Mathematics Grade 10 P2 Gauteng November 2020 QP (Eng)

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION NOVEMBER 2020 GRADE 10 MATHEMATICS (PAPER 2) TIME: 1 hour MARKS: 50 6 pages and 1 diagram sheet P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 2 GRADE 10 INSTRUCTIONS AND INFORMATION 1. This question paper consists of THREE questions and ONE diagram sheet. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, etc. which were 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. Where necessary, answers should be rounded-off to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Number the questions correctly according to the numbering system used in this question paper. 9. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 3 GRADE 10 QUESTION 1 In the diagram below PQRS is a kite with P (3; 5), S (–1; –4). PQ = QR and PS = RS. Q is a point such that PQ is parallel to the x-axis and PQ = 5 units. RQ is perpendicular to the x-axis. The diagonals intersect at A. y P(3;5) Q A O x R S(–1;–4) 1.1 Show that the coordinates of R are (8; 0). (4) 1.2 Write down the coordinates of A. (2) 1.3 Calculate the gradient of SQ. (3) 1.4 Determine the length of PR. (2) 1.5 Calculate the area of the kite PQRS. (3) 1.6 Show that PR is perpendicular to SQ. (3) 1.7 Show that ∆PSR is an isosceles triangle. (4) [21] P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 4 GRADE 10 QUESTION 2 2.1 Determine the value of sec 75° and round-off your answer to TWO decimal places. (2) sin 90  cos 60 2.2 Simplify without the use of a calculator. tan 45 (2) 2.3 In the diagram below, A(x ; y) is a point in the third quadrant, BOˆ A   and 5sin 𝜃+ 3 = 0. y x O  B r A(x ; y) 2.3.1 Determine the value of 30 tan 𝜃 without using a calculator. (6) 2.3.2 Calculate the size of BOˆ A , correct to TWO decimal places. (1) [11] P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 5 GRADE 10 QUESTION 3 3.1 Consider the function f (x) = 2 sin x. 3.1.1 Sketch the graph of f on the given diagram sheet for 0  x  360 . Clearly show all the intercepts with the axes. (2) 3.1.2 Write down the: (i) period of f. (1) (ii) equation of h, if h is the reflection of f about the x-axis. (1) 3.2 Solve for x, correct to ONE decimal place where 0° ≤ 𝑥 ≤ 90°. 3.2.1 4tan x + 1 = 3 (3) 3.2.2 cosec x 2 3 (3) P.T.O.

Downloaded from hlayiso.com 3.3 An architectural design of the front of a house is given below. The length of the house is 10 meters. An exterior stairway leading to the roof forms an angle of elevation of 30° with ground level. The slanted part of the roof is 7 meters in length. 7m roof Stairway to roof Front view of a house 3.3.1 Calculate the length of the vertical wall DE. Leave answer in simplest surd form. (2) 3.3.2 Calculate 𝜃, the angle of elevation at the top of the roof (A) from the ceiling BCD, correct to TWO decimal places. (3) 3.3.3 Calculate the length of the beam AC, correct to TWO decimal places. (3) [18] TOTAL: 50 END

Downloaded from hlayiso.com DIAGRAM SHEET NAME:_______________________________________________________ QUESTION 3.1.1 y x 0 90° 180° 270° 360°