Grade 11 November Examination 2018 Mathematics: Paper 1 .

Grade 11November Examination 2018Mathematics: Paper 1Time: 3 hoursMarks: 150Instructions and Information:Read the following instructions carefully before answering the questions.1.This question paper consists of 9 questions. Answer ALL the questions.2.Clearly show ALL calculations, diagrams and graphs that you have used indetermining your answers. All working should be shown in its proper place.3.Answers only will not necessarily be awarded full marks.4.An approved scientific calculator (non-programmable and non-graphical) maybe used, unless stated otherwise.5.If necessary, answers should be rounded off to TWO decimal places, unlessstated otherwise.6.Diagrams are not necessarily drawn to scale.7.A marking rubric is provided. Please attach this to the front of your answersheet and write your name and the name of your Maths teacher on it clearly.8.Number your answers according to the numbering system used in thisquestion paper.9.It is in your own interest to write legibly and to present your work neatly.Page 1 of 10November 2018

Question 1 [33]1.1 Solve for x in each of the following:1.1.1 2 x 3 x 5 0(2)1.1.2x 2 x 3 4 correct to 2 decimal place.(4)1.1.3x 2 x 4(6)1.1.4 𝑥 2 3𝑥 10 01.1.5 (3) (5)22 x 1 3 22 x 1 4 x 121.2 The roots of a quadratic equation are 𝑥 3 18 2𝑎2 . For which real(2)values of a will the roots be equal.1.3 Solve simultaneously for x and y:2𝑥 𝑦 7(7)𝑥 2 𝑥𝑦 21 𝑦 21.4 Given 𝑚 12. Show that 65 . 48 . 24 . 38 6𝑚12 without using a calculator.(4)Question 2 [17]NO CALCULATOR ALLOWED in this question. Show all necessary working.2.1Simplify: 16 2.1.1 81 2.1.22.2If 12(3)9𝑥 32𝑥 118𝑥 .2 𝑥14 63 28(5)can be written in the form 𝑎 𝑏, determine, without using a(4)calculator, the value(s) of a and b, where a and b are integers.2.3Erin had to find the product of 22007 and 52000 and then calculate the sum ofthe digits of the answer. Erin arrived at an answer of 11.Is she correct? Show ALL the calculations to motivate your answer.Page 2 of 10(5)November 2018

Question 3 [15]3.1Given the linear pattern: 156; 148; 140; 132; 3.1.1 Write down the 5th term of this pattern.(1)th3.1.2 Determine a general formula for the n term of this pattern(2)3.1.3 Which term of this linear number pattern is the first term to be negative?(3)3.1.4 The given linear number pattern forms the sequence of first differencesof a quadratic number pattern 𝑇𝑛 𝑎𝑛2 𝑏𝑛 𝑐 where 𝑇5 24.Determine the general formula (𝑇𝑛 ) of this quadratic pattern.3.2(5)A plant starts growing from a single shoot. At the end of the month, a flowerblooms at the tip of the shoot. The next month, two new shoots branch offfrom the first one, and at the end of that month, a flower blooms at the tip ofeach new shoot. This growth pattern is shown below.Month123Flowers124Shoots1373.2.1 How many flowers will appear on the plant during the 4th month?(1)3.2.2 Write down an expression for the number of flowers that will bloomduring month n.(1)3.2.3 How many shoots will there be on a 5-month-old-plant?Page 3 of 10(2)November 2018

Question 4 [9]The number of new businesses in a small town is growing according to a pattern. Examinethe table below and answer the questions that follow.YearNew businessesformed20012002200320043817304.1How many new businesses will be formed in 2005 if the pattern continues?4.2If there were no businesses in the town at the beginning of 2001, how manybusinesses were there in the town by the end of 2003?4.3(1)thFind a general term for the number of new businesses formed in the n year,where n 1 corresponds to the year 2001.4.4(2)(4)Use your model from 4.3 to determine how many new businesseswere formed in 2010.(2)Question 5 [14]5.1A machine costs R45 000 today and has a scrap value of R9 000 after 10years. Determine the annual rate of depreciation if it is calculated on thereducing balance method.(5)5.2.1 Lisa invested R14 500 in a bank for a period of 8 years at 6,5% p.a.compounded monthly for the first 5 years and at 8,4% p.a. effective for theremaining period. If Lisa runs into financial difficulties and withdraws R3 000after 6 years, calculate how much her investment is worth at the end of the 8years.(7)5.2.2 Calculate the effective interest rate which is equivalent to a nominal interestrate of 6,5% p.a. compounded monthly.Page 4 of 10(2)November 2018

