Mathematics Grade 10 P2 Gauteng June 2019 QP (Eng)

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION JUNE 2019 GRADE 10 MATHEMATICS PAPER 2 TIME: 1 hour MARKS: 50 6 pages and 1 answer sheet P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 GRADE 10 (Paper 2) GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS (Paper 2) TIME: 1 hour MARKS: 50 INSTRUCTIONS 1. This question paper consists of SIX questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs etc. which were used in determining the answers. 4. Answers only will not necessarily be awarded full marks. 5. An approved scientific calculator (non-programmable and non-graphical) may be used unless stated otherwise. 6. Where necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Number your answers according to the numbering system used in this question paper. 9. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 GRADE 10 (Paper 2) QUESTION 1 1.1 A right-angled triangle ABC with sides and and an anlge is drawn below. Write down the ratio of the following in terms of and 1.1.1 cos  (1) 1.1.2 sin(90 ) (1) 1.2 Make use of the diagram below to answer the questions without the use of a calculator. 1 2 1.2.1 Determine the value of sin  . (2) 4 1.2.2 Show that sec2   1 tan 2  . (3) [7] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 GRADE 10 (Paper 2) QUESTION 2 2.1 Use your calculator to determine the value of the following correct to 2 decimal places: 3 1 sec 40  tan 50   cos 62 (1) sin 28 4 2 2.2 Solve for  , correct to 1 decimal place: cos(2 10)  0, 091 and   0 ;90 (2) 2 2.3 Without the use of a calculator, determine the value of: 1 2sin 2 60  sin 45 . sec 45  tan10 . cot10 (4) 4 [7] QUESTION 3 3.1 ON THE ANSWER SHEET sketch the graphs of f ( x)  sin x  2 and g ( x)  2cos x on the same set of axes for 0 x  360 . The intercepts on both axes and the turning points should be clearly indicated. (4) 3.2 Use the sketch graphs to answer the following questions: 3.2.1 Write down the range of g . (1) 3.2.2 For which value(s) of will decrease? (2) [7] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 GRADE 10 (Paper 2) QUESTION 4 The points R(2 ; 5); U(  2 ; 1) and S(2 ;  3) are given. 4.1 Determine the midpoint of RS. (2) 4.2 Find the coordinate of point T, so that RUST forms a parallelogram. (3) 4.3 Calculate the length of RU. Leave your answer in surd form. (2) 4.4 Given that RU||SP and SP = 2RU. Find the coordinates of point P so that RUSP forms a trapezium. (8) [15] QUESTION 5 5.1 Complete the statement : If the opposite angles of a quadrilateral are equal then the quadrilateral is … (1) 5.2 In the diagram below, ABCD is a quadrilateral. E is a point on AD so that AE = AB and EC = CD. BEC = 90°. AD || BC. Let D = 2x and B1 = x. 5.2.1 Determine the value of . (4) 5.2.2 Prove that ABCD is a parallelogram. (4) [9] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 GRADE 10 (Paper 2) QUESTION 6 In the quadrilateral given, diagonals AC and BD bisect at O. If AC  4 xy, BC  x2  y 2 and BD  2 x2  2 y 2 , prove that ABCD is a rhombus. (5) [5] TOTAL: 50 P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 GRADE 10 (Paper 2) ANSWER SHEET NAME AND SURNAME: _________________________________________________ QUESTION 3 𝑦 𝑥 0 QUESTION 5 QUESTION 6 END