Mathematics Grade 10 P2 National November 2016 QP (Eng)

Downloaded from hlayiso.com = basic education y y Department: - ANU Basic Education WZ REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 10 FH MATHEMATICS P2 cf ' NOVEMBER 2016 J MARKS: 100 TIME: 2 hours This question paper consists of 10 pages and a 16-page answer book. AIM *K6P2* A Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 2 DBE/November 2016 CAPS — Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of 9 questions. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs et cetera that you used to determine the answers. Answers only will NOT necessarily be awarded full marks. If necessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. You must use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. Write neatly and legibly. Copyright reserved FUN ANAC UO A EE A Please tum over

Downloaded from hlayiso.com Mathematics/P2 3 DBE/November 2016 CAPS - Grade 10 QUESTION 1 The heights of 20 children were measured (in centimetres) and the results were recorded. The data collected is given in the table below. 127 128 129 130 131 133 134 134 135 136 137 138 139 140 141 142 142 143 144 145 11 Write down the median height measured. qd) 1.2 Determine: 1.2.1 The mean height (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. (2) [9] QUESTION 2 The intelligence quotient score (IQ) of a Grade 10 class is summarised in the table below. 1Q INTERVAL FREQUENCY 90<x< 100 4 100<x<110 8 110<x<120 7 120 <x < 130 5 130 <x < 140 4 140 <x < 150 2 2.1 Write down the modal class of the data. qd) 2.2 Determine the interval in which the median lies. (2) 2.3 Estimate the mean IQ score of this class of learners. (3) [6] Copyright reserved FUN ANAC UO A EE A Please tum over

Downloaded from hlayiso.com Mathematics/P2 4 DBE/November 2016 CAPS - Grade 10 QUESTION 3 3.1 Show that a triangle ABC, with vertices A(1 ; 1); B(3; 6) and C(6; 3), is an isosceles triangle. (4) 3.2 In the diagram below, ADCB isa kite with A(3 ;5) and B(-1 ;-4). AD=DC and AB=BC. D isa point such that AD is parallel to the x-axis and AD =S units. CD is perpendicular to the x-axis. The diagonals intersect at P. a y AG ; 5). D P ng fe) Cc " B(-1 ;-4) 3.2.1 Show that the coordinates of C are (8 ; 0). (2) 3.2.2 Write down the coordinates of point P. (2) 3.2.3 Calculate the gradient of line BD. (2) 3.2.4 Calculate the length of line AC. (2) 3.2.5 Calculate the area of the kite ADCB. (3) [15] Copyright reserved FUN ANAC UO A EE A Please tum over

Downloaded from hlayiso.com Mathematics/P2 5 DBE/November 2016 CAPS - Grade 10 QUESTION 4 41 A right-angled triangle has sides a, b and c and the angle 0, as shown below. 4.1.1 Write the following in terms of a, b and c: (a) cosd (1) (b) tan@ qd) (c) _ sin(90°-6) (2) 4.1.2 If it is given that a=5 and 0=50°, calculate the numerical value of b. (2) 42 Given that A =38,2° and B=146,4°. Calculate the value of 2cosecA + cos3B. (3) 43 Simplify fully, WITHOUT the use of a calculator: sin 45°. tan” 60° cos 45° (4) 44 Given that Scos8—3=0 and 0°<f<90°. If a+ B = 90° and 0°<a <90°, calculate the value of cot a. (4) [17] Copyright reserved FUN ANAC UO A EE A Please tum over

Downloaded from hlayiso.com Mathematics/P2 6 DBE/November 2016 CAPS - Grade 10 QUESTION 5 5.1 In the sketch below, AMNP is drawn having a right angle at N and MN = 15 units. A is the midpoint of PN and AMN =21°. P A M. 21 N 15 Calculate: 5.1.1 AN (3) 5.1.2 PMN (3) 5.13 MP (3) 5.2 Calculate 0 if 2sin(9+15°)=1,462 and 0°<@<90°. (3) [12] Copyright reserved FUN ANAC UO A EE A Please tum over

Mathematics/P2 QUESTION 6 Downloaded from hlayiso.com 7 CAPS — Grade 10 DBE/November 2016 The graphs of f(x)=asinx and g(x)=cosx+1 for xe[0; 360] are sketched below. a y 24 g io 0 oF -14 24 6.1 Write down the value of a. 6.2 Write down the period of f- 6.3 Write down the range of g. 6.4 For which values of x for xe[0° ; 360°] will {(x).g(x)>0? 6.5 The graph g is reflected about the x-axis and then shifted 2 units upwards to obtain the graph h. Write down the equation of h. Copyright reserved GAUTENG Please turn over (1) Q) (2) (2) (2) [8]

Downloaded from hlayiso.com Mathematics/P2 8 DBE/November 2016 CAPS - Grade 10 QUESTION 7 The diagram below represents a cross-section of the peaks of Table Mountain, T, and Lions Head, L, above sea level. Points M and N are directly below peaks L and T respectively, such that MPN lies on the same horizontal plain at sea level and P is directly below C. MN =3 100m. The angle of elevation of L from N is and the angle of elevation of T from M is @. It is given that tanO=0,35 and tanf#=0,21. T L Cc tan 8 = 0,35 tan B = 0,21 0 qc B x M 3 100 m P 7A Calculate the ratio of LM: TN. (4) 7.2 A cable car, C, travelling from the top of Table Mountain, T, follows a path along TCM. 7.21 Calculate the angle formed (MTN) between the cable and the vertical height TN. (2) 7.2.2 If the cable car, C, travels along the cable, such that TC = 400 m, calculate the height of the cable car above sea level at that instant. (5) [11] Copyright reserved FUN ANAC UO A EE A Please tum over

Downloaded from hlayiso.com Mathematics/P2 9 DBE/November 2016 CAPS - Grade 10 Give reasons for your statements in QUESTIONS 8 and 9. QUESTION 8 8.1 Complete the following statement: If the opposite angles of a quadrilateral are equal, then the quadrilateral ... qd) 8.2 Use the sketch below to prove that the opposite sides of a parallelogram are equal. A D (6) 8.3 In the sketch below, KPMN is a parallelogram. ON bisects KNM and OM bisects NMP. 8.3.1 Show that NOM = 90°. (3) 8.3.2 Prove that O is the midpoint of KP. (6) [16] Copyright reserved FUN ANAC UO A EE A Please tum over

Downloaded from hlayiso.com Mathematics/P2 10 DBE/November 2016 CAPS - Grade 10 QUESTION 9 91 Complete the following statement: The line through the midpoint of two sides in a triangle is parallel to and ... the third side. Q) 9.2 In APQR, A and B are the midpoints of sides PQ and PR respectively. AR and BQ intersect at W. D and E are points on WQ and WR respectively such that WD =DQ and WE=ER. Prove that ADEB is a parallelogram. (5) [6] TOTAL: 100 Copyright reserved FANN AMALIA EA

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