Mathematics Grade 10 IEB Paper 2 November 2013 Memo

Downloaded from hlayiso.com TEACHERS WITHOUT BORDERS PROGRAMME BROUGHT TO YOU BY With grateful thanks to our associate partners, The National Department of Basic Education, The Independent Examinations Board, Siyavula Education, Smarticks, Noteshare, Lemonlicious, datacentrix, and most of all, to the schools and teachers from both the public and private education sectors who as founder contributors, have lent content to the Teachers without Borders programme, for the benefit of all South Africa's learners. In Bill Gates words, at the Mandela Day ‘Living Together’ address: “Maintaining the quality of this country’s higher education system while expanding access to more students will not be easy. But it’s critical to South Africa’s future” – working together, we can help achieve this." Contributing schools to date: Clifton School Milnerton High Rustenburg Girls’ High St Peter's Durban Girls' Northwood High St Anne's DC St Stithians Fairmont High Roedean St John's DSG Wynberg Boys' High Herzlia High Rondebosch Boys’ St Mary's DSG Kloof Wynberg Secondary

Downloaded from hlayiso.com BROUGHT To YOU BY November Examination Grade 10 Mathematics Paper 2 Time: 2,5 hours Total: 100 Session: 1 M = M oO Date: 16 November 2013 Section A Section B Question 1 2 3 4 5 6 7 8 Total COG Level 1,2 1,2 1,2 1,2 3,4 3,4 3,4 3,4 Score Max Mark 8 8 20 15 7 7 22 13 100 Marker Signature MK = Mark orce Br Vounctine inclicake On Frent —\ merle " laits | SGuibel s Gy Sopot Instructions: \ J b “re 1, This paper consists of 8 questions and 19 pages including a formula sheet, Please check that your script is complete, 2. Complete all questions neatly and thoroughly. 3. Show all calculations in order to earn marks for method. 4, A calculator may be used unless otherwise stated. Round off your answers to 2 decimal places. aes a Gr 10 November Examination: Paper 2 Page 1

Downloaded from hlayiso.com Section A Question 1 1.1. The table below reflects the size of each of the nine provinces in South Africa, as provided on the site hitp://www.southafrica.info/about/facts.htm#provinces. Province Area (km?) Eastern Cape 169 580 Free State 129 480 Gauteng x KwaZulu-Natal 92 100 Limpopo 123 910 Mpumalanga 79 490 Northern Cape 361 830 North West 116 320 Western Cape 129 370 TOTAL AREA 1219 090 411.1 Calculate the value of x (2) m= 1QIG CFO — (sum ch, thes \yoina) W = W010 km” Vv 1.1.2 What is the median province in South Africa? (1) va n=q Mecltan eaaiders - Ace » _ ih largest - v : Qa = 12 S910 kn* 1.1.3 Determine the mean province size. (2) wes ome VA 2 &SY, UY lem 4 nai Gr 10 November Examination: Paper 2 Page 2

Downloaded from hlayiso.com 1.2. Complete the table, indicating how to calculate the angle size of the sector representing each eye colour in a pie chart. (Do not draw the pie chart) i ceaterh ie ) ts suffered a CAAAGUYO IN fOne EYE COLOUR FREQUENCY | v4 ANGLE Blue 12 N20 Sec” _ oO = % = (4u “ (30 Brown 9 ! © 7 q 266 —- 10% & Zz * Vv Dark Brown 4 Oo o tue” Sug” Green 5 gS 360° _ oS 30 x = 60 V\ TOTAL 30 o DEO Question 2 ALL the answers in this question have to be determined by analytical methods. 2.1.1 Determine midpoint K of the line segment DF, given point D(7; 5) and F(1; 2). (2) kK ( SI - Mit de ) yi = aie) 4 5) YY FECS K Cul 2.1.2. What is the gradient of the line x = 2? (1) W\ doe not ex st — vertical Ling — Gr 10 November Examination: Paper 2 Page 3 ord ¥ education

tid Downloaded from hlayiso.com 2.2.1 (3) The figure ABCD is a trapezium. Determine Bi 4 the value of a. : tbe AS nia 2-4 N= VY am Ons — Ss — \ a-4 ~ ~S \ "C10 Cas s)= (-Yo-u) Y Dil:-4} = —at Ly 2.2.2 (2) DiS; 6) Caiculate the length of the diagonal BD of the kite, given points B (-6; -5) and D (5; 6}. Leave answer in surd form. =|) (e-5)? +(-s-o)2 3 = Jein* + Caidz = fiz ria = far A ZJ2 —4 — Gr 10 November Examination: Paper 2 Page 4

tid kL: i Downloaded from hlayiso.com Question 3 3.1.1a) In which quadrant does the terminal arm of an angle of 182° lie? {1) 2 a) 3.1.1b) (1) Roughly illustrate an angle of 45° on the Cartesian grid alongside. Posiéme angle . anti -c Jock wo rSeO 3.1.16) {2) = Give 3 answers for the ratio tan a in the ’ figure on the left. In ACep: bnaase \ r el aw FE C * E | DH an ADWE * bon a= he VA cH VAN TnoA cups trna=nu Y — Gr 10 November Examination: Paper 2 Page 5 Prd ¥ —

Downloaded from hlayiso.com (2) What is the height of your kite if it is flown at an angle of 52° on a 15m long string? snba°= 4 / he = Nae WA hetghe oO \5 xk Btn Ba 3.1.3 (2) Calculate the angle of elevation @ of the plane if it is at a height of 600 m when itis a horizontal distance of 800 m from the point of take-off. foa6 a 806 Mm Gr 10 November Examination: Paper 2 Page 6

