Mathematics Grade 10 P2 North West June 2019 Question Paper

Downloaded from hlayiso.com GRADE 10 MATHEMATICS PAPER 2 MID – YEAR EXAMINATION 2019 MARKS: 75 TIME: 1 hour 30 minutes This question paper consists of 6 pages and 2 diagram sheets Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P2 NSC – Grade 10 NW/June 2019 INSTRUCTIONS AND INFORMATION 1. This question paper consists of 5 questions Answer. ALL the questions. 2. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining the answers. 3. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 4. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 5. Diagrams are NOT necessarily drawn to scale. 6. Number the answers correctly according to the numbering system used in this question paper. 7. It is in your own interest to write legibly and to present the work neatly. 2 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P2 NSC – Grade 10 NW/June 2019 Question 1 In the diagram below, P(7; 4), Q(6; 6), R(0; 3) and S(t; k) are the vertices of quadrilateral PQRS. y Q (6; 6) R (0; 3) P (7; 4) S (t; k) x 0 1.1 Calculate the length of PQ. Leave your answer in a surd form. (3) 7 7 1.2 If T ;  is the midpoint QS, determine the coordinates of S (3) 2 2 1.3 If the coordinates of S are (1; 1), show that PR = QS. (5) 1.4 Show that QR  RS. (5) 1.5 Hence, what type of special quadrilateral is PQRS? Motivate your answer. (2)  1.6 Calculate the size of R S Q . (3) [21] 3 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P2 NSC – Grade 10 NW/June 2019 Question 2 2.1 Determine the value of each of the following by using a calculator. Write down the answers correct to 2 decimal places. x  112,4 and y  48,6 1 2.1.1 sin x (2) 2 2.1.2 cos ec( x  y ) (3) x y 2.1.3 2 cos  (2)  2  1  2.1.4 tan x  (2) 3  2.2 Determine the value of θ, if θ  ( 0 ; 90) 2.2.1 tan   2,736 (1) 2.2.2 3 sin(3  60 )  0,531 (3) [13] Question 3 In the diagram below P (x; 5), OP = 13 units. Answer questions below without using a calculator. y P (x; 5) 13 α x 0 4 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P2 NSC – Grade 10 NW/June 2019 3.1 Determine; 3.1.1 x (3) 3.1.2 tan  (1) 3.1.3 sin 2   cos2  (2) 3.1.4 Sec (2) 3.2 Simplify without using a calculator. cos ec20. sin 20  tan 45. sec 60 (6) cot 45. sin 90 [14] Question 4 4.1 In the diagram below, KLMN is a rhombus with diagonals intersecting at O. LKM = 34  K L 34◦ 1 2 1 O 1 2 4 3 1 1 2 2 N M ^ 4.1.1 Write down the size of O1 . (2) ^ 4.1.2 Calculate the size of L 1 . (2) ^ 4.1.3 Calculate the size of K N M . (4) 5 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P2 NSC – Grade 10 NW/June 2019 4.2 In the diagram given below, ABEF is a parallelogram A F >> x 2x 7x B R >> E y S ^ 4.2.1 Express AFE in terms of x (3) 4.2.2 Calculate the value of x and y if SA = SF. (6) [17 ] Question 5 The diagram represents parallelogram ABCD with BE = DF A D F E B C Prove that: 5.1 ∆AEB ≡ ∆CFD (4) 5.2 AE‖CF (3) 5.3 AECF is a parallelogram (3) [10] 6 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P2 NSC – Grade 10 NW/June 2019 Diagram Sheet Name: ___________________________________ Question 1 y Q (6; 6) R (0; 3) P (7; 4) S (t; k) x 0 Question 3 y 3.1 (x; 5) 13 α x 0 Question 4 K L 4.1 34◦ 1 2 1 O 1 2 4 3 1 1 2 2 N M 7 Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P2 NSC – Grade 10 NW/June 2019 4.2 A F >> x 2x 7x B R >> E y S Question 5 A D F E B C 8 Demo NW/JUNE/MATH/ EMIS/6*******