Mathematics Grade 11 Paper 1 Limpopo November 2019 Question Paper

Downloaded from hlayiso.com LIMPOPO PROVINCIAL GOVERNMENT REPUBLIC OF SOUTH AFRICA DEPARTMENT OF EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P1 NOVEMBER 2019 MARKS: 150 TIME: 3 hours This question paper consists of 9 pages, an answersheet and an information sheet Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 2 LimpopoDoE/November 2019 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 9 questions. 2. Answer ALL questions. 3. Answer Questions 5.2.1 and Question 7 on the DIAGRAM SHEET PROVIDED 4, Answer correctly according to the numbering system used in this question paper. 5. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answer. 6. Answers only will not necessarily be awarded full marks. 7. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 8. If necessary, round off your answers to TWO decimal places, unless stated otherwise. 9. Diagrams are NOT necessarily drawn to scale. 10. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics PI 3 LimpopoDoE/November 2019 NSC QUESTION 1 ill Solve for x: L.1.1 5x? -33x-14=0 Q) 1.1.2 x?+7x+4=0 (answer correct to TWO decimal places) (3) ibe Given; V¥8-x =x-2 13 14 TS 1.2.1 Without soving the equation, show that the solution above will lie in the interval 2<x <8. (3) 1.2.2 Solve the equation. (5) 1.2.3. Hence or otherwise, solvex if —V8-x =x-2, @) Solve for x if x°+2x215 (4) Solve for x and ¥ in the given equations: 2) =32* and y=x—2x-18 (6) 44 /74+3 The solution of a quadratic equation is: x= ofr eae where peR. Determine the values of P so that: 1.5.1 The equation has equal roots (2) 1.5.2 The equation has non-real roots. (2) [29] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 4 LimpopoDoE/November 2019 NSC QUESTION 2 2.1 Simplify without the use of a calculator: 511 W8+x8 ° lk 50 (4) See nee 3) wie Zale ene (4) 2.2 Solve for x without the use of a calculator: 3)’ =27 re nie lat ie ) 2.2.2 4%_3.2%=40 (4) [16] QUESTION 3 During the 2019 Cricket World Cup the South African Captian Faf du Plessis hit a ball with all his might. After the ball left his bat, the hight of the ball in metres was expressed by the equation h(x) =-x’+4x after x seconds. Calculate the maximum height of the ball? (4) [4] QUESTION 4 4.1 Consider the following number pattern: 4; 9; 14; ... 4.1.1 Write down the next two terms of the pattern. (2) 4.1.2 Determine the expression for the n™ term of the pattern. iC) 4.1.3 Determine if 1099 is a term of the number pattern? (3) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 5 LimpopoDoE/November 2019 NSC 4.2 Consider the following quadratic number pattern: 6; 105 18:2. 4.2.1 Write down the following two terms of the pattern. (2) 4.2.2 Determine the equation of the general term in the form: T, =an’ +bn+c (4) 4.2.3 Calculate the value of 7, (2) 42.4 What term of the pattern will have a value of 766? (4) 4.3. A certian number pattern has the following properties: | ° [=k . 7,=14 Bee ° £-7,=10 (5) Determine the value of [. [24] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 6 LimpopoDoE/November 2019 NSC QUESTION 5 k 5.1 In the diagram below f(x) z ar +q where A(2;1) is the point of intersection of the x- asymptotes of fand B(0;—2) is the y-intercept. Ay ree ie | IB(0;— 2): 5.1.1 Write down the equations of the asymptotes of /. (2) 5.1.2 Determine the equation of f. (3) 5.1.3 Write down the domain of f (1) 5.14 Calculate the coordinates of D. (4) 5.1.5 Calculate the equation of the function h(x)=ax° +bx+¢which goes through the point B, C and D, where are C and D are the x-—intercepts of h. (5) 5.2 Given the graph of g defined by the equation: gia)= oe 5.2.1 Draw aneat sketch of gon the answer sheet provided. Show the asymptote and intercept with the axis. (3) 5.2.2 Determine the equation of g(x-3). (2) [20] Copyright reserved Please turn over

