Mathematics Grade 10 IEB Paper 1 November 2015 Memo

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BROUGHT To YOU BY GP education | datacentrix | v: NOVEMBER EXAMINATIONS 2015 MATHEMATICS PAPER 1: GRADE 10 Marks: 100 Time: 2 hours SESSION: 1 Date: 13 November 2015 Name of Learner: M Emme | Grade: Name of Teacher: (Please circle) For Examiner's use only: SECTION A SECTION B Question 3 4 8 9 Cognitive Levels Actual Mark 2 2 Possible Mark Marker’s == fee Mp8 Signature amin : I Read the following instructions carefully: This examination paper consists of 13 pages and 9 questions. Please check that your paper is complete. Read 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. Only non-programmablie, non-graphical calculators are permitted. ALL CALCULATIONS AND WORKING DETAILS MUST BE SHOWN. Itis in your own interest to write legibly and to present your work neatly. Unless otherwise stated, round off to ONE decimal place, where necessary. Note that the diagrams and sketches are NOT drawn to scale. Ord ¥ ‘education =<~ Grade 10 Mathematics Paper 1 — November 2015 Page 1 of 13

joaded.from, SECTION A QUESTION ONE: [9 marks] Simplify the following fully: 14 (2a-1)(a~3) (2) = Qa —- ba-a +3 Ym zs Qa —Ta ts SA on 1.2 13 (2) x-1 x4+i1 a (te) = 3 (2-1 Cre t) Cert), Va. < - aw ta laa vy lve - 1) Z m= 2 (72-1) = — 2 4a (ani) (oe -1) t+ 13° 52%-1 25*41 5 (3) 252% a _ oF -t 5 ECeery Ss o ff Zan s Berle Be TEPEE KYX a ot = 2 Sia 14 3% 43% ‘mM a 2 3% 4% ( 143 ) (2) rare oOo; we dee = 3 ainesiatit ¥ ‘education “~ Grade 10 Mathematics Paper 1 — November 2015 Page 2 of 13

— QUESTION TWO: Factorise the following fully. 2.1 m2 —2m+1 [8 marks] er fm —1\ Y vi 3x2 -—3 2 3 fn ~1) “a = 3 (wet \(w~!) “4. ax? — x? — 4ay? + 4y? 2 x (a~i\-& fa 1) 4h 7) a (a —') Ger ky) 2 (a-\)Ger2\Ge—ay) Ya Express this number line in interval notation: & WE pas a) V2 =~ Grade 10 Mathematics Paper 1 — November 2015 Page 3 of 13

QUESTION THREE: [8 marks] 3.1 Solve these equations for x: B11 ytog l. pee ee 3 2) x 3.12 2x-3 2x (3) 3 aaa 2 (ane -3) — idan 5 Qe . Wa Sa ke —-6& — |S@n 2 Boe — Uw = £ m2 r9 3.2. Solve for x and y: x+2y=1 and 2x+3y=6 (3) wn |[— 2 Kad (da 235 2b dx tea = 2\. B= Uy 434 eb Query = =o] a = uy ‘o) S —& S21 - 2 (-4) 2 AKA a 2etu(-u) = 2 a aA) Pre =1% 4 2-4 4a Grade 10 Mathematics Paper 1 — November 2015 Page 4 of 13

Nowniogaded Trom nlavisa co | QUESTION FOUR: [9 marks] 4.1 On the set of axes below sketch the graphs of f and g where: f(x) =x7-9 and g(x) = 3x-9 (5) Show all intercepts with the axes clearly. 4.2 Write down the range of f. (1) Ke Za 4 > 74. ow [-4} 0) 43 For what values of x is f(x) > g(x)? (2) ug 6g. Lt 44 If f is moved up 5 units, what is the equation of the new function? (1) Le | a = = ¥: Grade 10 Mathematics Paper 1 — November 2015 Page 5 of 13 aes ces

QUESTION FIVE: [6 marks] 5.1 5.2 Harry buys a fridge from Nakro which is priced at R12 700. He takes out a loan with PNB Bank for the full amount. The interest on the loan is 12,3% per annum, simple interest, and he pays off the loan over three years. How much are his monthly repayments, correct to the nearest cent? (3) O- > 2 vows ft + 123 3) = feo = (17386 30 MK 2. Mettlbh. = Bi7386,30 — 36 4 a kU et AT. Me Ul Louis invested a sum of money in November 2010. In November 2015 the amount in the account was R 162 108. If the interest was 6,2% per annum, compounded annually, how much, accurate to the nearest rand, did Louis invest in November 2010? (3) ee 7 - i Pe jo2 'oS = Pf [+ 47} Jere ; ig = Rive seo. 4a _ . ¥= Grade 10 Mathematics Paper 1— November 2015 Page 6 of 13

