Mathematics Grade 11 P2 Gauteng June 2017 Question Paper

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION JUNE 2017 GRADE 11 MATHEMATICS PAPER 2 TIME: 2 hours MARKS: 100 8 pages + 3 diagram sheets + 1 answer sheet P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 Paper 2 GRADE 11 GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS (Paper 2) Time: 2 hours Marks: 100 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of SIX questions. Answer ALL the questions. 2. Number your answers according to the numbering system that is used in the question paper. 3. Use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 4. Round-off the answer correctly to TWO decimal places, unless instructed otherwise. 5. Show ALL calculations, diagrams, graphs, etc. that were used in determining the answers. 6. Answers only will not necessarily be awarded maximum marks. 7. Diagrams are NOT necessarily drawn to scale. 8. Reasons MUST accompany statements made in QUESTIONS 4, 5 and 6. 9. Question 3.1 must be answered on the ANSWER SHEET provided on Page 9. Detach this page and insert it into your ANSWER BOOK. 10. It is in your interest to write legibly (in blue ink) and present all answers neatly and logically. 11. Use the diagram sheets on pages 10, 11 and 12 to assist you in answering Questions 4, 5 and 6 respectively. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 Paper 2 GRADE 11 QUESTION 1 [25] In the diagram below, points P (2; 4), R and M are the vertices of PMR. Line MR passes through the origin. The angle between lines PR and MR is θ and PR||MS. The equation of line MS is given as y – 5x + 14 = 0. y M (4 ; 6) P(2 ; 4) ● ● x O ● S ● R 1.1 Determine the equation of line MR. (3) 1.2 Calculate the equation of line PR. (4) 1.3 Calculate the size of θ, rounded-off to TWO decimal places. (5) 1.4 Show that the coordinates of point R can be given as (4; 6). (4) 1.5 Calculate the length of line MR, in simplified surd form. (2) 1.6 If the area of PMR = ½ PR.MR.sinθ, calculate the area of PMR. (5) 1.7 Write down the coordinates of point S, given that PMSR is a parallelogram. (2) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 Paper 2 GRADE 11 QUESTION 2 [26] 7 2.1 If cos    , and   (180° ; 360°) calculate the value of 25 14 tan θ, with the aid of a diagram and WITHOUT the use of a calculator. (4) 2.2 Simplify WITHOUT the use of a calculator: cos(90  x). sin(180   x) . tan 225   cos2 ( x) (6) 2.3 Determine the general solution of 2 cos 2θ = –0,44. (6) 2.4 Prove that tan   sin   tan  . 1  cos (5) 2.5 If α + β = 90°, determine WITHOUT the use of a calculator cos700  sin   . sin 70 sin( 90   ) (5) QUESTION 3 [14] Given f(x) = 2 cos x + 1 and g(x) = 1 – sin x 3.1 Use the ANSWER SHEET provided on Page 9, and sketch the graphs of f and g for the interval x [90 ; 360] . (6) 3.2 Write down the amplitude of f. (2) 3.3 Determine the values of for which f(x) – g(x) = 0. (6) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 Paper 2 GRADE 11 STATEMENTS AND REASONS ARE REQUIRED WHEN ANSWERING QUESTIONS 4, 5 AND 6. QUESTION 4 [13] 4.1 Using the diagram below, prove that the line drawn perpendicular from the centre of a circle to a chord will bisect the chord. O ● 11 22 1 P Q 1 R p Q Q (5) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 Paper 2 GRADE 11 4.2 In the diagram below, BD is the diameter of the circle with centre O. AB = AC, Ô1  40 , CD = 40 mm and AB = 15 mm. D O 2 1 1 2 C A B E Calculate 4.2.1 B̂. (2) 4.2.2 D̂. (2) 4.2.3 the length of line AE. (4) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 Paper 2 GRADE 11 QUESTION 5 [10] Points J, K, L, M and N are on the circumference of the circle drawn below. JK = KL and JN = MN. JL, JM and KN are straight lines. Ĵ1  x and Ĵ 3  y . K 1 2 1 Q J 1 2 3 2 4 3 L 4 3 1 P 2 M 1 2 N 5.1 Write down TWO other angles, equal to x. (3) 5.2 Prove that Q̂2  P̂2 . (4) 5.3 Prove that JQ = JP. (3) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 8 Paper 2 GRADE 11 QUESTION 6 [12] Two circles of different radii are drawn such that they intersect at points K and T respectively. Point P is the centre of the smaller circle and is also a point on the circumference of the larger circle. Line CP is produced to point A. C 1 K 2 T 1 2 1 2 4 3 P A Prove that 6.1 K̂ 2  Ĉ (3) 6.2 K̂1  2T̂2 (4) 6.3 P̂4  2Ĉ  K̂1 (5) TOTAL: 100 END

Downloaded from hlayiso.com MATHEMATICS 9 Paper 2 GRADE 11 QUESTION 4.1 O ● 11 22 1 P Q 1 R p Q Q QUESTION 4.2 D O 2 1 1 2 C B A E

Downloaded from hlayiso.com MATHEMATICS 10 Paper 2 GRADE 11 QUESTION 5 K 1 2 1 Q J 1 2 3 2 4 3 L 4 3 1 P 2 M 1 2 N

Downloaded from hlayiso.com MATHEMATICS 11 Paper 2 GRADE 11 QUESTION 6 C 1 K 2 1 T 2 1 2 4 3 P A

Downloaded from hlayiso.com MATHEMATICS 12 Paper 2 GRADE 11 ANSWER SHEET Name:__________________________________________________ Grade: 11 __ Please detach this page and insert into your ANSWER BOOK. QUESTION 3.1