Mathematics Grade 11 P2 North West June 2019 Question Paper

Downloaded from hlayiso.com GRADE 11 MATHEMATICS MID-YEAR EXAMINATION PAPER 2 JUNE 2019 MARKS: 100 JUNE EXAMINATION 2012 TIME: 2 hours This question paper consists of 9 pages and 4 diagram sheets. Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 7 questions. 2. AnswerALL the questions. 3. Number the answers correctly according to the numbering system used in this question paper 4. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in determining your answers. 5. Answers only will not necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. 7. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. Write neatly and legibly. Demo 2 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 QUESTION 1 A  3; 4  , B  1;1 and C  a ;  2  are three points in the Cartesian plane. Determine 1.1 the gradient of AB (2) 1.2 the value of a if  0;1 is the midpoint of AC (2) [4] QUESTION 2 The points P  2;3 , Q  m ; n  ; R  4;  5  and S are the vertices of quadrilateral PQRS. The angle between PQ and the positive direction of the x  axis is 45. RT is parallel to the x  axis. y P  2;3 S 45 x Q m; n R  4;  5  T 2.1 Determine the equation of the line through P and R (3) 2.2 Calculate the gradient of PQ (2) 2.3 Determine the lengths of PQ and QR in terms of m and n (3)  11 8  2.4 If PQRS is a rhombus, show that point Q is   ;   (6)  3 3 2.5 Determine the equation of QS if PQRS is a rhombus. (4) 2.6 ˆ Determine the size of QPS (5) [23] Demo 3 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 QUESTION 3 3.1 Given the point P  8;15 in the Cartesian plane such that POX ˆ  . y P  8;15  x O 3.1.1 Calculate the length of OP (2) 3.1.2 Determine, without using a calculator, the value of (a) tan  (1) cos( ) (b) 17 sin 180     (4) 8 3.1.3 Calculate the size of  , rounded off to one decimal digit. (2) 3.2 If sin 40  t , express the following in terms of t : 3.2.1 cos320 (4) 3.2.2 sin140 (2) 3.2.3 tan  220  (3) [18] Demo 4 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 QUESTION 4 4.1 Express as a single trigonometric ratio: sin  90  A  tan( A  540)  (6) cos  540  A  cos A.sin A 4.2 Determine the value(s) of x if sin120.tan 330 tan 2 x  and x   90 ;90 , without cos 240 using a calculator. (7) 4.3 Determine the general solution of: 4 cos 2 x  3 (4) [17] Demo 5 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 In the next four questions, ensure you give reasons for each statement you make. QUESTION 5 5.1 The opposite anglesof a cyclicquadrilateralare … (1) 5.2 In the diagram below PR is a diameter of the circle PRSU with centre Q. QU is drawn parallel to RS and meets SP in T. R ≫ S Q ≫ 1 U 2 T P 5.2.1 Write down with a reason, the size of Ŝ. (2) 5.2.2 If the diameter is 20 cm and SP = 16 cm, calculate the length of TU. (6) [9] Demo 6 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 QUESTION 6 In the diagram below O is the centre of the circle. KJ = JL and K̂  50. K 50 1 J 2 O  1 2 2 3 M 2 1 L 1 H N 6.1 Determine, giving reasons, the value of 6.1.1 ˆ MOL (2) 6.1.2 N̂ (3) 6.1.3 L̂1 (3) 6.2 Prove that MOLN is a cyclic quadrilateral. (2) [10] Demo 7 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 QUESTION 7 7.1 In the diagram below, O is the centre of the circle. PQ is a tangent to the circle at A. B and C are points on the circumference of the circle. AB, AC and BC are joined. ˆ B Prove the theorem that states that A ˆ. “ (5) 1 Demo 8 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 7.2 In the diagram, two unequal circles touch externally at P. APB and MPN are double chords. AM isa diameter of the bigger circle. BT is a tangent to the smaller circle at B. MP is joinedand produced to intersect the smaller circle at N. RPS is a common tangent. AMT is a straight line. T M 2 R B 1 1 2 2 3 P1 4 6 5 N A S Prove that 7.2.1 BN is a diameter of the smaller circle (3) 7.2.2 AM NB (5) 7.2.3 MPBT is a cyclic quadrilateral (4) 7.2.4 T̂ =90 (2) [19] TOTAL: 100 Demo 9 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 NAME OF LEARNER: ……………………………………………. CLASS: ……….. DIAGRAM SHEET 1 QUESTION 2 y P  2;3 S 45 x Q m; n R  4;  5  T QUESTION 3.1 y P  8;15  x O Demo 10 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 NAME OF LEARNER: ……………………………………………. CLASS: ……….. DIAGRAM SHEET 2 QUESTION 5.2 R ≫ S Q ≫ 1 U 2 T P QUESTION 6 K 50 1 J 2 O  1 2 2 3 M 2 1 L 1 H N Demo 11 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 NAME OF LEARNER: ……………………………………………. CLASS: ……….. DIAGRAM SHEET 3 QUESTION 7.1 Demo 12 NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2019 NAME OF LEARNER: ……………………………………………. CLASS: ……….. DIAGRAM SHEET 4 QUESTION 7.2 T M 2 R B 1 1 2 2 3 P1 4 6 5 N A S Demo 13 NW/JUNE/MATH/ EMIS/6*******