Nownloaged Tram niavisa com QUESTION SIX: [13 marks] Simplify all fractions fully. 6.1 There are six red tokens and four yellow tokens in a bag. 6.1.1 One token is chosen. What is the probability that a red token is chosen? {1) A P(pet) = & = wre TO 75 i 6.1.2. Two tokens are removed, one after the other, without replacement. What is the probability that they are both red? (Space for a tree diagram has been provided) (2) z 6.1.3. Two tokens are removed, one after the other, with replacement. What is the probability that they are different colours? (Space for a tree diagram has been provided) (3) Y ay az 8 = to ad - & « b 10 16 To 10 | = 43 a tp zx Lt te — lero SD lw | 2 Y datacentilr iy education = $= Grade 10 Mathematics Paper 1— November 2015 Page 7 of 13

6.2 Among a group of 20 boys, 11 play rugby, 8 play hockey and 3 play both sports. 6.2.1 Complete the Venn Diagram to represent the above information, and use the diagram to find the number of boys who play neither sport. (4) A boy is chosen at random. What is the probability that he plays hockey? 6.2.3. A boy is chosen at random. What is the probability that he plays hockey, but not rugby? (2) Le POu tat @) = 2 Lew 20 4 4 rd ‘education _ 7 == Grade 10 Mathematics Paper 1—- November 2015 Page 8 of 13

SECTION B QUESTION SEVEN: [20 marks] 71 Solve forx: ax—b=x (3) 7.2 Solve for x: 5x?2+3 = 8x (4) <A Out —-B% 43 =D. - “et wr ee Ya “a 73 Simplify this expression fully : ——~— (3) pitt ' — t- on |! T° \ mo LY 74 v _ 19 1 ag (3) 2 2 x tt fut. +26) Dtsch » 2 = } 2 iM(ue wi - 4). a i) ? | ee {oy -r)lu-4) le, Ls ae) zo Factorise this expression fully: [=| | i ay = Grade 10 Mathematics Paper 1— November 2015 Page 9 of 13

Simplify as far as possible: 1 yei'x2-1'1-x l a tte ZL \ tee | bree me A 3, Mm we wnt tte - (4) (e+) Ge =19 an — 2 frees) Coens) Lia 2 fx -1) fot) (me = 1) 2. SL a Solve for x : aT 8 vain “~ Grade 10 Mathematics Paper 1—November 2015 Page 10 of 13

QUESTION EIGHT: [17 marks] 8.1 In the diagram there are two functions: a p@) = zt b and q(x) = m.2* +t p and q have the same horizontal asymptote and meet at A(2;—1) q crosses the y-axis at S. Write down the range of p. J eg or * (3) 0) ot G33) Write down the range of q. yak gr (— 96° = 37) Find the values of a and b. b= 37%, Find the values of m and t. ‘aineiialt 4 ‘educabon ~~ Grade 10 Mathematics Paper 1— November 2015 Page 11 of 13

8.2 The lines EAB and CD are perpendicular to the x-axis. In the diagram two functions are shown: f(x) = 16—x* and g(x) =x+4. Y f B D g —E -+O c x 8.2.1 If OE is 2 units, calculate the lengths of AE and BE, and hence find AB. (4) Lon mes (-+4 ze 2 gE > tb-(-2.y = 2. VAS > ee wan = lo i t. 8.2.2 If CD is 7 units, calculate the length of OC. (4) ag AA “a 7? = Ib — x Pa ca! ~ Oo Aon (m -2) (s+ +>) 2 O Ym ‘ oc = 2B niles “~ ns dw | @ | TY | cammcotr gs i cal Oca “=~ Grade 10 Mathematics Paper 1— November 2015 Page 12 of 13

QUESTION NINE: {10 marks] 9.1 Solve this inequality for x and show the solution on a number line: (4) 9.2 9.3 i> -1<2-3x <8, xER —3<-%< 6.4%" lo > we D2 “ae —-32<4~%€2 L. 4 : Sf Sb-d Ma What is the 2015" letter in this pattern? MATHMATHMATHMATHMA............ {2) Show your working clearly. Anos =u hee rem 2m tos” Sts & TT. Aa Nial and Liam each deposited the same sum of money into accounts at One Direction (4) Bank in January 2010. The deposits earn the same simple interest paid annually. After four years, in January 2014, Nial has R1980 and after seven years,in January 2017, Liam has R2340. What was the initial deposit that both made, and what rate of simple Interest did they earn 1430 = P(ts bia), \Y 2340 : P Cis 2.7). / ABO. 28K% = tae f+7e Vy [180 + 138600 = 28204860), |“ Ueeo ec = 260 J fC ahh Aa fchisen “Wa TOTAL 100 MARKS Ord vs _~ Grade 10 Mathematics Paper 1— November 2015 Page 13 of 13

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