Mathematics P1 ie Downloaded from hlayiso.com LimpopoDoE/November 2019 NSC QUESTION 6 The graph of f(x)=-x*?+bx+c and the straight line g are sketched below. A and D are points of intersection of f and g. Point A is the turningpoint of f. Points D and B (1 ; 0) are the x-intercepts of f. The axis of symmetry of f is x=—1. 6.1 Write the coordinates of D. 6.2 Show that b=—2 and c=3 6.3 Determine : 6.3.1 the range of f. 6.3.2 the equation of g in the form y=mx+c 6.4 For which values of x is : x.f(x)>0 6.5 For which values of & will Hf (x) =k have non-real roots? | 6.6 Tis a point on the x-axis and M isa point on f such that TM x-axis. TM intersects 2 at P. Calculate the maximum length | of PM. Copyright reserved Please turn over (1) (4) (2) (3) (4) (3) (4) [21]

Downloaded from hlayiso.com Mathematics P1 8 LimpopoDoE/November 2019 NSC QUESTION 7 The function f defined by f(x)= —* 144 has the following properties: x+p e Thedomain: xeR; x¥3 e y=-x+4 isa line of symmetry. e a>0 Draw a neat graph of this function on the answer sheet provided. Your sketch must include the asymptotes. (3) [3] QUESTION 8 8.1 Jaco bought a new car for R250 000. At the end of 6 years the value of the car depreciates to R150 000. If the car depreciates in a reducing balanced method Calculate the rate of the depreciation. 8.2 Calculate the effective interest rate p.a. if the nominal rate is 8,9% p.a., compounded monthly. (3) p 8.3 Mary opened an investment account and deposited R35 000. The account earns an interest of 8% per annum compounded half yearly for the fisrt 18 months and after that 6,5% per annum compounded monthly. How much money will be in Mary’s account exactly 5 years after the initial deposit? (5) 8.4 Donald deposited R15 000 into his new savings account at a rate of 16% p.a. compounded monthly. Exactly 3 years after his initial deposit he deposited an additional ammount of R10 000 into the same account. Exactly 5 years after his initial ammount was deposited he withdrew an ammount of R8 000 from the account. How much money will Donald have in his savings account exactly 7 years after his initial deposit? (5) [16] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 9 LimpopoDoE/November 2019 NSC QUESTION 9 9.1 Given: P(A)=0,2 2 (B ) =0,5 P(Aand B)=0,1 Onl Are the events A and B mutually exclusive? Give reasons for your answers. ] ee?) Are the events A and B independent? Give reasons for your j answers. 9:2 The Venn-diagram below shows the probabilities of two independant events A and B. Determine the values of x and y. Show all calculations. 9.3 Kobus has a bag with 60 marbles, each of which is green, blue or red in color. = of the marbles are green and 15% of the marbles are blue. Kobus picks TWO marbles out of the bag, one at a time and without putting the first one back. OSL How many red marbles are there in the bag? } 932 Draw a tree diagram to represent the situation above. | 933 What is the probability that Kobus will pick a BLUE and GREEN marble. (round off your answers to THREE decimal places) TOTAL: Copyright reserved Q) (3) (4) (2) (3) (3) {17] [150]

Downloaded from hlayiso.com 11 NSC Mathematics P1 LimpopoDoE/November 2019 Information Sheet Mathematics -b+ Vb? —4ac 2a A=Pil-tm) “A= Pd=ni) A=P(l-i)" A=P(+i)" ft i I Mian co tu T, =a+(n-l)d S, => Qa+(n-Dd) i=l isl Ta g -N a) , r#l 8, =; -1<47 21 i r-l St pati -1 ptl=0+)""] i i wo S(xt+h)— f(x) ‘(x)= lim ————7—+ fe) h>0 h X,+x J, = d= G22), 1 )e M222 21272) 2 2 y=met+e y-y, =m(x-x,) a22e m=tand ema (x-a) +(y-4) =r? InAdpe, = but of a* =b* +c2 —2be.cos A sinA sinB sinC area ABC =— ab.sin C sin(@ + B) = sin a.cos # +cosa.sin B cos(a + )=cos@.cosf-sin a.sin B cos’ a—sin® a cos2a@ =41-2sin* @ 2cos* a-1 (x; y) > (xcos6+ ysin @; ycos@ — xsin 0) = n _ n(A) P(A)= lS) poatbx o> Copyright reserved sin(a = A) = sin a.cos B —cosa.sin 3 cos(a — 8) = cosa.cos 8 +sin a.sin B sin 2a = 2sin a.cosa@ (x3 y) > (xcosO- ysin@; ycos@ + xsin 6) n 2 Dlx, -¥) 2 i=l oO An P(A of B) = P(A) + P(B) — P(A and B) XG-x)0-7) Y@-x)