Mathematics Grade 10 IEB November 2016 Question Paper

Downloaded from hlayiso.com ST PETER’S COLLEGE JULY EXAMINATIONS 2016 MATHEMATICS PAPER I: GRADE 10 Date: 18 July 2016 Time: 2 hours SESSION: 1 Marks: 100 Examiner: I. Havenga Moderators: S. Louw; M. Horwood; W. Sokana; S. Tudhope; N. Munilall Name of Student: _____________________________________________________ Name of Teacher: S. Louw M. Horwood W. Sokana S. Tudhope I. Havenga (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 1/2 2 1/2 3 3/4 3 4 Levels Actual Mark Possible 7 14 8 8 13 19 8 13 10 100 Mark Read the following instructions carefully: 1. This examination paper consists of 14 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. No loose sheets are allowed. 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 correct to TWO decimal places, where necessary. Grade 10 Mathematics Paper I – 18 July 2016 Page 1 of 15

Downloaded from hlayiso.com SECTION A – 50 Marks QUESTION 1 [7] 1.1 Classify the following numbers as rational, irrational or non-real: 3 1.1.1 √9 (1) 1.1.2 √9 (1) 1.1.3 √−9 (1) 1.2 ̅̅̅̅ as a common fraction. Express 0,15 (4) QUESTION 2 [14] Simplify: 2𝑥 2 −8 2.1 (𝑥 − 1)(𝑥 2 + 1)(𝑥 + 1) (3) 2.2 (3) 2−𝑥 Grade 10 Mathematics Paper I – 18 July 2016 Page 2 of 15

Downloaded from hlayiso.com 𝑥 2 −1 1 1 2.3 × 𝑥−1 − 2 (5) 20 n 1.4 n 3 2.4 (3) 16 n 1.5 n QUESTION 3 [8] 3.1 Solve the following equations: 3.1.1 𝑥(𝑥 − 4) = 0 (2) 3.1.2 (𝑥 − 4)(𝑥 + 5) = 10 (3) Grade 10 Mathematics Paper I – 18 July 2016 Page 3 of 15

Downloaded from hlayiso.com 3.1.3 125 y 2  252 y 1 (3) QUESTION 4 [8] Factorise the following expressions: 4.1 3𝑥 5 𝑦 4 − 9𝑥 2 𝑦 7 (2) 4.2 3 − 2𝑥 − 𝑥 2 (2) 4.3 𝑥𝑡 − 𝑦𝑡 + 𝑦𝑚 − 𝑥𝑚 (4) Grade 10 Mathematics Paper I – 18 July 2016 Page 4 of 15

Downloaded from hlayiso.com Grade 10 Mathematics Paper I – 18 July 2016 Page 5 of 15

Downloaded from hlayiso.com QUESTION 5 [13] 2 The diagram below shows f ( x)   6 and g ( x)  8x . x 5.1 Determine the coordinates of A, the 𝑥-intercept of f. (2) Grade 10 Mathematics Paper I – 18 July 2016 Page 6 of 15

Downloaded from hlayiso.com 5.2 Write down the equations of the asymptotes of f. (2) 5.3 Give the domain of f. (2) 5.4 For which values of 𝑥 is f increasing? (1) 5.5 Determine the coordinates of B and C, the points of intersection of f and g. (6) Grade 10 Mathematics Paper I – 18 July 2016 Page 7 of 15

Downloaded from hlayiso.com SECTION B – 50 Marks QUESTION 6 [19] Consider the functions of 𝑓, 𝑔 and ℎ below: Given: 𝑔(𝑥) = 𝑥 − 3 6.1 Determine the equation of 𝑓. (3) Grade 10 Mathematics Paper I – 18 July 2016 Page 8 of 15

Downloaded from hlayiso.com 6.2 Determine the co-ordinates of 𝐵. (1) 6.3 Determine the equation of ℎ. (3) 6.4 Determine the length of 𝑅𝑆 if 𝑂𝑇 = 1. (4) Grade 10 Mathematics Paper I – 18 July 2016 Page 9 of 15

Downloaded from hlayiso.com 6.5 If the equation of 𝑓(𝑥) = −2𝑥 2 + 18, determine the co-ordinates of 𝑊. (6) 6.6 Give the range of 𝑓(𝑥). (2) Grade 10 Mathematics Paper I – 18 July 2016 Page 10 of 15

Downloaded from hlayiso.com QUESTION 7 [8] 7.1 Factorise the expression 𝟑𝒙𝟐 − 𝒙 − 𝟐 . (2) 7.2 Study the factorised versions of these expressions: 6𝑥 2 − 𝑥 − 5 = (6𝑥 + 5)(𝑥 − 1) 8𝑥 2 − 𝑥 − 7 = (8𝑥 + 7)(𝑥 − 1) 100𝑥 2 − 𝑥 − 99 = (100𝑥 + 99)(𝑥 − 1) Now factorise the expression: 𝟐𝟎𝟏𝟎𝒙𝟐 − 𝒙 − 𝟐𝟎𝟎𝟗. (2) 7.3 Hence, factorise the expression: 𝒌𝒙𝟐 − 𝒙 − (𝒌 − 𝟏). (4) Grade 10 Mathematics Paper I – 18 July 2016 Page 11 of 15

Downloaded from hlayiso.com (2) QUESTION 8 [13] Solve for 𝑥: 8.1 2𝑥+1 + 2𝑥 = 12 (4) 𝟑𝒙 𝟓𝒙 𝟏 8.2 ≤ −𝟑 (4) 𝟓 𝟒 𝟒 8.3 𝑚(𝑥 − 𝑚) = 𝑛(𝑥 − 𝑛) (5) Grade 10 Mathematics Paper I – 18 July 2016 Page 12 of 15

Downloaded from hlayiso.com QUESTION 9 [10] Simphiwe, a student at St Peter’s College, has decided to sell doughnuts as part of the Grade 10 fundraising. She bought ingredients for which she had to pay R40. The cost of making the doughnuts amounted to R2 each. Simphiwe intends to sell the doughnuts at R4 each. She writes out the following equations for expenses and income: Expense amount: 𝑦 = 2𝑥 + 40 Income amount: 𝑦 = 4𝑥 y Expen ses Amount (R) Income x 0 Number of doughnuts (x) Calculate: 9.1.1 How many doughnuts must Simphiwe sell before her income exceeds her expenses? (4) Grade 10 Mathematics Paper I – 18 July 2016 Page 13 of 15

Downloaded from hlayiso.com 9.1.2 Her profit after selling 30 doughnuts. (2) 9.2 Sketched is 𝑦 = 𝑓(𝑥) and 𝑃(𝑐; 𝑑). y f P(c ; d) x Give the co-ordinates of P in terms of c and d if: 9.2.1 𝑦 = 𝑓(𝑥) + 2 (2) Grade 10 Mathematics Paper I – 18 July 2016 Page 14 of 15

Downloaded from hlayiso.com 9.2.2 𝑦 = 2𝑓(𝑥) (2) Grade 10 Mathematics Paper I – 18 July 2016 Page 15 of 15