Mathematics Grade 11 P2 Gauteng June 2022 QP (Eng)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION JUNE 2022 GRADE 11 MATHEMATICS PAPER 2 TIME: 2 hours MARKS: 100 7 pages and 2 diagram sheets P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 (Paper 2) GRADE 11 INSTRUCTIONS AND INFORMATION 1. This question paper consists of 3 questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining the answers. 4. Answers only will NOT necessarily be awarded full marks. 5. Use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round off the answers to TWO decimal places, unless stated otherwise. 7. Write your name and class grade on the diagram sheet, detach and hand them in with your ANSWER BOOK. 8. Diagrams are NOT necessarily drawn to scale. 9. Number the answers correctly according to the numbering system used in the question paper. 10. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 (Paper 2) GRADE 11 QUESTION 1 1.1 The points D(–1 ; 2), E(4 ; –2), F(–5 ; –3) are vertices of DEF. Determine: 1.1.1 The gradient of DF (2) 1.1.2 If line DE is perpendicular to DF, write down the gradient of DE (1) 1.1.3 The equation of the line DE in the form y = mx + c (3) 1.1.4 The equation of a line parallel to DE passing through point F in the form y = … (3) 1.1.5 If G(6 ; y) is a point on DE, determine the value of y (2) 1.1.6 The length of DF is equal to DE. What type of triangle is ∆DEF? (5) 1.1.7 The area of triangle DEF (2) 1.2 Quadrilateral PQRS is drawn below and has the following properties: • RQ ‖ SR • The coordinates of R(–4 ; 1) and S(10 ; 3) are given • The coordinates of Q(–7 ; y) and P(x ; –9) are partially given y S(10 ; 3) R(–4 ; 1) x 0 Q(–7 ; y) P(x ; –9) Determine: 1.2.1 What type of quadrilateral is PQRS? (1) 1.2.2 The value of x if RS = 15 units (5) 1.2.3 The co-ordinates of T, the midpoint of RS (2) 1.2.4 The value of y (3) 1.2.5 The coordinates of W, a point on SP such that PQRW is a rectangle (3) [32] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (Paper 2) GRADE 11 QUESTION 2 2.1 In the diagram, P is a point in the first quadrant such that 5sin ( 90 −  ) − 3 = 0 . R(k ; 6) is a point in the second quadrant such that PÔR = 90°. In the diagram below: • PQ̂R = 90 and PÔR = 90 • R(k ; 6) is a point in the quadrant 2 • P is a point in quadrant 1 such that 5sin ( 90 −  ) − 3 = 0 y R(k ; 6) P  x Q 0 Determine: 2.1.1 sin  (3) 2.1.2 The value of k (3) 2.2 Simplify fully: 2.2.1 tan 315 + cos300 sin150 + tan135 (6) 2.2.2 sin (180 + x ) cos (180 − x ) .sin 50 tan ( 315 ) .cos 2 ( 360 − x ) .cos140 (6) 2.3 If x  − 180 ; 180 , determine sin ( x + 10 ) − cos ( x − 30 ) = 0 . (7) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 (Paper 2) GRADE 11 2.4 In the quadrilateral below: • AB ˆ D = 80°, BD ˆ C = 36°, CB ˆ C = 60° • Lines AB = 74 m and BC = 52 m A 74 m B 36° 80° 52 m 60° D C Calculate: 2.4.1 ˆD The value of BC (1) 2.4.2 The length of line CD (2) 2.4.3 The length of diagonal AD (4) 2.4.4 The area of quadrilateral ABCD (4) [36] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 (Paper 2) GRADE 11 QUESTION 3 3.1 In the sketch below, O is the centre of the circle. Chord PQ is perpendicular to OM at M. Q O M P Prove the theorem that states that the line drawn from the centre of the circle perpendicular to a chord will bisect the chord. (5) 3.2 In the sketch below: • O is the centre of the circle • AB = 10 cm and is perpendicular to OC at point D • C is a point on the circumference of the circle • The radius of the circle = 13 cm O D A B C Calculate the length of line DC. (5) 3.3 Calculate the remaining area in the circle if the area of ∆OAB is excluded. (3) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 (Paper 2) GRADE 11 3.4 In the sketch below: • PQRS is a cyclic quadrilateral • Line AB is a tangent to the circle at point S • PQ = QR • PR = SR • PQ ║ SR • ˆR= x BS P A Q 12 3 12 1 2 S R 3 B 3.4.1 Determine, giving reasons, FIVE angles that are equal to BŜR. (10) 3.4.2 Calculate the value of Ŝ1 in terms of x as well as the value of TWO other angles that are equal to Ŝ1 . (6) 3.4.3 Prove that PS = QR. (3) [32] TOTAL: 100 END

Downloaded from hlayiso.com MATHEMATICS 8 (Paper 2) GRADE 11 DIAGRAM SHEET 1 QUESTION 3 3.1 Q O M P 3.2 O D A B C

Downloaded from hlayiso.com MATHEMATICS 9 (Paper 2) GRADE 11 DIAGRAM SHEET 2 3.3 P A Q 1 3 2 1 2 S 2 1 3 R B