Mathematics Grade 10 IEB Paper 2 November 2013 Question Paper

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Downloaded. from hlayiso.com | iiiouainer | ¥ education November Examination Grade 10 Mathematics Paper 2 Time: 2,5 hours Total: 100 ® Session: 1 Date: 16 November 2013 i - ae i } Section A Section B ; | —— — Question 1 2 3 4 5 6 7 & 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 Instructions: 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. rr ba a — tas nen Gr 10 November Examination: Paper 2 Page 1 > De S| ee

= | > Downloaded from hlayiso.com Question 1 Section A 1.1 The table below reflects the size of each of the nine provinces in South Africa, as provided on the site http://www.southafrica, info/about/facts.htm#provinces. my ond ¥ education 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 1.1.1 Calculate the value of x (2) 1.1.2 What is the median province in South Africa? {2) 1.1.3. Determine the mean province size. (2) i — 2 RE aor we Gr 10 November Examination: Paper 2 Page 2

=| HD Downloaded from hlayiso.com 4.2 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.) (3) EYE COLOUR FREQUENCY ! ANGLE ~ 7 Blue 12 | Brown 9 Dark Brown 4 Green 5 TOTAL 30 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) 2.1.2 What is the gradient of the line x = 2? (1) — oo ———- een Gr 10 November Examination: Paper 2 Page 3 Y Pd ¥ education

Downloaded from hlayiso.com 2.2.1 (3) the value of a. "The figure ABCD is a trapezium. Determine Bt 4} D(C; -1} 2.2.2 (2) ACH 4) D5; 8) J 4 Va B (6-5) @0) Calculate the length of the diagonal BD of the kite, given points B (-6; -5) and D (5; 6). Leave answer in surd form. 2S Re ST OB) 2) U | a | gee Se Br I Gr 10 November Examination: Paper 2 Page 4

Downloaded from hlayiso.com Question 3 3.1.1a} In which quadrant does the terminal arm of an angle of 182° lie? (1) 3.1.1b) (4) Roughly illustrate an angle of 45° on the Fs Cartesian grid alongside. 3.1.4¢) (2) Give 3 answers for the ratio tan a in the figure on the left. | = = rs ass __* pre eee Ble ee en Re Sr Gr 10 November Examination: Paper 2 Page 5

Downloaded from hlayiso.com 3.1.2 (2) What is the height of your kite if it is flown at an angle of 52° on a 15m long string? 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. Gr 10 November Examination: Paper 2 Page 6 | S| TY | cate vs = —_ @

Downloaded from hlayiso.com 3.2 lf tan@ = = and @ & [0°; 90°], determine the value of 3 sin @ + cos @ without the use of a calculator. (4) 3.3. Calculate the value of: 2tanx+4 a) —_—— given; x = 104,2° and y = 241,7°. (2) b) A given: tan A = 2sin35° and A & [180°: 360" (3) Sr ew tee ee = —=_ — ——— =— aa Gr 10 November Examination: Paper 2 Page 7

tid Downloaded from hlayiso.com c) cosA+2 tan) given: A= 229,8° (3) Question 4 44 Find the size of the angles ato g (in that order), giving reasons. Lines AB and CD are parallel, Lines AD and DC are equal in length. (7) Statement Reason 0 se Gr 10 November Examination: Paper 2 pe

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> 4.2 Downloaded from hlayiso.com In the diagram below QS|[TV; PQIIST; QT = TR = 9 emand PS = 15 cm. Pp s5em as Som t fom R 4.2.1 Prove VR = 7 cm. (4) 4.2.2 a) Calculate PQ if PQ = =vr (2) Gr 10 November Examination: Paper 2 Page 10

Downloaded from hlayiso.com b) Hence prove that angle PQR = 90° (2) 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 < 300 300 <x < 500 500 < x < 700 700 <x < 900 900 <x < 1100 EL re) es 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) 5.1.3 Plot a histogram from the information in the table in 5.1.1. (2) Gr 10 November Examination: Paper 2 Page 12

i> 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) 6.2 (2) | if DC is extended to E such that DC = CE, } find the values of a and b. E (a,b) (61) B (1,0) / (4,-2) a AG) | : | A oe Re =—s Gr 10 November Examination: Paper 2 Page 13 a ee dn

Downloaded from hlayiso.com 6.3 Each successive triangle is half the height of the previous one. Find the perpendicular height DY of ADCE, given AB = BC = 10 mand AC = 6m. (2) . ; Ne 25 a, K a we ™ | ne x x coo YO e —- ss Question 7 7.1 {fA and B are complementary angles, and sin A = = make use of an appropriate diagram and determine, without the use of a calculator, the value of 3sin dA +5 cos 8, (6) pore Gr 10 November Examination: Paper 2 Page 14

Downloaded from hlayiso.com i | 7.2 (5) ‘Use the accompanying sketch and PROVE the | trigonometric identity sin’X +cos*X = 1 x y Ye Liz ou: ee oven ove Gr 10 November Examination: Paper 2 Page 15 samconite | WY Semen

Downloaded from hlayiso.com In the figure: angle EAR = 28,2° angle CEF = 48,3° AE = 64,8cm AB = 98,4cm Calculate to one decimal place: 7.3.1 RB (3} [ | | | | 7.3.2) BC (4) a Gr 10 November Examination: Paper 2 Page 16 fy nr ¥ saveaton H = | vip)

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