Downloaded from hlayiso.com 3 3.2 if tan@= is and @ & [0°; 90°], determine the value of 3 sin @ + cos @ without the use of a calculator. (4) 3 Bin O@+ co ) =2 \S5 Sti teu hon BB+ CR) veneer Bye ml male F amsuer queen 2 {34 3.3 Calculate the value of: a) — given: x = 104,2° and y = 241,7°. (2) 2 ban Ciou,2°) + Ceca 341, 7° ) | 5 =a 14,0 V subsefeuhors a | b) A given: tan A = 2sin35° and A € [180°; 360°] (3) Lan A=agsn2S” “147 ¥ | ; © y fe Ae IP04RbL = ange Goo | / coset Gr 10 November Examination: Paper 2 - Page 7

Downloaded from hlayiso.com c} cos A+ 2tanS) given: A = 229,8° (3) Cop Bag,8° + 2 Gor (PRE aa, ) ~~ C645 TO ber iw os = OG, boy, S + 2x2, isu) Mm =4 3 —» —4, 166 | ~~ \ Ste onky rounct at enc - Question 4 4.1 (7) Find the size of the angles a to g (in that order), giving reasons. Lines AB and CD are parallel. Lines AD and DC are equal in length. Ti Statement Reason a= Go° VAS ve roe Ps? alt Us =, 4B/|DCW ls = VA isos A ADC bese ls= vas Gr 10 November Examination: Paper 2 Page 8

> Downloaded from hlayiso.com Suny ine Li Az (8? “A Str U's on SEF bine Xe * cpp fe (©8) ay Stepp o us WAN Coreg (2 Usa A gl dc A elt i =, AB/IDG “\ | _—— Gr 10 November Examination: Paper 2 Page 9

Downloaded from hlayiso.com 4.2. Inthe diagram below QS||TV; PQ||ST; QT = TR = 9 cmand PS = 15 cm. D3 oe a> 7 7 Som T ee R Th 4.2.1 Prove VR = 75 cm. (4) In LV RQP 2 Tis micipent o B&R anc Ts || Pa LY e Sts mict pent ty PR 1 Jo S=iSem wv Smmilorky fr A Kes: VS mretpa'nt f skRv yee SMe45)= TE cr a) 422 a) Calculate PQif PQ = =VR (2) PQ = Jey TLS SJ substiburen ~ 6 — + Loetk vats answer fens — Micon Y Lic Be | ania Gr 10 November Examination: Paper 2 Page 10

ti Downloaded from hlayiso.com b) Hence prove that angle PQR = 90° (2) <S; clos 4 a Park = it Ry! Som = =S=t & t GS Y oR PROVE a Re so” — catico (cleo Section B Question 5 5.1 The following figures show the daily income (in rand) for a small business in Sunninghill over a 30 day period. 436 520 980 684 798 842 346 472 591 257 745 763 892 385 427 445 676 848 907 605 412 306 584 527 634 701 549 1002 812 596 5.1.1 Group the data into the 5 equal intervals, and complete the frequency table. (3) income (rand) Frequency 100 < x < 300 | A 300 < x < 500 ZS Vv 500 < x < 700 1O 4 700 < x < 900 Z A 900 <x < 1100 ~ 3 Vv nie mse Gr 10 November Examination: Paper 2 Page 11

1 =| i> Downloaded from hlayiso.com 5.1.2. The owner decides that if he is to keep his business, he has to earn a daily income of R600 or more for at least 60% of the time. By suitable calculation, determine what income the owner is in fact earning 60% of the time. (2) Le 4 Fay 5 Go% mene pct) — go Sot) jem ~ “joe MA Thie fatlo as a) RS6O 8 5c << Qo Trove ane ie youn, SE Se ef, the way Chreugh cakegey = — 500+ w! Valke mm pis catego 4 > Bo Che sd wie CLuner Should eto.fy tive. lousine S 5.1.3 Plot a histogram from the information in the table in 5.1.1. {2} sian eater tea ~ Bin ne sin rand Pa —— aman Gr 10 November Examination: Paper 2 Page 12

ti Downloaded from hlayiso.com Question 6 ALL the answers in this question have to be determined by analytical methods. 6.1 Prove that the points K(2; 3), L(2+4t; 3-5t) and M(2+4u; 3-5u) are collinear for all real values of t and u. {3} Dtae 2 ae 4 ~ —S ._ -S Wy = 3-5u-S = =o uu 4 vo A ‘ oo Pointe are. cllinecy 6.2 (2) If DC is extended to E such that DC = CE, find the values of a and b. OD »rCas CSe& ve (Ky) > (2<44; 443) “,a3n G2 =% yy ACT 3) = Gr 10 November Examination: Paper 2 Page 13 ‘y a | Yee

Downloaded from hlayiso.com 6.3 B . ' oo ' ‘ mn , = 2 ; \ ‘ \ T ZL | a GB 4 Cc y [= S Each successive triangle is half the height of the previous one. Find the perpendicular height of ADCE, given AB = BC = 10 mand AC = 6m. (2) BX? = Ag® — Ax*® Pythegy AX = Bm since = \ot - SZzA DS ABS is [sesceles =i Bx = Var YW : Ja” Ld) = & = Se 4m wm Question 7 7.1 if Aand B are complementary angles, and sin A = =, make use of an appropriate diagram and determine, without the use of a calculator, the value of 3 sin A + 5cos B. (6) ; ketch taps apy & 3 na + Sia 8 7 oketh ole TTS 2 (=) 5.) CR Voubstituten Us = |S j eS +t v Fyfaey St Peter’s College a> NO calculator Gr 10 November Examination: Paper 2 —) So cdecimek or Stas ay 7 Page 14 Wack fer

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