G10 Maths July Paper 1 2012 Memo Generic hlayiso.com

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 Grade 10 Mathematics July Examination Paper 1 Time: 2 hours Total: 100 Date: 24 July 2012 Session: 1 Name: Meme Maths Teacher: A Question 1 2 | 3 Ts 6 7 FY TOTAL LO’s 1 1 1 1 2 1 2 2 Cog Level 1;2 1;2 2;3 233 | 2;3 3,4 1;2;3 | 2;3;4 Score Mark 15 zo | 22 | 11 | 9 11 9 13 100 INSTRUCTIONS: e This test consists of thirteen pages and eight questions. e Work neatly and show all calculations. e Unless stated, give answers to TWO decimal places. e Only non-programmable, non-graphical calculators are permitted. BROUGHT To YOU BY Page 1 | iin | ¥ education

Downloaded from hlayiso.com SECTION A QUESTION 1 1.1 Consider the following list of numbers, and then answer the questions that follow: Oo; v-27 ; vI2; V8; 3,4;-4 ; 14 15 3 1.1.1 Write down any non-real number in the jist. (1) [J _ i727 ae @ 1.1.2 Between which two rational numbers does the irrational number lie? Show ail relevant working in order to obtain full marks. (3) Sq < fz 2 Je uw i Band & + @ 1.1.3 Convert the recurring decimal to a rational fraction in the form 3 b#0, (4) leh xe = 3, Guy ~---. © — _ Q -O qe BM 12° 3 o BROUGHT To YOU BY w | | @ if Uj datacentrix ¥ education Page 2

Downloaded from hlayiso.com 1.1.4 Add the two real numbers closest to each other, but NOT EQUAL to each other. (2) a i @ 15 Vv ae = ~3 at(-2) = _O 1.2. Aset of numbers is represented on the number line below: F r n a q 3 -i -l g@ 1 2 3 4 1.2.1, Use inequalities to describe the set of numbers. (2) Vv! —3< x Sur xe R — @) 4.2.2. What is the smallest integer in this set of numbers? (1) ~3 ua Cy) 1.2.3. Express in interval notation. (2) Casa] @ [15] BROUGHT To YOU BY w | | a iy L} datacentix” ¥ education Page 3

Downloaded from hlayiso.com UESTION 2 Factorise the following: 2.1 3x3 —12x (2) Bx 20-4) 2.2 2x? -—5x—3 (2) : > (Me DS GS 2.3 Sxy—3y+10x-6 (3) = 4 ( Sx- 3) $Q(Sx-B) i 2.4 8x3 —27y% (3) =(axayy(ux' reas 41y) , Q) [10] QUESTION 3 3.1 Simplify the following: aa1 SZ _ =e (4) wr —— ~ aan 1S ua = GAxtal-Sx 10 ; @ - yxtrst bo ——> ee page 4

Downloaded from hlayiso.com x2—x—-2 x24 xe tants 1.2 + x 3 2-9 x2+Bx x24x (8) 2 (x) (e+ y i x(x Rea acal CRIED da KOT = Cx +2) a _ 3.2 Simplify without using a calculator, writing alt answers with positive exponents. (10) (2x)? = | —<p 2x! 21 > 2“ a “1 { (2x) — ina a 2 2x"* _~ x uu - se, 2y" x x - — —___—_» (2) a a x 2 i Sa 2 ue (2° Q~ ——> BROUGHT To YOU BY w | | & i L} datacentrix. ¥ scan i ane a Page 5

Downloaded from hlayiso.com (4 2.2" = 2 oa Par ~ 2 2 x a _ 243" * % ve -=Q 543 a af ( | each ) [22] QUESTION 4 Solve the following equations: 4.1 (x-7)-3(€x-1)=3-x (2) 4.2 [all 31 - BTS = B-3c Se Ba ye 7 SB7SHT “in @ xo -T7 os (x-3)(*-2)=6 uu x - 2x -3 x +6 -6 =O a xv -G =O uw ae @ x=0 Of x= —> BROUGHT TO YOU BY (4) Page 6

