Solve this inequality for 𝑥 and show the solution on a number line: (4) −1 < 2 − 3𝑥 ≤ 8, 𝑥∈ℝ 9.2 What is the 2015th letter in this pattern? MATHMATHMATHMATHMA………… (2) Show your working clearly. 9.3 Nial and Liam each deposited the same sum of money into accounts at One Direction (4) Bank in January 2010. The deposits earn the same simple interest paid annually. After four years, in January 2014, Nial has R1980 and after seven years, in January 2017, Liam has R2340. What was the initial deposit that both made, and what rate of simple interest did they earn TOTAL 100 MARKS Grade 10 Mathematics Paper 1 – November 2015 Page 13 of 13 Powered by TCPDF (www.tcpdf.org)