Mathematics Grade 10 P2 Gauteng June 2016 QP (Eng)

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION JUNE 2016 GRADE 10 MATHEMATICS (Paper 2) TIME: 60 minutes MARKS: 50 7 pages + 2 answer sheets P.T.O.

Downloaded from hlayiso.com MATHEMATICS Grade 10 2 (Paper 2) GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS (Second Paper) TIME: 60 minutes MARKS: 50 INSTRUCTIONS AND INFORMATION 1. Answer ALL the questions. 2. Clearly show ALL calculations, diagrams, graphs etc. that you have used in determining your answers. 3. Answers only will not necessarily be awarded full marks. 4. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 5. If necessary, answers should be rounded-off to TWO decimal places, unless stated otherwise. 6. Diagrams are NOT necessarily drawn scale. 7. Answer sheets for Questions 4 – 7 are located at the end of the question paper. Write your name in the spaces provided and submit them together with your ANSWER BOOK. 8. Number the answers according to the numbering system used in this question paper. 9. It is in your interest to write legibly and to present your work neatly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS Grade 10 3 (Paper 2) QUESTION 1 sin  1.1 If point P( x ; y) is a point on the Cartesian plane and OP = r units. Determine . cos  y P (x ; y) r O (3) 1.2 In PQR, Qˆ  90 and Rˆ   . PQ  5 units, QR  12 units and PR  13 units. P 13 5 Q R 12 Write down the values of: 1.2.1 sin  (1) 1.2.2 sec  (1) 1.2.3 tan  (1) [6] P.T.O.

Downloaded from hlayiso.com MATHEMATICS Grade 10 4 (Paper 2) QUESTION 2 If 4 tan  3 and cos  is positive, use a sketch to calculate the value of : 2.1 5 sin   3 cot  (5) 2.2 25 cos 2  (2) [7] QUESTION 3 3.1 If x  42 and y  68 , by using a calculator, determine the value of: 3.1.1 sin x  2 cos 3 y (2) 3.1.2 3 tan 2 ( x  y) (2) 3.2 Determine the value of  , if   0    90, correct to 3 decimal places. 3.2.1 2 sin   1,432 (2) 3.2.2 tan 3  6,345 (3) [9] P.T.O.

Downloaded from hlayiso.com MATHEMATICS Grade 10 5 (Paper 2) QUESTION 4 4.1 In the diagram below BDFE is a rectangle with BD = 155 m. AD = 475 m and BC = 800 m. The angle of elevation from B to C is 22. 155 m 475 m Calculate: 4.1.1 Â (2) 4.1.2 CF (3) 4.2 Without the use of a calculator, calculate the value of : sin 2 45  cos 60  tan 10. cot 10 (4) [9] P.T.O.

Downloaded from hlayiso.com MATHEMATICS Grade 10 6 (Paper 2) QUESTION 5 In the diagram, Qˆ  30, Rˆ 2  110 and PR  RS . Determine, with reasons, the sizes of the following angles: 5.1 P̂1 (2) 5.2 P̂2 (3) [5] QUESTION 6 In quadrilateral ABCD, AD//BC and Bˆ  Dˆ . Prove that ABCD is a parallelogram. (5) [5] P.T.O.

Downloaded from hlayiso.com MATHEMATICS Grade 10 7 (Paper 2) QUESTION 7 7.1 In the quadrilateral, diagonals, AC and BD bisect at O. If AC  4 x y; BC  x 2  y 2 and BD  2 x 2  2 y 2 , prove that ABCD is a rhombus. A B O D C (5) 7.2 PQRS is a parallelogram, SR = ST and P̂  120 . P S >> 1 2 1 2 Q >> T R If Sˆ 2  4 x , calculate the value of x . (4) [9] TOTAL: 50 END

Downloaded from hlayiso.com MATHEMATICS Grade 10 8 (Paper 2) ANSWER SHEET 1 NAME OF LEARNER: _________________ GRADE: _______ QUESTION 4 155 m 475 m QUESTION 5

Downloaded from hlayiso.com MATHEMATICS Grade 10 9 (Paper 2) ANSWER SHEET 2 NAME OF LEARNER: _________________ GRADE: _______ QUESTION 6 QUESTION 7 7.2 P S >> 1 2 1 2 Q >> T R