Downloaded from hlayiso.com 4.3 —-5 <2x-—3 <7. Illustrate your answer graphically. (5) ~S43 <£ ax £743 -2 ax £10 om ma oOo ~ 4x €S > - ot { ~I S [11] QUESTION 5 5.1 Express 3y + 2x = 12 instandard form (i.e.y =mx+c) (1) ro) exe 2 i L7 EE ys -gxte 610 3 3 3 4-73 + 5.2 Now determine the equation of a line parallel to the fine in 5.1, but passing through (3 ; - 4). (2) YE VetS ~y= “AHa+S Mme = 7% ys are YA - ube (3" = “hx?! Ss io. Y= 6x * BROUGHT To YOU BY oN (‘Tt o . w | | eee by datacentrix ¥ education Page 7

Downloaded from hlayiso.com 5.3 Determine the equations of the lines {a), (b) and (c). (6) y (b) (c) (a) -2;1) x -_ -4 v =k Sas ee ee (2) ¥ ° a) mmx re Cc 20 ae C 4 Rall ha i oe cry M Suws (27) i ra | 1 = 72m mea (4 lines) “2 a \ ~! = ° A= ™ a oe Y= ax -l “— ow Ye ——=— [9] BROUGHT TO YOU BY as i | datacentix | Yow Page 8

Downloaded from hlayiso.com SECTION B QUESTION 6 Given: IP =e and Q= _ 5.1. Simplify P (7) xs Sq x = (34 Qn a + 2-3 (2.3) 24-2 Bu int = 3 ; “2 . Qe -¢ ate -3 =3* Temas SX TE ~WG UTES us | = 2'.9° = 3B 2, ®D 12. 6.2 SimplifyQ (3) Q= 2+ QaraQ' XQ a -_ 2 : ~ TY => _e& » @ | 6.3 Write a mathematical expression (equation) to show the relationship between P andQ. (1) P = ae va Q) [11] ee _ se Page 9

Downloaded from hlayiso.com QUESTION 7 7.1 Rafael Nadal plots the bounce of a tennis ball on a graph. He calculates that the formula he needs to use is: H = —2t” + 12£, where H is the height of the ball above the ground (in metres ) and t is the time elapsed ( in seconds ). y Height {m) 0 6 * Time (s) 7.1.1 How long will it take the ball to reach its maximum height ? (1) | 3 seconds : U @ | 7.1.2 What is the maximum height of the ball ? (2) H = -2(3y +12(D 1 . =-a(a) tae -T @® = AB +36 _ (Sm = \ em BROUGHT TO YOU BY

Downloaded from hlayiso.com 7.1.3 At what time(s) will the ball be 16m above the ground ? (3) - 2 tla = 161 ar~ lk $16 =o 3) t*- 6b +e so! . - (t ~u yt - 2) 2° U second > Gay or t F2 2 scconds n 7.2 The graph of f(x) = —3% +3 is drawn below: 7.2.1 Write down the asymptote of f. (1) Ys , a ‘@) 7.2.2. Determine the co-ordinates of A. (1) ons uo C{) 7.2.3 Determine the co-ordinates of B. (1) Cue, OG [9] BROUGHT To YOU BY rr Cy " w | | a i Yj | datacentiiz” | ¥ al Page 11

Downloaded from hlayiso.com UESTION 8 Given: z fix)=x*-9 i— 9 g(x) = mx +c f 8.\ Find the values of m and c. (3) y Swmowre = G Cc val 4 F=MWW+6 B32, @) O = 3mt+s ~Bm =G ms - 2 a &.2 Find the co-ordinates of D, a point of intersection between f and g. (4) xi-G = -2x+6 a | xP +24xn-%-G =O BROUGHT TO YOU BY “rt ” : Page 12 w | | a 1 Lf datacentrix ¥ ecucation

Downloaded from hlayiso.com Powered by TCPDF (www.tcpdf.org)