Mathematics Grade 11 P2 Gauteng November 2016 Question Paper

Downloaded from hlayiso.com basic education SE. y y Department: 4 Ky Basic Education SSG REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 11 i MATHEMATICS P2 i: F NOVEMBER 2016 : Cee ee ee ee ee MARKS: 150 TIME: 3 hours This question paper consists of 13 pages and a 22-page answer book. ANN *L6P2* Copyright reserved FUN ANAC UO A EE A Please turn over

Downloaded from hlayiso.com Mathematics/P2 2 DBE/November 2016 NSC - Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of 12 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 may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. Write neatly and legibly. Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 3 DBE/November 2016 NSC - Grade 11 QUESTION 1 The table below shows the number of cans of food collected by 9 classes during a charity drive. 5 8 15 20 25 27 31 36 75 1.1 Calculate the range of the data. qd) 1.2 Calculate the standard deviation of the data. (2) 1.3 Determine the median of the data. qd) 1.4 Determine the interquartile range of the data. (3) 1.5 Use the number line provided in the ANSWER BOOK to draw a box and whisker diagram for the data above. @) 1.6 Describe the skewness of the data. qd) 1.7 Identify outliers, if any exist, for the above data. qd) [12] QUESTION 2 The table below shows the time (in minutes) that 200 learners spent on their cellphones during a school day. TIME SPENT (IN MINUTES) FREQUENCY 95 <x<105 15 105<x<115 27 115<x<125 43 125<x<135 52 135<x< 145 28 145 <x< 155 21 155 <x< 165 10 165<x<175 4 2.1 Complete the cumulative frequency column in the table provided in the ANSWER BOOK. (2) 2.2 Draw a cumulative frequency graph (ogive) of the data on the grid provided. (3) 2.3 Use the cumulative frequency graph to determine the value of the lower quartile. (2) 2.4 Determine, from the cumulative frequency graph, the number of learners who used their cellphones for more than 140 minutes. (2) [9] Copyrigherssened FUN ANAC UO A EE A Peseta over

Mathematics/P2 4 DBE/November 2016 Downloaded from hlayiso.com NSC - Grade 11 QUESTION 3 In the diagram, A(6;— 2), B(2; 15) and C(—4; 3) are the vertices of AABC. M is the midpoint of AB. N is a point on CA such that MN || BC. 3.1 3.2 3.3 3.4 3.5 Copyrigherssened FUN ANAC UO A EE A Peseta over ~ y B(2 ; 15) C4 ; 3) ve fe) | A(6 ; -2) Determine the coordinates of M, the midpoint of AB. Determine the gradient of line MN. Hence, or otherwise, determine the equation of line MN, inthe form y=mx+c. Calculate, with reasons, the coordinates of point N. If ABCD (in that order) is a parallelogram, determine the coordinates of point D. (2) (3) (2) (4) (4) [15]

Mathematics/P2 5 DBE/November 2016 Downloaded from hlayiso.com NSC - Grade 11 QUESTION 4 In the diagram, R and A are the x- and y-intercepts respectively of the straight line AR. The equation of ARis y= -pxe4. Another straight line cuts the y-axis at P(O0; 2) and passes through the points M(k;0) and N(3 ; 4). a and £ are the angles of inclination of the lines MN and AR respectively. 41 4.2 43 44 Copyrigherssened FUN ANAC UO A EE A Peseta over Le Ay 4 ) R\ Given that M, P and N are collinear points, calculate the value of k. Determine the size of 8, the obtuse angle between the two lines. Calculate the length of MR. Calculate the area of AMNR. (3) (4) GB) (3) [13]

