Mathematics Grade 10 IEB Paper 2 June 2012 Memo

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Downloaded from hlayiso.com BROUGHT TO YOU BY JULY EXAMINATIONS 2012 MATHEMATICS PAPER II: GRADE 10 Marks: 100 Time: 2 hours Date: 31 July 2012 SESSION: 1 MEMO Grade: Name of Learner: Name of Teacher: (Please circle) For Examiner’s use only: SECTION A SECTION B Question 1 2 3 4 5 6 7 8 9 10 | 21 | 12 Total Learning LO3 | LO3 | LO3 | LO3 | LO3 | LO3 | LO3 | LO3 | LO3 Outcomes Cognitive Levels Actual Mark Possible 9 15 17 3 7 4 6 8 8 12 4 7 100 Mark Read the following instructions carefully: 1, This examination paper consists of 15 pages and 12 questions. Please check that your paper is complete. 2. ead the questions carefully. Take note of the mark allocation and the wording of the questions. Answer ALL the questions on the question paper in the spaces provided. 3 4. Only non-pragrammable, non-graphical calculators are permitted. 5. ALL CALCULATIONS AND WORKING DETAILS MUST BE SHOWN. 6. It isin your own interest to write legibly and to present your work neatly. 7. 8 Unless otherwise stated, round off correct to TWO decimal places, where necessary, Note that all diagrams and sketches are NOT drawn to scale. ~—e| .. Grade 10 Mathematics Paper ll — July 2012 Page 1 of 15

Downloaded from hlayiso.com Formulae you may need for this examination: - x +x + d= VQ, —41)? +0, - 1)? meas (4 aed Xy —% SECTION A QUESTION ONE: [9 marks] 1.20 IfA=112,4°, B= 48,6° and C = 12,1°; calculate the following, correct to two decimal places: 1.1.2 cos(A—B) (2) = Cos (63;8°) ~ : = 0 - 74 Q 1.1.3 3 cot3C (2) = 3 ot (3xniv = 4, 08, VA @ | 1.1.4 cosec (=) (2) ] = Cosec (Ba +8,6") | = Cosec (31,4°)“ = 139 ~~ @) | 1.2 Solve for the unknown angle in the equation below: | 3 cosB = 2,1 {2) | cos B= 057 va p= 45, 57° ~— Q .. Grade 10 Mathematics Paper {I —July 2012 Page 2 of 15

Downloaded from hlayiso.com QUESTION TWO: [15 marks] 2.1 No calculator is allowed for this question. If 17cosB + 15 = 0 and sinf < 0, determine, with the aid of a diagram, the value of the following expressions: 211 tan2e@t+1 21.2 2cosB + = sing I7cos BTIS =O Osp = EV ond yw B<O 2 Bom apsdrut 3; ont H2-IS and ral. 7*-Cis) Chytnas) By 234 — 225 2.2 In which quadrant does 0 lie if 0° < 9 < 360° and 2.2.1 cos? <0 & sin@ <0? 2.2.2 sin@>0O & tand<0? 3 7 2 @ conan = csuuny GFAd@ 10 Mathematics Paper lt —July 2012 Page 3 of 15

—————— 2.3 Downloaded from hlayiso.com Cisthe foot of a vertical tower DC. From a point P, 28m from C, the angle from P going up to Dis 46° (i.e. DPC). 2.3.1 Draw a sketch of the above scenario. danbibo (4, 280% rset) Order of Poti on AL~ 2.3.2 Determine the height of the tower. Fe = tone? be = 28 tan 4e° be = 24m _ (28,99) / Q Hea Sh twee = 29) wud, cum GFAde 10 Mathematics Paper |i — July 2012 Page 4 of 15

Downloaded from hlayiso.com QUESTION THREE: [17 marks] AABC has co-ordinates A(—4; 2), B(1; 2) and €C(—1;6), and AC = 5 units. 3.1 Determine the lengths of AB and BC. Leave your answers in surd form. (4) AB = 5 units, uw 7 Lo “ be = Jen 2 BCl.2) ; CC1;6) Be a0 unt a 3.2. What kind of triangle is AABC? Give a reason for your answer. (2) AApc is |sosceles. “ (Ag =Ac)~ © Grade 10 Mathematics Paper II ~ July 2012 Page 5 of 15

Downloaded from hlayiso.com 3.3 Determine the co-ordinates of M, the mid-point of AC. AC-4.2) c(-1;6) Am = stu Um = 221 = -£ = 4 2 MCE ay 3.4 co-ordinates of D. If D is the point (x;y), such that nas 7) is the midpoint of CD, determine the =% > Determine the gradients of the line segments AC, AB, BD and CD. 3.5 AC-#,2), BCK2),CC1 6), D(sk-3) on BaaE Vac = Sev = ul Mer = e4su WA PA =z g—é vt Mae =. Tr = 0 Mp = oa = (4) WA 7 | 3.6 What type of quadrilateral is ABDC? Give a reason for your answer. Mac = Mean > Ac || ap! y “YY s. ABDC is a Trapezium } von Gade 10 Mathematics Paper II ~July 2012 Page 6 of 15

