Mathematics Grade 10 P2 Gauteng November 2023 QP (Eng)

Downloaded from hlayiso.com Mathematics 1 (Paper 2) 10612/20 PROVINCIAL EXAMINATION NOVEMBER 2023 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 Read the following instructions carefully before answering the questions. 1. This question paper consists of NINE questions. 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 otherwise stated. 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 3 (PAPER 2) GRADE 10 QUESTION 1 The maximum temperature (in degrees celcius) at 20 tourist resort centres were measured and recorded. The results were recored in the table below. 22 23 24 25 26 28 29 29 30 32 32 33 34 35 36 37 37 38 39 40 1.1 Write down the median temperature measured. (1) 1.2 Determine: 1.2.1 The mean temperature (2) 1.2.2 The range (1) 1.2.3 The interquartile range (3) 1.3 Draw a box and whisker diagram to represent the data above. (2) 1.4 The tourism sector claims that 20% of the resort centres recorded temperatures too hot for tourist activities. Determine the minimum recorded temperature that satisfies the above claim. (2) [11] QUESTION 2 A supermarket sells light bulbs. The store keeps a record of the wattage of the light bulbs that they sold in the month of October 2023. The monthly sales are summarised in the table below. Wattage Interval Frequency 80 ≤ x < 95 3 95 ≤ x < 110 17 110 ≤ x < 125 31 125 ≤ x < 140 16 140 ≤ x < 155 10 2.1 How many light bulbs were sold in the month of October? (1) 2.2 Write down the modal class of the data above. (1) 2.3 Determine the interval in which the median lies. (2) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (PAPER 2) GRADE 10 2.4 Express the number of light bulbs with the most popular wattage as a percentage of the October sales. (2) 2.5 Estimate the mean wattage of the light bulbs that were sold. (3) 2.6 The manager of the store decided to display the data collected on a pie chart. Calculate the size of the largest angle of the pie chart. (2) [11] QUESTION 3 In the diagram below, P (2;9), A, R(n ; –13) and M are vertices of parallelogram PARM. PMT is a straight line such that M is the midpoint of PT. T (10; –3) is a point such that PT ⊥ RT. y P(2 ; 9) M x O T(10 ; –3) A R(n ; –13) 3.1 Determine: 3.1.1 The length of PT (Leave your answer in surd form.) (2) 3.1.2 The gradient of PT (2) 3.1.3 The gradient of AR (1) 3.1.4 The coordinates of M (3) 3.2 Determine the equation of PM in the form y = mx + c. (3) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 (PAPER 2) GRADE 10 3.3 Show that n = 5. (3) 3.4 Calculate the area of RMT. (4) [18] QUESTION 4 4.1 Use a calculator to find the values of the following, correct to two decimal places. 4.1.1 4sin 65 (1) 4.1.2 cos 2 (32 − 10 ) tan 22 (2) 4.2 Calculate  where 0° ≤  ≤ 90°. θ 3sin ( – 20) = 0,85 2 (4) 4.3 Without the use of a calculator, determine the value of: cos 45 + 5cosec 90° x 3tan230° sin 45 (4) [11] QUESTION 5 If 5cos β = −3 and 180° ≤ β ≤ 360°, with the use of a diagram, calculate the value of the following: (Do NOT calculate the value of β.) 5.1 cosβ (3) 5.2 tan2 β − cot2 β (2) [5] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 (PAPER 2) GRADE 10 QUESTION 6 The graphs of f (x) = a sin x + q, h(x) = p cos x and g(x) = tan x for x  [0° ; 360°] are drawn below. 6.1 Determine the values a, p and q. (3) 6.2 For which values of x is h(x) ≤ 0 for x  [0 ; 360]? (2) 6.3 Determine for which value(s) of x will f (x) = h(x). (3) 6.4 Write down the range of f. (2) [10] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 (PAPER 2) GRADE 10 QUESTION 7 The diagram below shows a spotlight at point B, which is mounted 12 m directly above point C at the front of the field. The spotlight swings 44,3° from the vertical to illuminate another point, D, the midpoint of AC. B 12 m A D C 7.1 Calculate the length of DC. (3) 7.2 Calculate through how many degrees the spotlight must swing in order to illuminate point A (i.e. calculate  ). (3) [6] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 8 (PAPER 2) GRADE 10 QUESTION 8 8.1 In the diagram below, a polygon ABEFD is drawn. AD is produced to a point, C, that lies on BC. AC||FE Given  = 3x, B̂ = x and AĈB = 2x 8.1.1 Determine, with reasons, the numerical value of x. (2) 8.1.2 What type of triangle is ABC? Give a reason for your answer. (2) 8.2 In the diagram below ABC is drawn. AB = BC and B̂1 = B̂3 . Prove that Ê1 = D̂ 2 (5) [9] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 9 (PAPER 2) GRADE 10 QUESTION 9 9.1 In the diagram below, a parallelogram ABCD is drawn such that AD || BC and DC || AB. AC and DB intersect at point O. D C O A B .. Prove that DO = OB and AO = OC. (6) 9.2 PQRS is a square. X is a midpoint of SP, and Y is the midpoint of PQ. S R O X P Y Q 9.2.1 Prove that SPY  RSX. (6) 9.2.2 Given that R̂1 = x. Identify, with reasons, another angle equal to x. (2) 9.2.3 Prove that SY ⊥ RX. (5) [19] TOTAL: 100 END