Mathematics Grade 11 P2 Gauteng June 2019 QP (Eng)

Downloaded from hlayiso.com testpapers.co.za GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION JUNE 2019 GRADE 11 MATHEMATICS PAPER 2 MARKS: 100 TIME: 2 hours 9 pages + 3 diagram sheets P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 Paper 2 GRADE 11 GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS (Paper 2) Marks: 100 Time: 2 hours INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 7 questions. Answer ALL questions. 2. Number the answers according to the numbering system used in the question paper. 3. Use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 4. Round off answers to TWO decimal places unless instructed otherwise. 5. Show ALL calculations, diagrams, graphs etc. that you have used in determining the answers. 6. Answers only will NOT necessarily be awarded full marks. 7. Diagrams are NOT necessarily drawn to scale. 8. Write legibly and neatly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 Paper 2 GRADE 11 QUESTION 1 1.1 In the sketch below points A , B , and C , are given. 1.1.1 Calculate the length of line AB. (3) 1.1.2 Determine the coordinates of point D if point C is the midpoint of line BD. (3) 1.1.3 The coordinates of point E is the point . Determine the value of if points E, C and A are collinear. (4) 1.1.4 Show that quadrilateral ABED is a kite. (4) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 Paper 2 GRADE 11 1.2 In the sketch below f(x) = –x + 4 intersects the x-axis and the y-axis at point R and point P respectively. Point Q is equidistant to point R with respect to the origin and PQ̂R  45. 1.2.1 Determine the coordinates of point P. (1) 1.2.2 Calculate the coordinates of point R. (1) 1.2.3 Determine the equation of g. (2) 1.2.4 Calculate the magnitude of: 1.2.4.1 (2) 1.2.4.2 (2) [22] QUESTION 2 2.1 Given sin = and . With the aid of a sketch and WITHOUT (4) the use of a calculator determine the value of cos 2.2 Simplify: 2.2.1 45 + sin 330 . 210 (6) 2.2.2 (6) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 Paper 2 GRADE 11 2.3 Simplify to ONE trigonometric ratio of . √ (5) 2.4 Consider the expression: cos 2 x.tan x sin 2 x determine the value(s) of x, x ( 0 ; 180 ), for which the expression will be UNDEFINED. (3) [24] QUESTION 3 The graphs of and are sketched below. 3.1 Write down the values of , and . (3) 3.2 Determine the value(s) of given that [ ] where: 3.2.1 (2) 3.2.2 (2) 3.3 Sketch the graph of f(x) , [ ], on DIAGRAM SHEET 1. Clearly show ALL asymptotes and intercepts with the axes. (4) [11] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 Paper 2 GRADE 11 QUESTION 4 4.1 Complete: The angle at the centre of a circle is … (1) 4.2 In the sketch below, point O is the centre of the circle where A, B, and C are points on the circumference of the circle. Use DIAGRAM SHEET 2 to prove that AÔB  2AĈB. (6) [7] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 Paper 2 GRADE 11 QUESTION 5 5.1 Complete: The opposite angles of a cyclic quadrilateral are … (1) 5.2 In the sketch below point O is the centre of the circle with PQ RS. Line PS and line RQ intersect at point T and Ŝ  x. 5.2.1 Name (giving reasons) THREE angles equal to . (6) 5.2.2 Calculate PT̂R in terms of . (3) 5.2.3 Prove that quadrilateral PTOR is a cyclic quadrilateral. (3) [13] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 8 Paper 2 GRADE 11 QUESTION 6 In the sketch below point O is the centre of the circle where line AB is a diameter. Given that BC ║ OD, where point E is the point of intersection of line AC and line OD. The radius of the circle is and AC . 6.1 Prove that AE = EC. (4) 6.2 Prove that Ê1  90. (3) 6.3 Calculate the length of ED. (4) [11] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 9 Paper 2 GRADE 11 QUESTION 7 In the sketch below RSPD and SWTD are cyclic quadrilaterals. Line TD is a tangent to cyclic quadrilateral RSPD at point D. Line RS and line DP are produced to intersect at point W. It is given that DR PS and Ŝ4  Ŝ2 . Prove that: 7.1 TS is a tangent to the cyclic quadrilateral RSPD at point S. (6) 7.2 TW || PS (6) [12] TOTAL: 100 END

Downloaded from hlayiso.com MATHEMATICS 10 Paper 2 GRADE 11 DIAGRAM SHEET 1 Detach and insert into your ANSWER BOOK. Name / Surname: ______________________________________ Grade: _________________ QUESTION 3.3 y x

Downloaded from hlayiso.com MATHEMATICS 11 Paper 2 GRADE 11 DIAGRAM SHEET 2 Detach and insert into your ANSWER BOOK. Name / Surname: ___________________________________ Grade: ______________ QUESTION 4.2 QUESTION 5.2

Downloaded from hlayiso.com MATHEMATICS 12 Paper 2 GRADE 11 DIAGRAM SHEET 3 Detach and insert into your ANSWER BOOK. Name / Surname: ___________________________________ Grade: ______________ QUESTION 6 QUESTION 7