Downloaded from hlayiso.com Mathematics/P2 6 DBE/November 2016 NSC - Grade 11 QUESTION 5 5.1 In the diagram below, P(-8 ; f) is a point in the Cartesian plane such that OP = 17 units and reflex XOP=0. y (| oO x 17 P(-8; 1) $5.11 Calculate the value of ¢. (2) 5.1.2 Determine the value of each of the following WITHOUT using a calculator: (a) cos(—0) (2) (b) 1-sind (2) 5.2 If sinl7°= a, WITHOUT using a calculator, express the following in terms of a: 5.2.1 tan17° (3) 5.2.2 sin 107° (2) 5.2.3 cos” 253° + sin? 557° (4) 53 Simplify fully, WITHOUT the use of a calculator: cos(—225°).sin 135° + sin 330° 6) tan 225° ae 1 -1 5.4 Prove the identity: =, 5 (4) (cosx+1)(cosx-1) tan*x.cos*x 5.5 Determine the general solution for 2sin x.cos x =cos x. (6) [31] Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 7 DBE/November 2016 NSC - Grade 11 QUESTION 6 In the diagram the graphs of f(x)=cosx and g(x)=sin(x+b) are drawn for the interval —180°< x < 90°. ty | 30 30 90” 4 1 (st 4 6.1 Write down the value of 5. qd) 6.2 Write down the period of g. qd) 6.3 Write down the value(s) of x in the interval -180°< x <90° for which S(x)— g(x)=0. (2) 6.4 For which values of x in the interval -180°< x < 90° is sin(90°-x) > g(x)? (3) 6.5 The graph of h is obtained by shifting f 3 units upwards. Determine the range of h. (2) 9] Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 8 DBE/November 2016 NSC - Grade 11 QUESTION 7 7A In the figure below, acute-angled AABC is drawn having C at the origin. . B x | , TAA Prove that c? =a? +b? —2abcosC. (6) b b- 4 71.2 Hence, deduce that 1+cosC= (at b+ lat b—oe) 4) 2ab 72 Quadrilateral ABCD is drawn with BC=235m and AB=90,52m. It is also given that ADB =31,23°; DAB=1 09,16° and CBD = 48,88°. A Determine the length of: 721 BD (3) 7.2.2 cD (3) [16] Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 9 DBE/November 2016 NSC - Grade 11 QUESTION 8 The diagram below shows a water tank which is made up of a cylinder and cone having equal radii. The height of the tank is 1,8m and the radius is 0,5 m. The angle between the perpendicular height, AB, and the slant height, AC, of the conical section is 35,5°. Volume of cone aperh Total surface area of cone =r? +21 Volume of cylinder = 1r7h Total surface area of cylinder = 2777+ 2arh 1,8m 8.1 Calculate the perpendicular height, AB, of the cone. (2) 8.2 When the tank is full, an electric pump switches on and pumps the water from the tank into an irrigation system at a rate of 0,52 m’/h. The pump automatically switches off when the tank is 7 full. Calculate how long, in hours, the pump feeds water into the irrigation system. (4) [6] Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 10 DBE/November 2016 NSC - Grade 11 Give reasons for your statements and calculations in QUESTIONS 9, 10, 11 and 12. QUESTION 9 91 Complete the statement so that it is TRUE: The angle subtended by an arc at the centre of a circle is ... (2) 9.2 O is the centre of circle TNSPR. POS=60° and PS =NT. T N R 1 P s Calculate the size of: 9.2.1 PRS (2) 9.2.2 NST (2) [6] Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 11 DBE/November 2016 NSC - Grade 11 QUESTION 10 D, E, F, G and H are points on the circumference of the circle. G, =x+20° and H=2x+10°. DEI| FG. 10.1 Determine the size of DEG in terms of x. (2) 10.2 Calculate the size of DHG. (4) [6] Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 12 DBE/November 2016 NSC - Grade 11 QUESTION 11 O is the centre of the circle PTR. N is a point on chord RP such that ON 1 PR. RS and PS are tangents to the circle at R and P respectively. RS = 15 units; TS =9 units; RPS = 42,83°. P d | 15 R 11.1 Calculate the size of NOR. (5) 11.2 Calculate the length of the radius of the circle. (4) [9] Copyrigherssened FUN ANAC UO A EE A Peseta over

Downloaded from hlayiso.com Mathematics/P2 13 DBE/November 2016 NSC - Grade 11 QUESTION 12 12.1 Use the diagram below to prove the theorem which states that EFG = EDF. D. F G (5) 12.2 In the diagram below, BOC is a diameter of the circle. AP is a tangent to the circle at A and AE=EC. P Prove that: 12.2.1 BA||OD (4) 12.2.2 AOCD is a cyclic quadrilateral 6) 12.2.3 DC isa tangent to the circle at C (4) [18] TOTAL: 150 Copyrigherssened FUN ANAC UO A EE A Pa

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