Mathematics Grade 10 IEB Paper 2 June 2012 Question Paper

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BROUGHT TO YOU BY | ieee | ¥ education JULY EXAMINATIONS 2012 MATHEMATICS PAPER If: GRADE 10 Marks: 100 Time: 2 hours SESSION: 1 Date: 31 July 2012 Name of Learner: Grade: Name of Teacher: (Please circle) For Examiner’s use only: SECTION A SECTION B Question 3 4 9 10 Learning Outcomes Lo3 Cognitive Levels Actual Mark Possible Mark Read the following instructions carefully: 1. This examination paper consists of 15 pages and 12 questions. Please check that your paper is complete. Read the questions carefully. Take note of the mark allocation and the wording of the questions. Answer ALL the questions on the question paper in the spaces provided. Only non-programmable, non-graphical calculators are permitted. ALL CALCULATIONS AND WORKING DETAILS MUST BE SHOWN. It is in your own interest to write legibly and to present your work neatly. Unless otherwise stated, round off correct to TWO decimal places, where necessary. Note that all diagrams and sketches are NOT drawn to scale. somninaend Grade 10 Mathematics Paper II — July 2012 Page 1 of 15

Downloaded om niayiso.com Formulae you may need for this examination: - + + d= Vy, -x,) +Qr -»y m= 227% (= 5 th ) xX SECTION A QUESTION ONE: [9 marks] 1.1 fA =112,4°, B = 48,6° and C = 12,1°; calculate the following, correct to two decimal places: sinA 111 — 2 1.1.2 cos(A— B) 1.1.3 3 cot3C 1.1.4 cosec (5%) | 1.2. Solve for the unknown angle in the equation below: 3 cosB = 2,1 (2) Sa eae ee ree = == Grade 10 Mathematics Paper Il —July 2012 Page 2 of 15 ry az ry education

2.1 UESTION TWO: No calculator is allowed for this question. If 17cosB + 15 = 0 and sinB < 0, determine, with the aid of a diagram, the value of the following expressions: 2.11 tan?B+1 2.1.2 2cosB + ; sing [15 marks] 2.2 In which quadrant does 6 lie if 0° < 9 < 360° and 2.2.1 cos6 <0 & sin8 <0? 2.2.2 sind >O & tand<0? Grade 10 Mathematics Paper Il —July 2012 Page 30f 15

; Downloaded from hlayiso.com 2.3. Cis the foot of a vertical tower DC. From a point P, 28m from C, the angle from P going up to Dis 46° (Le. DPC). 2.3.1. Draw a sketch of the above scenario. (2) 2.3.2 Determine the height of the tower. (3) Grade 10 Mathematics Paper Il - July 2012 Page 4 of 15

QUESTION THREE: AABC has co-ordinates A(—4; 2), B(1; 2) and C(—1; 6), and AC = 5 units. [17 marks] 3.1 Determine the lengths of AB and BC. Leave your answers in surd form. (4) 3.2. What kind of triangle is AABC? Give a reason for your answer. Grade 10 Mathematics Paper II — July 2012 Page 5 of 15

Downloaded from hlayiso.com 3.3 Determine the co-ordinates of M, the mid-point of AC. 3.4 If Dis the point (x; y), such that Es; 7) is the midpoint of CD, determine the co-ordinates of D. 3.5 Determine the gradients of the line segments AC, AB, BD and CD. 3.6 What type of quadrilateral is ABDC? Give a reason for your answer. Grade 10 Mathematics Paper II — July 2012 Page 6 of 15

Downloaded from hlayiso.com QUESTION FOUR: Carefully study the diagram below. Calculate the value of x, y and z (in alphabetical order), with reasons. \ / [3 marks] Statement suaug, GtAdE 10 Mathematics Paper I! — July 2012 Page 7 of 15

Downloaded from hla QUESTION FIVE: Refer to the figure above and prove AABC /// ADBA. [7 marks] Statement Reason Calculate AB if BC = 15cm and DC = &cm. Round off your answer to 1 decimal place. * Grade 10 Mathematics Paper II — July 2012 Page 8 of 15

Downloaded from hlayiso.com___ QUESTION SIX: [4 marks] Determine whether A(—2; 3), B(1; 4) and C(—4; 1) are collinear. “['m thinking of a number between (3x2)+6 and (7x9)+(8x2).” iw fae go Grade 10 Mathematics Paper Il — July 2012 Page 9 of 15

Downloaded from hlayiso.com SECTION B QUESTION SEVEN: [6 marks] Solve for the unknown angles in the equations below: cotot+s =5 2 7.1 (3) o (2 — age) = 72 3sin(2—40°)=2 (3) QUESTION EIGHT: [8 marks] Calculate a in each of the following cases: 8.1 The distance between (2; 3) and (6; a) is 5 units. {5) : Grade 10 Mathematics Paper |i —July 2012 Page 10 of 15

Downloaded from hlayiso.com 8.2 PQ hasa gradient of —2 where P(2; a) and Q(3;—6). QUESTION NINE: [8 marks] Given: AD = 90° , AC_L BD, B = 70° and AB = 40mm. Calculate the length of CD. Continue your answer on the next page ... Grade 10 Mathematics Paper Il —July 2012 Page 11 of 15

Downloaded from hlayiso.com [12 marks] QUESTION TEN: i E /48,3° F In the diagram it is U given that: DC//AB; ; AE = 64,8 m; AB = 98,4 m and EFBR is a square 28,2" C1 ia A R B Determine the following: 10.1 Length RB. rol sy Grade 10 Mathematics Paper II — July 2012 Page 12 of 15

10.2 Length CB. _Downloaded from hlayiso.com 104 DCA . Grade 10 Mathematics Paper I] — July 2012 Page 13 of 15

Downloaded from hlayiso.com QUESTION ELEVEN: [4 marks] A farmer wants to install new water pipes leading from the farm dam to the farmhouse (A to B) as well as to the two apple orchards (A to C and A to D). What is the minimum number of metres of piping he has to buy? Round off your answer to the nearest whole number. Grade 10 Mathematics Paper || —July 2012 Page 14 of 15 my ae ax tf duction

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