QUESTION FOUR: Carefully study the diagram below. Calculate the value of x, y and z (in alphabetical order), with Downloaded from hlayiso.co [3 marks] reasons. A 70° Statement Reason | 2x+10° = 7° Corr Lis ; Adi] EF Qn = 60° x = 30° “ 7 2x tw +5y +45° = 180° Sum of Ls bk Agee 7 oo tio + Sy +45" = [80° Su = 65" scm, Grade 10 Mathematics Paper —July 2012 Page 7 of 15

1 HE | QUESTION FIVE: 5.1 c Refer to the figure above and prove AABC /// ADBA. {7 marks] Statement in ARBC and A baa \- AA COnmen 1 2. wy) poth equal WW U4 By Ai L.-J b >, Arec \lAbaa™ | £,e,6 U1 CH) 5.2 Calculate AB if BC = 15cm an d DC = 8cm. Round off your answer to 1 decimal place. = Tem > toot ( Arec II] ASBA) i? ecg, OFade 10 Mathematics Paper II — July 2012 Page 8 of 15

Downloaded iSOCOmM QUESTION SIX: Determine whether A(—2; 3), B(1; 4) and C(—4; 1) are collinear. rc Mae = eet sev =) <A, p amd ©. Mec = ee SU ane not “Collnreac. —— == ; | | Mae = SEF (H) he = Ree i | | “Wa thinking pf a number belerpen {7s.25¢6 and f roa 4:3 sed a gins _, ....,., Grade 10 Mathematics Paper Il —July 2012 Page 9 of 15

Downloaded from SECTION B QUESTION SEVEN: [6 marks] Solve for the unknown angles in the equations below: cotO+s =5 (3) 71 Zz cot @ +5 = 10 Cot = 5 ~ ban G= 0;2 wv oz ia w~ © f 72 3sin(E- 40°) =2 £40? = 41, 3103... Be = 81, 8103--- - o Uw p= 163, 62 3) QUESTION EIGHT: [8 marks] Calculate a in each of the following cases: 8.1 The distance between (2; 3) and (6; a) is 5 units. (5) /Co-2) + (a3y = 5X lo + a —b6at4 = 25 aba =O aCa-6)=0 : =o" oF Aa=G ——— a 7 aS seam, Grade 10 Mathematics Paper Il — July 2012 Page 10 of 15

Downloaded from hlayiso.com PQ has a gradient of —= where P(2; a) and Q(3; —6). _—G-aul_ =2 0 a ee BC-6-a) = -2 —Bea—-l%=-2 -Za= 16 a are) 3 = QUESTION NINE: [8 marks] Given: AD = 90°, AC_L BD, B = 70° and AB = 40mm. Calculate the length of CD. A AC sino? 1 Ac = 40 Sin 7 AC = 31,54¢mm ~~ A . . B = t80%a0° 10" Cum of US 6 AABD) 20° Continue your answer on the next page... _., Grade 10 Mathematics Paper I! — July 2012 Page 11 of 15

Downloaded from hlayiso.com QUESTION TEN: [12 marks} Doe eeneeeeee ee ee eee > ve ee ee eeeneeeeeee nee c E/48,3° 4 F In the diagram it is “A ‘ u given that: DC//AB; oud AE = 64,8 m; > oo AB = 98,4 m and EFBR is asquare 28,2° C1 ' A B Bim Determine the following: 10.1 Length RB. ; Wt RR cos 28,9°%= gage! AR = 64,8 cos (28,2 2 AR = STm_ = - RB = AWB4m — ST Mm ae I A ade Wik seen, Grade 10 Mathematics Paper ji —July 2012 Page 12 of 15

10.2 LengthCB. Downloaded from hlayiso.com tan 4g 3 V_ ceY! CF = 41,24 x tan(y9,2) CF 46 Am ~~ Ce A HV 24m + 46,34tm (FOR Aa Sapnare ) 31,63) ~~ vovi ec wnt (4) 10.2 CAE tancAp= ce AG banche = banka = 37,62 Fs 4 eal 0,89054. +1 Che = 4169 — CRE = +1, 6% —28,0° = 3,49" (3) # dagrte symbole 10.4 DCA Catt Us , Kell aa) 2) aatncentFtt Grade 10 Mathematics Paper il —July 2012 Page 13 of i5

Downloaded from hlayiso.com QUESTION ELEVEN: [4 marks] A farmer wants to install new water pipes leading from the farm dam to the farmhouse (A to B) as well as to the two apple orchards (A to C and Ato D). What is the minimum number of metres of piping he has to buy? Round off your answer to the nearest whole number. act = (173,2) - Is0°1 = 2999824 — 22500 = 493,24 »-AC= $6,594m,. 1 ae = (be, sar lo% 7 Chythag 1 = 7497, 8281 — 100 = 1397, 281 $6, olm , +1 rf Ab \ Toy t purus nacded. > 150m +86 ,54m+t 86,01m | "= 302,6m Z = 29Geiwie newest wholé no. Grade 10 Mathematics Paper |! - July 2012 Page 14 of 15

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