Mathematics Grade 10 IEB Paper 1 June 2012 Question Paper

Downloaded from hlayiso.com TEACHERS WITHOUT BORDERS PROGRAMME BROUGHT TO YOU BY With grateful thanks to our associate partners, The National Department of Basic Education, The Independent Examinations Board, Siyavula Education, Smarticks, Noteshare, Lemonlicious, datacentrix, and most of all, to the schools and teachers from both the public and private education sectors who as founder contributors, have lent content to the Teachers without Borders programme, for the benefit of all South Africa's learners. In Bill Gates words, at the Mandela Day ‘Living Together’ address: “Maintaining the quality of this country’s higher education system while expanding access to more students will not be easy. But it’s critical to South Africa’s future” – working together, we can help achieve this." Contributing schools to date: Clifton School Milnerton High Rustenburg Girls’ High St Peter's Durban Girls' Northwood High St Anne's DC St Stithians Fairmont High Roedean St John's DSG Wynberg Boys' High Herzlia High Rondebosch Boys’ St Mary's DSG Kloof Wynberg Secondary

Downloaded from hlayiso.com Grade 10 Mathematics July Examination Paper 1 Time: 2 hours Total: 100 Date: 24 July 2012 Session: 1 Name: Maths Teacher: A ; Question 1 2 3 4 5 7 8 TOTAL LO’s 1 1 1 1 2 1 | 2 | 2 Cog Level 42 | 1:2 | 233 | 2:3 | 233 | 3:4 | 1253 | 23,4 | Score | Mark 15 | 10 | 22] 11 | 9 11 9 2B 100 | INSTRUCTIONS: e This test consists of thirteen pages and eight questions. Work neatly and show all calculations. Unless stated, give answers to TWO decimal places. Only non-programmable, non-graphical calculators are permitted. BROUGHT To YOU BY Th - Page 1 w | | @ s Uj datacentrix ¥ education a

Downloaded from hlayiso.com SECTION A QUESTION 1 1.1. Consider the following list of numbers, and then answer the questions that follow: 2; v-27 ; V2; V8; 3,4 ;-2; -14 1.1.1 Write down any non-real number in the list. (1) 1.1.2 Between which two rational numbers does the irrational number lie? Show all relevant working in order to obtain full marks, (3) 1.1.3 Convert the recurring decimal to a rational fraction in the form a b+#0. (4) Page 2 «a ‘TL “ w | | pas bs UY datacentrix ¥ education

Downloaded from hlayiso.com 1.1.4 Add the two real numbers closest to each other, but NOT EQUAL to each other. (2} 1.2. Aset of numbers is represented on the number line below: oO bi 3 -2 -Ilo@ i 2 3 4 1.2.1 Use inequalities to describe the set of numbers. (2) 1.2.2 What is the smallest integer in this set of numbers? (1) 1.2.3. Express in interval notation. (2} [15] BROUGHT To YOU BY datacentrix. ¥ education Page 3

Downloaded from hlayiso.com QUESTION 2 Factorise the following fully: 21 3x3-—12x (2) 2.2 2x2-—5x-3 ; ; (2) 23 Sxy—3y+10x-6 (3) 24 8x2 —27y6 ; ; (3) [10] QUESTION 3 3.1 Simplify the following: Bx+7 x-2 3.11 T-T (4} BROUGHT TO YOU BY datacentrix, Page 4

Downloaded from hlayiso.com 3.2 Simplify without using a calculator, writing all answers with positive exponents. (10) (2x)? ax° (2x)7* 2x7 BROUGHT TO YOU BY Tu 7 i Page 5 if L dcisounitar ¥ education I

Downloaded from hlayiso.com 2.2" 2" +2" 2*+3" [22] QUESTION 4 Solve the following equations: 41 (x-7)-3(*-1)=3-x (2) | 42 (x-3)(x-2)=6 (4) Page 6 ¥ education

Downloaded from hlayiso.com 4.3 —5 <2x-—-3 <7. Illustrate your answer graphically. (5) (11) QUESTION 5 5.1 Express 3y + 2x = 12 instandard form (ie. y =me+c) (1) 5.2 Now determine the equation of a line parallel to the line in 5.1, but passing through (3 ; — 4). (2) BROUGHT TO YOU BY w | | @&® | igen | — | | ee Page 7 myewnse

Downloaded from hlayiso.com 5.3 Determine the equations of the lines (a), (b) and (c). (b) is parallel to the y-axis (6) ay (b) (c) (a) oN -—2;1) (3) BROUGHT TO YOU BY w | | Q& TL | Peneer | yo Page &

Downloaded from hlayiso.com SECTION B UESTION 6 - _ ott et 2st _ +2 Given: P= [a and Q= oar a 6.1 Simplify P (7) 6.2 Simplify Q (3) i | | | | | 6.3 Write a mathematical expression (equation) to show the relationship between P and Q. (1) [11] BROUGHT TO YOU BY Tu “ i Page 9 w | | & sa L} datacenttit ¥ education ig

Downloaded from hlayiso.com QUESTION 7 7.2 Rafael Nadal plots the bounce of a tennis ball on a graph. He calculates that the formula he needs to use is: H = —2t? + 12¢, where H is the height of the ball above the ground (in metres) and f is the time elapsed { in seconds ). y Height (m) 0 6 * Time (s) 7.1.1 How long will it take the ball to reach its maximum height ? (1) 7.1.2 What is the maximum height of the ball ? (2) BROUGHT TO YOU BY w@ IT 5 .; w | | a My datacentiix yo Page 10 = cD

Downloaded from hlayiso.com 7.1.3 At what time(s) will the ball be 16m above the ground ? (3) 7.2. The graph of f(x) = —3* +3 is drawn below: K B a asymptote of f. 7.2.1. Write down the equation of the asymptote of f. (1) 7.2.2. Determine the co-ordinates of A. (1) 7.2.3. Determine the co-ordinates of B. (1) i (9] BROUGHT To YOU BY w | | & IT iinet Poe Page 11 Siem aan Eee

Downloaded from hlayiso.com QUESTION 8 Given: y fxjax°-9 ~<\D g(x) =mx +e f E (0; 6) N ~ “ A i] 8 . g 8.1 Find the values of m and c. (3) 8.2 Find the co-ordinates of D, a point of intersection between f and g. (4) BROUGHT TO YOU BY w | @&® IT L} datacentiix” ¥ education Page 12

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