Mathematics Grade 10 P2 North West November 2024 QP (Eng)

PROVINCIAL ASSESSMENT GRADE 10 MATHEMATICS P2 NOVEMBER 2024  100 MARKS: TIME: 2 hours This question paper consists of 10 pages, and a 13-page answer book. Copyright reserved Please turn over

Mathematics/P2 2 NW/November 2024 Grade 10 INSTRUCTIONS AND INFORMATION 1. This question paper consists of SEVEN questions. 2. Answer ALL questions in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL your calculatio ns, diagrams , graphs , etc that you have used to determine the answer. 4. Answers only will NOT be necessarily awarded full marks. 5. If necessary , round off answers to TWO decimal places , unless stated otherwise. 6. Diagrams are NOT necessarily drawn to scale. 7. You may use an approved scientific calculator (non - programmable and non - graphical) , unless stated otherwise. 8. Write neatly and legibly. Copyright reserved Please turn over

Mathematics/P2 3 NW/November 2024 Grade 10 QUESTION 1 Mr Baloyi conducted a survey on the amount of airtime (in Rands) EACH learner had on his or her cellphone. 12 16 20 22 26 30 32 38 40 46 54 60 68 1.1 Draw a box and whisker to represent the data. (3) 1.2 Determine the interquartile range (IQR). (2) 1.3 Calculate the range of the data. (2) 1.4 Comment on the skewness of the data. (1) [8] QUESTION 2 The histogram below shows the distribution of examination scores for learners in Introductory stats. SCORES IN INTRODUCTORY STATISTICS Frequency Examination Scores 2.1 How many learners wrote the examination? (1) 2.2 Identify the modal class of the data. (1) 2.3 Estimate the mean of this data. Show all calculations. (4) 2.4 Estimate the median mark obtained by the group. (2) 2.5 In which interval does the upper quartile lie? (1) [9] Copyright reserved Please turn over

Mathematics/P2 4 NW/November 2024 Grade 10 QUESTION 3 In the figure, ABC has vertices A(-11;2), B(3;-5) and C(6;1). 3.1 Calculate the length of BC. Leave the answer in surd form. (2) 3.2 Write down the coordinates of the midpoint D, of AB. (4)  (5) 3.3 Prove that ABC  90 . 3.4 Calculate the area of ABC. (4) [15] Copyright reserved Please turn over

Mathematics/P2 5 NW/November 2024 Grade 10 QUESTION 4  In the diagram is a right-angled triangle has sides a, b and c and the B  90 . 4.1 Write down the following in terms of a, b and c. 4.1.1 sin A (1) 4.1.2 cot C (1) 4.1.3 If it is given that a = 5 and A =50, calculate the numerical value of c. (3) 4.2 Given: 13cos  12 , where 0  x  90 ,without using a calculator, use a sketch to determine the following. 4.2.1 sin  (4) 4.2.2 tan - cosec2 (3) 4.3 Simplify, without the use of a calculator. cosec60.cot30  cos45.cosec45. (5) 4.4 Solve for x, correct to two decimal places: 3  sec x  5 and 0  x  90 (3) [20] Copyright reserved Please turn over

Mathematics/P2 6 NW/November 2024 Grade 10 QUESTION 5 In the diagram below, the graphs of f(x)  cos x  a and g(x) =b sin x are drawn for x [-180 ;180] . 5.1 Write down the values of a and b. (2) 5.2 Write down the period of g. (1) 5.3 Determine the range of f. (2) 5.4 Write down the amplitude of g. (1) 5.5 Determine the number of solutions to f(x)  g(x) for -180  x  180 . (1) 5.6 For which values of x is g(x)  0 . (2) 5.7 The graph of f is reflected about the x-axis and then moved 2 units downwards to form the graph of h. Determine: 5.7.1 The equation of h (2) 5.7.2 The range of h (2) [13] Copyright reserved Please turn over

Mathematics/P2 7 NW/November 2024 Grade 10 QUESTION 6 An observer on the top of a cliff, 200 m above the sea level, observes the angles of depression of the two ships to be 45° for ship A, and 30° for ship B, as shown below.  6.1 Determine the size of BDC . (2) 6.2 Calculate the length of BC. (2) 6.3 Determine the distance between Ship A and Ship B. (4) [8] Copyright reserved Please turn over

Mathematics/P2 8 NW/November 2024 Grade 10 QUESTION 7 Given the rectangular prism below: V = L.B.H SA = 2(L.B)+ 2(L.H)+2(H.B) 5m 3m 8m 7.1 Calculate the surface area of the prism. (2) 7.2 Calculate the volume of the prism if the height is doubled and the (2) breadth halved. 7.3 Calculate the volume if the length is doubled, the height is halved and the breadth is tripled. (3) [7] Copyright reserved Please turn over

Mathematics/P2 9 NW/November 2024 Grade 10 Give reasons for ALL geometry statements used in QUESTION 8 and 9. QUESTION 8 ABCD is a parallelogram and AC is a diagonal,with A,F,E and C as colinear points. 8.1 Prove that: 8.1.1 ∆ABE ≡ ∆CDF (4)   (3) 8.1.2 CEB  AFD 8.1.3 AF = CE (3) [10] Copyright reserved Please turn over

Mathematics/P2 10 NW/November 2024 Grade 10 QUESTION 9 In the diagram below, R is the midpoint of QT and S is the midpoint of PT. The length   of SR is 2x +4. Q  39 and P  55 . 9.1 Determine the length of PQ in terms of x. (2) 9.2 If the length of PQ is 18, determine the value of x. (3) 9.3 Prove that TRS ||| TQP (5) [10] TOTAL : 100 Copyright reserved