2018 GRADE 12 TRIAL EXAM P1 FS_hlayiso.com_.pdf

Downloaded from hlayiso.com Department of Education FREE STATE PROVINCE PREPARATORY EXAMINATION GRADE 12 MATHEMATICS P1 SEPTEMBER 2018 TIME: 3 HOURS MARKS: 150 This question paper consists of 9 pages and I information sheet. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 2 F§/September 2018 Grade 12 Prep. Exam. INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. 10. The question paper consists of 11 questions. Answer ALL the questions. Number your answers correctly according to the numbering system used in this question paper, Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers, Answers only will not necessarily be awarded full marks, An approved scientific calculator (non-programmable, non-graphic) may be used, unless stated otherwise. If necessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. An information sheet with formulae is included at the end of the question paper. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 3 FS/September 2018 Grade 12 Prep. Exam. QUESTION 1 Li Solve for x: LL -3x°+2x+2=0 (Round off the answer to TWO decimal places) (3) 142 x +2x-3=5 3) 1.1.3 x°-2x-15<0 @G) 114 -V2x-1=2-x (4) 115 73° -3" =36 3) 1.2 Solve x and y simultancously: Qx-l=yp and x? ~xyy =3x-3 6) 1.3 Simplify without using a calculator: og xel V5.Ni95 - = (3) [24] QUESTION 2 2.1 Consider the arithmetic sequence: 3;-2;-7;—12)... 2.1.1 Calculate the 21“ term of the sequence. (2) 2.1.2 Which term of the sequence is equal to —177? Q) 2.2 The sum of the first terms in an arithmetic series is given by: S, =n" —2n Calculate: 2.2.1 the sum of the first 13 terms, (2) 2.2.2 the 13" term. (2) 2.3 Given the quadratic pattern: x;659; 3 24;... Calculate the sum of x and y. (5) Copyright reserved : Please turn over

Downloaded from hlayiso.com Mathematics P1 4 FS/September 2018 Grade 12 Prep, Exam, QUESTION 3 3.1 Prove that atar tar’ +... (ton terms) = ame) et —r 3.2 Given: 3-40,2)" a=l 3.2.1 Write down the first THREE terms of the series, 3.2.2 Calculate the sum to infinity of the series, 3.2.3 Hence calculate the smallest number of terms of the series whose sum will differ by less than 0,0001 from the sum to infinity of the series, ) (1) (3) (6) 113] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 5 FS/September 2018 Grade 12 Prep. Exam. QUESTION 4 In the sketch below, the graphs of A(x)=ax” +bx+c and g(x) =4x+8 are drawn. P and R are the x-intercepts of # and D is the turning point of 4. C and F are the y-intercepts of hand g respectively. The two graphs intersect at P and E (6332). y D E(6 3 32) c A B Pp R * fe) &, 4.1 Write down the coordinates of point P. Q) 42 If the equation of the axis of symmetry of his x=4, write down the coordinates of point R. (2) 4.3. Determine the equation of / in the form (x)= ax’ +bx+e. (4) 4.4 — Calculate the length of FC. Q) 4.5 Determine the range of A. (2) 4.6 For which values(s) of x is h(x)g(x)<0? (2) 4.7 Determine the value of kif y=4x+k is a tangent to A(x)=—x* +8x +20. (4) [18] 2 e Copyright reserved ne Please turn over

