Mathematics Grade 11 P2 North West June 2018 Question Paper

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P2 MID-YEAR EXAMINATION 2018 MARKS: 100 JUNE EXAMINATION 2012 TIME: 2 hours This question paper consists of 8 pages and 3 diagram sheets. Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 6 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. 10. Write neatly and legibly. 2 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION 1 1.1 A  1;  1 , B  2;0  and C  5; p  are three points in a Cartesian plane. Determine the value(s) of p if: 1.1.1 A, B and C are collinear. (2) 1.1.2 AB is perpendicular to BC. (3) 1.1.3 the length of BC is 5 units. (3) 1.2 In a diagram P  4;5 , Q  4;1 and R  1;  4  are the vertices of a triangle in the Cartesian plane with M on PQ. M  2;2  is the midpoint of straight line RS. S x ; y  y P  4;5  M  2; 2  Q  4;1 x O R  1;  4  1.2.1 Determine the gradient of PQ. (2) ˆ  90 1.2.2 Show that PMS (3) 1.2.3 Determine the coordinates of S. (3) 1.2.4 Prove that QRS is isosceles. (3) 1.2.5 Determine the area of PRS. (5) [24] 3 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION 2 2.1 Given: 17sin  15  0 and 90    270 With the aid of a sketch and without using a calculator, determine: 2.1.1 tan  (3) 2.1.2 cos   180  (2) 2.2 If tan 70  p, write the following in terms of p : 2.2.1 tan110 (2) 2.2.2 sin 290 (3) 2.3 Simplify the following without using a calculator: sin150.tan 225 (6) sin  30  .sin 420 [16] QUESTION 3 3.1 Simplify without using a calculator: cos 390  tan  360  x  .cos 180  x  .cos  x  90  (8) cos(30) 3.2 Prove the identity: cos x.tan 2 x  cos x  1 (6) 1 1 cos x 3.3 Determine the general solution of 4 6 cos x  5  ; cos x  0 (6) cos x [20] 4 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION 4 ˆ  106. ˆ  26, AB  DC and EOC O is the centre of circle ABCDE with DEC Calculate the size of: 4.1 ˆ BCA (2) 4.2 Â1 (2) 4.3 ˆ OCD (6) [10] 5 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION 5 5.1 Complete the missing information in the theorem below: The angle subtended by the diameter at the circumference of the circle is … (1) 5.2 Given: Circle centre O, tangent CPT at P chord PM and the point B on the major arc. Complete the proof: ˆ  ˆ Required to proof: MPT PBM Construction: Draw diameter PA and join AM Proof: ………………………………………………………………………….. …………………………………………………………………………... ………………………………………………………………………….. (5) 6 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 5.3 ˆ  x. BC // PQ. PA and PB are tangent to circle M with AC  BC. A 2 M A 1 2 x 1 B 1 2 4 C 2 3 1 S4 2 3 Q 2 3 1 1 2 R P 5.3.1 Determine with reasons FOUR other angles equal to x. (8) 5.3.2 Prove that ABRP is a cyclic quadrilateral (2) 5.3.3 Prove that AP  BQ (3) [19] 7 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION 6 Refer to the diagram below, ST is a diameter of the circle. ˆ OS // PN, TO bisects STP. Prove that 6.1 PUNK is a cyclic quadrilateral (5) 6.2 SO is a tangent to circle KUST (6) [11] TOTAL: [100] 8 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 NAME: ………………………………………………….. CLASS: …………. DIAGRAM SHEET 1 QUESTION 1.2 S  x; y y P  4;5 M  2; 2  Q  4;1 x O R  1;  4  QUESTION 4 9 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 NAME: ………………………………………………….. CLASS: …………. DIAGRAM SHEET 2 QUESTION 5.2 QUESTION 5.3 M A 1 2 x 1 B 1 2 4 C 2 3 1 S4 2 3 Q 2 3 1 1 2 R P 10 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2 Mid-Year Examination NW/ Jun 2018 NSC- Grade 11 NAME: ………………………………………………….. CLASS: …………. DIAGRAM SHEET 3 QUESTION 6 11 Demo NW/JUNE/MATH/ EMIS/6*******