Mathematics Grade 12 Paper 1 NSC June 2013 Question Paper

_ Downloaded from hlayiso.com basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA SENIOR CERTIFICATE EXAMINATION MATHEMATICS P1 STANDARD GRADE 2013 MARKS: 150 TIME: 3 hours MATHEMATICS SG: Paper 1 3012E 30121E This question paper consists of 8 pages and 1 formula sheet. X@5 IMM Copyright reserved GAUTENG Please turn over

Downloaded from hlayiso.com Mathematics/SG/P 1 2 DBE/2013 SCE INSTRUCTIONS AND INFORMATION Read the instructions below carefully before answering the questions. 1. 2 This question paper consists of SEVEN questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining the answers. You may use an approved calculator (non-programmable and non-graphical) unless stated otherwise. If necessary, round answers off to TWO decimal places, unless stated otherwise. Number the answers correctly according to the numbering system used in this question paper. Diagrams are not necessarily drawn to scale. A formula sheet is included at the end of the question paper. Write neatly and legibly. Copia A Pe oe

Downloaded from hlayiso.com Mathematics/SG/P 1 é} DBE/2013 SCE QUESTION 1 1.1 Solve for x: 11d 3x? =5x-2 (3) 1.1.2 x? +5x-—4=0 (Correct to ONE decimal place) (4) 13 vx+17 =x-3 (5) 1.2 Solve for x and y if they satisfy the following equations simultaneously: 2y+x=3 and 2x? +xy-y? =0 (8) [20] QUESTION 2 ; oe 2 7 Determine the roots of the equation x" = 16° (1) 2.2 Determine the nature of the roots of 6x” —7x—3=0 without solving the equation. (4) 2.3 Find the values of k for which the equation x” + (2k +4)x+9k =0 has equal roots. (5) 2.4 When x? +mx?—5x+4 is divided by x+2, the remainder is 8. Determine the value of m. (4) 25 Factorise x° — 6x? +11x—6. (6) [20] Copied 0 0 Pes en oe GAUTENG

Downloaded from hlayiso.com Mathematics/SG/P1 4 DBE/2013 SCE QUESTION 3 3.1 y - px The sketch above, not drawn to scale, shows the graphs of a parabola f(x) =2(x-1) ~18 and a circle g(x)=+4vr? —x’ . The graph of f has a tuming point at D, intersects the y-axis at C and cuts the x-axis at A and B. The graph of g passes through B. Determine: 3.1.1 The coordinates of A, B, C and D 3.1.2 The coordinates of E if CE// AB 3.1.3 The range of f 3.1.4 The equation of the circle g Copyright reserved CAANY ANA UGA deaaidaaiidea GAUTENG (8) (4) (2) (2)

Downloaded from hlayiso.com Mathematics/SG/P1 5 DBE/2013 SCE 3.2 v The straight line g cuts the hyperbola f for x>0 at D (2; 6), the y-axis at C and the x-axis at B (1 ; 0). The line y=x cuts the graphs of f and g at E and A respectively. 3.2.1 Find the equations of f and g. (5) 3.2.2 Determine the coordinates of C, A and E. (5) [26] QUESTION 4 2x-1 @3x+2 4.1 Show that Tye = 2 . , (6) 4.2 Simplify the following without using a calculator: 427-13 4.2.1 (2) V3 log16+log4 4.2.2 log16—log4 3) Corer Ag Penne GAUTENG

Downloaded from hlayiso.com Mathematics/SG/P 1 6 DBE/2013 SCE 43 Solve for x, without using a calculator: 4.3.1 2.3% =45-3""1 (4) 4.3.2 get aset (3) 43.3 log, (2x-—3)—log, 5=2 (3) 44 Solve for x: 5 =10 GB) [24] QUESTION 5 5.1 The first term of a sequence is 2. The fifth term is 162. Determine the numerical value of the third term in each of the following cases: a If the sequence is arithmetic (4) ee If the sequence is geometric (4) 5.2 The geometric series 16+8+4+... has 12 terms. Calculate the sum of the series correct to TWO decimal places. (4) 53 Determine 1 if > (6k -1)=320 (6) k=l 5.4 John's starting salary is R150 000,00 p.a. His annual increase is R7 500,00. After how many years will he reach his maximum salary of R262 500,00 p.a.? (4) 5.5 The value of a car costing R169 999,00 depreciates at 12% per year, compounded annually. What is the value of the car after 5 years? (4) [26] Cop res A gq Pe tow

Downloaded from hlayiso.com Mathematics/SG/P1 Ze DBE/2013 SCE QUESTION 6 6.1 The height s (in metres) attained by a shell fired vertically upwards t seconds after release, is given by s(t)=100t—5St?. What is the average speed of the shell between the second and the fourth seconds? (3) 6.2 Determine f’(x) from first principles if f(x) ara (5) 6.3 Differentiate the following with respect to x: vx 6.3.1 a(x) =~ — 2x (3) xe+x?-1 [15] QUESTION 7 71 The diagram below shows the graph of f(x) =—x° + ax” + bx. A and B (3 ; 0) are the turning points of f. T is the point of contact of a tangent to the graph of f. Fé BG ; 0) « 7 oO >x ‘y v gil Show that a=6 and b=-9. (3) 712 Determine the coordinates of A. (4) 7.13 T has an x-coordinate of 2. Find: (a) The y-coordinate of T (2) (b) The equation of the tangent to the graph at T (5) Copyright reserved FART AOO GA Please um over GAUTENG

Downloaded from hlayiso.com Mathematics/SG/P 1 8 DBE/2013 SCE 7.2 The sketch below, not drawn to scale, shows the graphs of a parabola f(x) =-x? +2x+3 anda straight line g(x)=—2x+8. P isapointon g and Q is a point on f y nf P Q & < 0 \ mx 7 Y Determine the shortest vertical distance PQ between the graphs of f and g. (5) [19] TOTAL: 150 Copsright reserved FIC AQAN TOCA UAT A

Downloaded from hlayiso.com Mathematics/SG/P 1 DBE/2013 SCE Mathematics Formula Sheet (HG and SG) Wiskunde Formuleblad (HG en SG) ae —b+Vb? —4ac 2a T,=a+(n-1)d Sy= 5 (a+ Ty) or/of Sy =F(a+4) ce =5 [2a + (n -1)d] n a T,=ar"-! Sy = ah-"") Guns, -te N40 1-r a Sop = ("\<7) 1-r n n A= P| 1+—— or/of A = P| 1-—— 100 100 PG = lim LEAM= FO) h>0 >! h d= (x2 - 41) +02-n)P y=mxte Y-Yy = M(x - 2) m=22771 x2 — xy m = tanO Xy +X. i+ V2 CPA (x3393) ( 2 ’ 2 } veya? (x-pY +(y-gP =r? In AABC: ab _€ snA sinB sinC a® =b* +c? -2bc.cosA area AABC = Jab.sin Cc ae CUI AUTO GAUTENG