Mathematics Grade 12 P1 NSC June 2012 Question Paper (Eng)

Downloaded from hlayiso.com basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA SENIOR CERTIFICATE EXAMINATION MATHEMATICS P1 STANDARD GRADE 2012 MARKS: 150 MATHEMATICS SG: Paper 1 3012E TIME: 3 hours 30121E This question paper consists of 7 pages and 1 formula sheet. X@5 IMI 5 GAUTENG Please turn over Copyright reserved

Downloaded from hlayiso.com Mathematics/SG/P 1 2 DBE/2012 SCE INSTRUCTIONS AND INFORMATION Read the instructions below carefully before answering the questions. iL This question paper consists of SEVEN questions. Answer ALL the questions. 2. Clearly show ALL calculations, diagrams and graphs that you have used in determining the answers. eh You may use an approved calculator (non-programmable and non-graphical) unless stated otherwise. 4. If necessary, round answers off to TWO decimal places, unless stated otherwise. 5. Graph paper is NOT required in this question paper. 6. Number the answers correctly according to the numbering system used in this question paper. 1h Diagrams are not necessarily drawn to scale. 8. A formula sheet is included at the end of the question paper. 9. Write neatly and legibly. Comme 0 Pease ame GAUTENG

Downloaded from hlayiso.com Mathematics/SG/P 1 3 DBE/2012 SCE QUESTION 1 1.1 Solve for x: 11d x(x +4) =21 (3) 1.1.2 3x? -2x-4=0 (Round off the answer correct to TWO decimal places.) (4) 113 x-vx=6 (5) 1.2 Solve for x and y if they satisfy the following equations simultaneously: x-2y+7=0 2 4 axy+y?-21=0 (8) - (20) QUESTION 2 2.1 If 5 is one root of the equation x? +kx-15=0, determine the value of &, and the other root. (5) 2.2 Given: f(x) =3x? —6x+m Determine the values of m if f(x)=0 has non-real roots. (4) 2.3 Determine the value of a if x*>+ax’?—x+5 is divided by x-—2 and gives a remainder of 23. (3) 2.4 The expression x° + px” —qx—6 is exactly divisible by (x - 1), (x + 2) and (x + r). Determine the values of p, q and r. (7) [19] Conrad 0 Pes aoe

Downloaded from hlayiso.com Mathematics/SG/P 1 4 DBE/2012 SCE QUESTION 3 3.1 y “ _~ we CS ~ * v M al vy) 7 The figure above, not drawn to scale, shows the graphs of a parabola f and a straight line g. The graph of f has a turning point J(3 ; 4) and intersects the y-axis at L(0;—5). f cuts the x-axis at K and M. The graph of g passes through J and M. Determine: 3.1.1 The values of a, band c¢ if f(x)=ax? +bx+c 3.1.2 The coordinates of K and M 3.1.3 The range of f 3.1.4 The equation of the straight line g (5) (4) (2) (3) TL) FEU ATTA IAA A Please nn over GAUTENG

Downloaded from hlayiso.com Mathematics/SG/P1 3 DBE/2012 SCE t 32 The accompanying diagram, not drawn to A scale, shows the graphs of a circle and a hyperbola intersecting at A, B, C B i 3: < FE and D with A (-3;4). + E 7 px E and F are the x-intercepts of the circle. D Cc y 3.2.1 Determine the equations of the hyperbola and the circle. (5) a2 Determine the length of EF. (2) g23 Write down the coordinates of D. (2) [23] QUESTION 4 4.1 Simplify each of the following expressions without using a calculator: 2°* -7(2* 41.1 Ze : (4) 6 log125 7 om log(+) (4) 4.2 Solve for x without using a calculator: x-2 42.1 (4) =9%8 (4) 3 42.2 log,(x +1)+1og,(x—2)=1 () 43 Given: 4%! =12.2" 43.1 Show that the equation can be written in the form 2* = 3. (3) 43.2 Solve for x, correct to ONE decimal place. (3) [23] Co ene 0 Pec oe GAUTENG

Downloaded from hlayiso.com Mathematics/SG/P 1 6 DBE/2012 SCE QUESTION 5 5.1 The 10" term of an arithmetic sequence is 28 and the 7" term is 19. Calculate: 5.1.1 The common difference and the first term of the sequence (4) 5.1.2 The 84" term of the sequence (3) By) The sum of the first 84 terms of the sequence (3) 5.2 Given the geometric sequence: 1,21; 1,331; ... 5.2.1 Determine the 12" term of the sequence. (3) 5.2.2 Calculate the sum of the first 10 terms of the sequence. (3) 40 5.3 Evaluate: > (2r—5) ml (5) 5.4 A taxi owner buys a minibus that costs him R640 000. Determine the book value of the minibus after 4 years if the depreciation is calculated at 20% per annum compounded annually. (3) [24] QUESTION 6 6.1 Determine f'(x) from first principles if f(x) =—3x’. (5) 6.2 Given: f(x) =x? -3x 6.2.1 Determine the average gradient of f between the points x=—-l and x =3. (3) 6.2.2 Determine the gradient of the tangent to the graph of y= x°—3x at the point x=2. (3) 6.3 Differentiate the following with respect to x: 6.3.1 2(x)= (3x -1)(x +2) (3) 63.2 y=2Wx-—+ x (4) [18] Copprigh reserved CUDA TOG IAG A A Please turn over

Downloaded from hlayiso.com Mathematics/SG/P I 7 DBE/2012 SCE QUESTION 7 71 Given: (x) =x? +3x? -4. TAA Show that f(-1) =0 (1) 7A2 Hence, or otherwise, determine the x- and y-intercepts of the graph of f. (5) 7.1.3 Determine the coordinates of the turning points of the graph of / (5) 7.1.4 Draw a neat sketch graph of f Clearly show all the intercepts with the axes and the turning points on the graph. (4) TAS For which values of x is f increasing? (2) 72 MacDonald wishes to make a kite as shown in the figure. He cuts a piece of hard galvanised wire, that is 90 cm long, into two lengths for the diagonals AB and CD (that is, AB + CD = 90 cm). CE = ED and CD =x cm. A c++ pd B 721 If CD = x cm, express the length of the other diagonal AB, in terms of x. (1) q22 The area of the kite is equal to twice the area of AABD. Use this observation to show that: ; @) A= 45x-—x? 2 7.2.3 Determine the value of x that will give the maximum area of the kite. (2) [23] TOTAL: 150 Copprigh reserved UMMM AE EA GAUTENG

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Downloaded from hlayiso.com Mathematics/SG/P 1 SCE Mathematics Formula Sheet (HG and SG) Wiskunde Formuleblad (HG en SG) —b+ Vb? -4ac 2a T,=a +(n-1)d Sy=5 (a+ T) or / of Sy =F(a+2) Sy =5 [2a +(n -1)d] Soo => (<2) a=a{ 1+) or/of 4-9 1-5) 100 100 h>0 h d = \(x2- 4) +(¥2- 1) y=mxte Y- yy = m(x—- x1) m=22741 x2 7— XY m=tanO xXy+x + (3393) = ge | aya? (x- p +(y-g) =r? In AABC: a@__6 _-¢ sinA sinB sinC a? =b? +c? —2bc.cosA area AABC = Fabsin Cc Connie reserved ETT AGUA A A GAUTENG DBE/2012