Gr10 Math P2 (English) November 2017 Question Paper_hlayiso.com_.pdf

basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 10 Hi MATHEMATICS P2 Hi i au i u i NOVEMBER 2017 " Mee als See Se Sele ae ee ele a eee ale eels 6 Sete Sle Ste 2 Se See MARKS: 100 TIME: 2 hours This question paper consists of 10 pages and a 15-page answer book. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 2 DBE/November 2017 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 have used to determine the answers. Answers only will NOT necessarily be awarded full marks. 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. Please turn over

Downloaded from hlayiso.com Mathematics/P2 3 DBE/November 2017 CAPS — Grade 10 QUESTION 1 The data below shows the number of laptops sold by 15 sales agents during the last financial year. 43 48 62 52 46 90 58 37 48 73 84 68 54 34 78 1.1 Determine the median of the number of laptops sold. (2) 1.2 Calculate the range of the data. (2) 1.3. Calculate the interquartile range (IQR). (3) 1.4. Draw a box and whisker diagram for the data above. (3) [10] QUESTION 2 A learner did a project on climate change. At 14:00 each day, she recorded the temperature (in °C) for a certain town. The information is given in the frequency table below. TEMPERATURE (IN °C) | FREQUENCY 20<T <24 2 24<T <28 4 28<T <32 9 32<T <36 5 36<T <40 7 40<T <44 3 2.1 For how many days did the learner collect the data? qd) 2.2 Write down the modal class for the data. qd) 2.3. Estimate the mean of the data. (3) 2.4 Calculate the percentage of days on which the temperature was at least 28 °C. (2) [7] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 4 DBE/November 2017 CAPS — Grade 10 QUESTION 3 In the diagram below, P(7 ; 4), Q(6; 6), R(O; 3) and S(¢ ; k) are the vertices of quadrilateral PQRS. R(;3) K 7 Spa;a) x 0 3.1 Calculate the length of PQ. Leave your answer in surd form. (2) 32 6If (3: 3) is the midpoint of QS, determine the coordinates of S. (3) 3.3 If the coordinates of S are (1; 1), show that PR=QS. (2) 3.4 Showthat QR 1RS. (4) 3.5 Hence, what type of special quadrilateral is PQRS? Motivate your answer. (2) 3.6 Calculate the size of RSQ. (3) [16] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 5 DBE/November 2017 CAPS — Grade 10 QUESTION 4 4.1 Given 4cot@+3=0 and 0° <6 <180°. 4.1.1 Use a sketch to determine the value of the following. DO NOT use a calculator. (a) cos@ (A) 3sin A sec O (b) ae (4) 4.1.2 Hence, show that sin?0 -1=—cos’0. )) 42 Simplify the following expression WITHOUT using a calculator: cos30° tan 60° + cosec 745° sin? 60° (3) 43 Solve for @ correct to TWO decimal places, if Sind =c0s37" and 0°<@<90°. Q) [16] QUESTION 5 Given f(x)=sinx—1 and g(x)=2cosx for 0°<x<270°. 5.1 Sketch, on the grid provided in the ANSWER BOOK, the graph of f and g for 0° <x<270°. (6) 5.2 Write down the following: 5.2.1 Amplitude of g qd) 5.2.2 Rangeof f (2) 5.3 Use your graph to determine the following: 5.3.1 Number of solutions to f(x) = g(x) in the interval0° < x < 270° (ql) 5.3.2 Value(s) of x inthe interval 0° <x<180° forwhich sinv =2+2cosx ra Copyright reserved Please turn over

Downloaded from hlayiso.com CAPS — Grade 10 Mathematics/P2 DBE/November 2017 QUESTION 6 RQ isa vertical pole. The foot of the pole, Q, is on the same horizontal plane as P and S. The pole is anchored with wire cables RS and RP. The angle of depression from the top of the pole to point P is 47°. PR is 21 mand QS is 17m. RPQ=8. ceee ee --2- =p =4 R aos/ : 21m / f ’ \ / \ ‘@\ CI p- Ss R 17m 6.1 Write down the size of @. QQ) 6.2 Calculate the length of RQ. (3) 6.3 Hence, calculate the size of §. (2) 6.4 If P, Q and § lie ina straight line, how far apart are the anchors of the wire cables? (4) [10] Copyright reserved Please turn over

Downloaded from Mathematics/P2 7 CAPS -- Grade 10 QUESTION 7 hlayiso.com DBE/November 2017 The diagram below shows the cross-section of a solid made up of a hemisphere placed on top of a right circular cone with radius r and slant height s. h, is 6,5 cm and the volume of the cone is 83,38 cm’. The perpendicular height of the cone, Formulae: Surface area of sphere = 47 r? Volume of sphere = an r Surface area of cone= ar? +27 Volume of cone = 3 rh Calculate, correct to TWO decimal places: 7.1 Theradius, r, of the cone 7.2 The slant height, s, of the cone 7.3. The surface area of the solid Copyright reserved Please turn over 2) 2) (2) [6]

Downloaded from hlayiso.com Mathematics/P2 8 DBE/November 2017 CAPS — Grade 10 Give reasons for ALL statements in QUESTIONS 8 and 9. QUESTION 8 8.1. KLMN isa rhombus with diagonals intersecting at O. LKM =34°. K | L N ' M 8.1.1 Write down the size of 6,. () 8.1.2 Calculate the size of t,. (2) 8.1.3 Calculate the size of KNM. (2) 8.2 Given parallelogram PQRS with diagonals PR and QS intersecting at M. Prove that the diagonals bisect each other. (4) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 DBE/November 2017 CAPS - Grade 10 8.3. Inthe diagram, ABCD isa parallelogram with diagonals intersecting at E. The diagonals of parallelogram DECF intersect at G. The diagonals of parallelogram FGCH intersect at K. Prove that DB = 4KC. (4) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 10 DBE/November 2017 CAPS — Grade 10 QUESTION 9 AABCis right-angled at B. F and G are the midpoints of AC and BC respectively. H is the midpoint of AG. E lies on AB such that FHE isa straight line. B A 91 Prove that E is the midpoint of AB. G3) 9.2 If EH =3,5cm and the areaof AAEH =9,5cem’, calculate the length of AB. (3) 93 Hence, calculate the area of AABC. (3) 19] TOTAL: 100 Copyright reserved