Downloaded from hlayiso.com Mathematics Pl 6 FS/September 2018 Grade 12 Prep. Exam, QUESTION 5 2+x The sketch below shows the graph of /f" (x) =<—. Aand B are the x- and the y-intercepts of f. 5.1 Write down the equation of f in the form f(x)=—~4¢. (3) x+p 5.2 Determine the equations of the asymptotes of f (2) 5.3. Write down the coordinates of A, the x-intercept of f Q) 5.4 The graph of k(x) is obtained by shifting the graph of / (x) horizontally such that point A is at the origin, O. Write down the equation of the vertical asymptote of k(x). (1) [8] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 7 FS/September 2018 Grade 12 Prep. Exam. : QUESTION 6 6.1 Given: f(x)=3™ 6.1.1. Write down the equation of f(x), the inverse of f (x), in the form f'@)=.. @) 6.1.2 On the same set of axes, sketch the graphs of f (x) and f7'(x) in your ANSWER BOOK. Clearly indicate the intercepts with the axes and one other point on the graphs and label the TWO graphs. (4) 6.2 A linear function satisfies the following conditions: p(-3)=10 and , p (x) =~2. Determine the inverse of p in the form p™ (x) =. (4) [10] QUESTION 7 7.1. An investment company offers interest on a fixed deposit at the rate of 9,6% compounded monthly. Calculate the effective annual interest rate correct to two decimal places. (3) 7.2. A motor car costing R150 000 depreciated annually at a rate of 8,8% per annum on a reducing-balance method, Calculate how long it took for the car to depreciate to R60 000 under these conditions. . G3) 7.3 David is paying off a loan of R250 000 over 10 years by making monthly instalments. He made his first payment exactly one month after the loan is granted. Interest is charged at 10% per annum compounded monthly. 7.3.1 Calculate David's monthly payment. (4) 7.3.2 Calculate the balance outstanding immediately after David paid his 36" instalment. (4) [14] QUESTION 8 8.1 Determine f'(x) from first principles if /| (x) = 3x? (4) dy 4 3 8.2 Determine = if y=7x*- 5¥x —= (4) dx x 8.3 It is given that g(x)=ax* —24x+d has a local minimum turning point at (- 2; 17). Determine the values of @ and b. (5) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 8 FS/September 2018 Grade 12 Prep. Exam. QUESTION 9 Given: f(x) =—x? +10x? -17x~28 9.1 Calculate the coordinates of the intercepts of f with the axes. (5) 9.2 Calculate the coordinates of the turning points of St (5) 9.3 Sketch the graph of f, clearly indicating the intercepts with the axes and the turning points, (3) 9.4 Determine the values of & for which—x° +10x? -17x =25+k will have only one real root. (2) {15} QUESTION 10 In the sketch, A ABC is an equilateral triangle with sides equal to y units. DEFG is a rectangle. BE = FC = x units. D G B = ra C 10.1 Prove that the area of the rectangle is 4 =/3xy — 23x, (4) 10.2 Determine, in terms of y, the maximum area of the rectangle. (5) 19] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 9 FS/September 2018 Grade 12 Prep. Exam, QUESTION 11 11.1 11.2 P(A) = 0,45 and P(B) = 0,29. Calculate the P(A or B) if: 11.1.1 A and B are mutually exclusive events. (2) 11.1.2 A and B are independent events. (4) The probability that it will be sunny tomorrow is > If it is sunny, the probability that Pitso plays soccer is . If it is not sunny, the probability that Pitso plays soccer is * Determine the probability that Pitso does not play soccer. (4) How many four character codes can be formed if the first character must be an alphabetical letter and the remaining characters must be digits that may not be repeated? (3) [13] TOTAL: 150 Copyright reserved

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Downloaded from hlayiso.com Mathematics P1 FS/September 2018 Grade 12 Prep. Exam. INFORMATION SHEET _ ~btvb? —4ac 2a A=P(1+ni) A= P(l—ni) A=P(1-i)” A=P(+i)’ T, =a+(n-Dd S, =F @ar(n-Ha) T, = ar"! 5,1! sre S.=(fos-i<r<l r- -r palsy = paid") i 7 i _ Sxthy-f@) “(x)= tim ¢ Le) ho h Xp+X, Y, ty d=Vlq-%) +0 -y,) Ord y=mxtco yry, =m(x-x) mare 41 m=tand X27 b c —a¥ 4(y—bY =? In AABC: 1. =—7— = (a +O-6) = " sind sinB sinC a? =b? +0? —2be.cos A area KAABC =F ab.sin€ sin(a+ B)=sina.cos B + cosa.sin 8 sin(e — f)=sina.cos f - cosa.sin B cosa + f)=cosa.cos f -sina.sin 8 cos (a ~ B)=cosa.cos 8 + sina.sin 8 cos’ asin’ a cos 2@ = 41-2sin’? a sin 2a = 2sina.cosa 2cos? a=1 n 2 x Xt, x) a of? ==! n n n(A PA)= a8) P(A or B) = P(A) + P(B) — P(A and B) (&-3)y-79) seats pe , Yaz) Copyright reserved

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