DEPARTMENT OF MATHEMATICS

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1 Wynberg Boys High School DEPARTMENT OF MATHEMATICS Name: Teacher: Class: PAPER 2 GRADE 9 MATHEMATICS JUNE 2017 MARKS: 75 TIME: hours EXAMINER: Mr Biggs This examination booklet consists of 12 pages. Answer all questions in this booklet. BG Turn over only when given permission to do so.

2 Gr 9 Mathematics 2 of 12 WBHS/June 2017 Instructions and Information Read the following instructions carefully before answering the questions. 1. This examination booklet consists of 7 questions over 12 pages. All questions must be answered in this examination booklet. If extra paper is used, staple it to the back of this booklet and clearly indicate that you have used it. 2. Clearly show ALL working, constructions, or diagrams which you have used in determining the answers. Answers only will not necessarily be awarded marks. 3. You may use an approved scientific calculator (non-programmable and nongraphical), unless stated otherwise. 4. If necessary, round off answers to TWO decimal places. 5. Diagrams are NOT necessarily drawn to scale. 6. Write neatly and legibly in black or blue ink. Diagrams must be drawn in pencil.

3 Gr 9 Mathematics 3 of 12 WBHS/June 2017 QUESTION 1 Complete the following statements by filling in the missing words. Write your answers in the answer boxes provided. 1.1 Co-interior angles are when inside parallel lines. (1) 1.2 The theorem of Pythagoras states that, in a right-angled triangle, (2) 1.3 The reason given when two angles are equal in an isosceles triangle is (1) 1.4 The exterior angle of a triangle is equal to the sum of (1) 1.5 The complement of 57 is (1) [6]

4 Gr 9 Mathematics 4 of 12 WBHS/June 2017 QUESTION 2 In the diagram below, it is given that A DF = 46, BC = DC, FG HI, and DE BC. G B b I A D f c a d C e E F H Find, in alphabetical order, the values of a through to f. Give a reason for each step. (12) [12]

5 Gr 9 Mathematics 5 of 12 WBHS/June 2017 QUESTION 3 In this question, you must show all construction lines, and label all diagrams fully. 3.1 Construct triangle JKL with JK = 33 mm, KL = 56 mm and JL = 65 mm. (5) 3.2 Using a protractor, measure angle K in 3.1 and label the angle on the diagram above. (1)

6 Gr 9 Mathematics 6 of 12 WBHS/June Using only a compass and ruler, construct the perpendicular bisector of the line segment YZ shown below: (3) Y Z 3.4 Without using a protractor, bisect the angle F GH below. F G H (3) [12]

7 Gr 9 Mathematics 7 of 12 WBHS/June 2017 QUESTION 4 In each of the following questions, determine the value of the unknown variable. Remember to give reasons where necessary. 4.1 In the diagram below, it is given that HI JK. Solve for y. H 3y 15 I J y K (3) 4.2 In the diagram below, QR TS. Solve for x. Q T x 3x 26 2x + 50 P R S (5) [8]

8 Gr 9 Mathematics 8 of 12 WBHS/June 2017 QUESTION In quadrilateral PQSR shown below, PQ RS and PR QS. P Q R Using congruency, prove that PQ = RS and PR = QS. (5) S 5.2 In the diagram below, AB = AC and BDC = BEC. A D F E B C Prove that BDC CEB. (4) Hence prove that BD = EC. (1)

9 Gr 9 Mathematics 9 of 12 WBHS/June In the diagram below, right-angled TUV has altitude UV, and UWV has altitude WX. U X T W V Prove that UT WX. (1) Hence or otherwise, prove that TUV UXW. (6) [17]

10 Gr 9 Mathematics 10 of 12 WBHS/June 2017 QUESTION In MNP below, MN = 53 cm, QM = 28 cm, and QN is an altitude of the triangle. N 53 cm R M 28 cm Q P Determine the length of NQ. (3) If RN is four times the length of QR, find the length of QR. (2) Determine the length of MR. Round your answer off to two decimal places if necessary. (3)

11 Gr 9 Mathematics 11 of 12 WBHS/June In quadrilateral RBYN, RB NY, RT RB and TB BY. R 36 cm B 26 cm N 10 cm T 50 cm Y Give, with a reason, the magnitude of angle N TR. (1) Determine the length of BY. Round your final answer off to two decimal places. (6) [15]

12 Gr 9 Mathematics 12 of 12 WBHS/June 2017 QUESTION 7 In the diagram below, ST = PT, SL NT, and NS ST. S N P L T You have been asked to prove that SP bisects the angle N SL by completing the partial proof given below. Fill in all missing steps, indicated by the dotted lines. (5) To prove: SP bisects N SL Let SPT = x PST = x SLP = PSL = NSP = NSP = PSL SP bisects NSL ( ) (Given) ( ) (Given NS ST) [5] TOTAL: 75 Supera Moras

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