Mathematics Grade 10 P2 Gauteng November 2021 QP (Eng)

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION NOVEMBER 2021 GRADE 10 MATHEMATICS (PAPER 2) TIME: 2 hours MARKS: 100 9 pages P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 (Paper 2) GRADE 10 INSTRUCTIONS AND INFORMATION 1. This question paper consists of 8 questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs etc. that you have used to determine the answers. 4. Present your answers according to the instructions for each question 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. Where necessary, round-off answers to TWO decimal places, unless otherwise stated. 8. Diagrams are NOT necessarily drawn to scale. 9. Number the questions correctly according to the numbering system used in this question paper. 10. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 (Paper 2) GRADE 10 QUESTION 1 A group of learners at Beacon High School carried out a survey of the number of sweets in 25 packets produced by Dotito brands. Their results are shown in the diagram below. Key: 2 4 means 24 sweets in a packet 1.1 Write down the modal number of sweets in a packet. (1) 1.2 Determine the following measures of spread: 1.2.1 Median (1) 1.2.2 Lower quartile (1) 1.2.3 Upper quartile (1) 1.3 Calculate the range. (2) 1.4 Give the number of packets of sweets, as a percentage, that have sweets above the upper quartile. (2) [8] QUESTION 2 The amounts spent by 120 motorists at KG petrol garage on a certain day were recorded as shown in the table below. Amount spent Number of Motorists (in 𝒙 Rands) 0 < 𝑥 ≤ 50 12 50 < 𝑥 ≤ 100 38 100 < 𝑥 ≤ 150 42 150 < 𝑥 ≤ 200 20 200 < 𝑥 ≤ 250 8 2.1 Write down the interval that has the least number of motorists. (1) 2.2 Draw a histogram to represent the data. (2) 2.3 Identify in which interval the thirtieth (30th) percentile lies. (2) 2.4 Calculate the size of the angle that will represent the modal class on a pie chart. (2) [7] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (Paper 2) GRADE 10 QUESTION 3 In the Cartesian Plane below, points A(5; 5), B(–7; 1) and C(1; –7) are the vertices of a triangle. Point S is the midpoint of BC. The line AS is perpendicular to BC. y A(5;5) B(-7;1) x S C(1;-7) 3.1 Determine the coordinates of point S. (3) 3.2 Determine the gradient of the line AC. (2) 3.3 Determine the distance of BC. (3) 3.4 Determine the area of ∆ABC . (5) [13] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 (Paper 2) GRADE 10 QUESTION 4 4.1 2 Using the diagram above and without the use of a calculator, determine the value of: 4.1.1 sin 𝜃 (3) 4.1.2 sin 𝜃 cos 𝜃 (2) 4.2 If 𝑥 = 60° and 𝑦 = 45°, determine the value of the following, without the use of a calculator: 1 𝑥 𝑠𝑖𝑛 2𝑦 −[2 𝑡𝑎𝑛2 (2)]cos 𝑥 (6) 2 4.3 Determine the acute angle 𝛽, to 2 decimals: 4.3.1 sin(𝛽 − 17.8°) = 0,215 (3) 4.3.2 tan 3𝛽 = √3 (2) 𝛽 4.3.3 3 sin = 2,012 (3) 2 4.4 Determine the value of the expression, without using a calculator. 𝑡𝑎𝑛30°.𝑐𝑜𝑠𝑒𝑐 60° 𝑐𝑜𝑡45°.𝑠𝑖𝑛2 45° (4) [23] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 (Paper 2) GRADE 10 QUESTION 5 5.1 The following are given: • 7sin 𝑥 = 4 where (𝑥 < 90°) • tan 𝑦 = 𝑡 • x and y are complementary angles. Determine the value of 𝑡 2 , without the use of a calculator and with the aid of a sketch. (6) 5.2 Assume that 𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 = 1 for all values of 𝑥. Now simplify the following expressions: 5.2.1 1 − 𝑐𝑜𝑠 2 𝑥 − 𝑠𝑖𝑛2 𝑥 (3) 5.2.2 𝑐𝑜𝑠 2 𝑥 +tan 𝑥. 𝑐𝑜𝑡𝑥 + 𝑠𝑖𝑛2 𝑥 (3) 5.3 E 26,2° 34,4° S M H From the top of the lighthouse, 55 m above sea level, two boats M and H, sailing due east, have angles of depression of 26,2° and 34,4° as shown. Calculate the distance between the two boats. (5) [17] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 (Paper 2) GRADE 10 QUESTION 6 The diagram below represents the graphs of f (x) = a sin x and g (x) = b cos x for x  [0° ; 360°]. 6.1 Write down the values of a and b. (2) 6.2 For which value(s) of x will g be a decreasing function? (2) 6.3 What is the amplitude of f ? (1) 6.4 What is the range of g? (2) 6.5 For which value(s) of x is f (x) – g (x) = 2 (2) [9] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 8 (Paper 2) GRADE 10 QUESTION 7 In the sketch, RSTQ is a parallelogram with RS // QT and QR // TS. VQ bisects 𝑅𝑄̂ 𝑇 and VT bisects 𝑄𝑇̂𝑆. Prove that : 7.1 ̂2 = 90° V (5) 7.2 RS = 2RQ (6) [11] P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 9 GRADE 10 QUESTION 8 8.1 In ∆𝐴𝐵𝐶 , M and N are the midpoints of AB and AC respectively. Prove the theorem that states that MN // BC. (6) 8.2 In ∆𝑃𝑄𝑅, QT = TU = UP. QS = SR and UV = 𝑥 𝑐𝑚. Determine the length of VR in terms of 𝑥. (6) [12] TOTAL: 100 END