Question 6 [23]6.1The graph of 𝑓(𝑥) 𝑎. 2𝑥 1 (a is a constant) passes through the origin as shownbelow.6.26.1.1Show that 𝑎 1(2)6.1.2Determine the value of 𝑓( 15) correct to FIVE decimal places.(1)6.1.3Determine the value of x, if (𝑥; 0,5) lies on the graph of f.(3)6.1.4Give the range of f.(2)Given the functions:3ℎ(𝑥) 𝑥 2 3 and 𝑔(𝑥) 𝑥 36.2.1Use the set of axes provided on the diagram sheet to draw neat sketchgraphs of h and g. Label each graph and show any intercepts with theaxes and any asymptotes. Also show at least one other point on eachgraph.(6)6.2.2Write down the domain of h.(2)6.2.3Determine the equation of function k which is the reflection of h in the(2)y-axis.6.2.4If the graph of h is reflected across the line with the equation𝑦 𝑥 𝑐, the new graph coincides with the graph of 𝑦 ℎ(𝑥).6.2.5Page 5 of 10Determine the value of c.(2)Using your graph, give the value(s) of x for which 𝑥. ℎ(𝑥) 0.(3)November 2018

Question 7 [14]yThe sketch alongside represents the graphs of functions ffDand g where:AM𝑓(𝑥) 𝑥 2 2𝑥 4 and 𝑔(𝑥) 𝑥 1Bgx7.1Calculate the co-ordinates of the turning point of f.(3)7.2Calculate the co-ordinates of D if DM is parallel to the x-axis and 𝑂𝑀 7 units.(4)7.3Calculate the minimum length of AB if AB is parallel to the y-axis, with A on theparabola and B on the straight line.7.4For which value(s) of x isPage 6 of 101𝑓(𝑥).𝑔(𝑥)(5)undefined?(2)November 2018

Question 8 [7]Amy, an enthusiastic basketball player, is practising her shooting.BAShe throws from a point 1,7m from the floor. Each throw follows the path of a parabola. Onone of her throws, the ball reaches its maximum height of 3,1625m when it has covered ahorizontal distance of 3m. Unfortunately the ball does not go into the basket but hits the rimwhich is 3m above the floor.Determine how far Amy’s hand is from the front of the rim at the moment shereleases the ball (i.e. the length of AB).Page 7 of 10November 2018

Question 9 [18]9.1For events A and B: P(A) P(B) 0,4 P(A and B) 0,19.1.1 Are events A and B mutually exclusive? Give a reason for your answer.(2)9.1.2 Show whether events A and B are independent or not. Give a reason(2)for your answer.9.1.3 Determine P(A or B).9.2(2)In a survey, a group of 283 workers were asked what mode of transportthey use to get to work. The results of the survey are summarized below. x workers take a car (C), a bus (B) and a taxi (T) to get to work. 110 workers take a car and a taxi. 38 workers take a taxi and a bus. 32 workers take a car and a bus but not a taxi. 60 get to work by taxi only. 110 workers take a bus. 172 workers take a car. No workers use any other mode of transport.9.2.1 Draw a Venn diagram to represent the information above.(8)9.2.2 Determine the number of workers who take a car, a bus and a taxi towork (i.e. x).(2)9.2.3 What is the probability that a worker picked from the sample takes a(1)car and a bus to work? Give your answer as a fraction.9.2.4 What is the probability that a worker picked from the sample takes a(1)bus but not a car? Give your answer as a fraction.Page 8 of 10November 2018

TOTAL:Grade 11 Paper 1150 MARKSDIAGRAM SHEETNovember 2018Name: Maths Teacher:Q1Q2Q3Q4Q5Q6Q7Q8Q9EquationsAlgebraPatterns &SequencesPatterns ility3317159142314718TOTAL150Question 6.2.18y642x 8 6 4 22468 2 4 6 8Page 9 of 10November 2018

INFORMATION SHEET: MATHEMATICSx b b 2 4ac2aA P (1 ni)Sn Tn a (n 1)dTn arSn x 1 i 1F inA P(1 i ) nn 2a (n 1)d 2n 1 A P(1 i ) nA P (1 ni) a r n 1r 1P f ( x h) f ( x )hh 0S r 1;a1 r ; 1 r 1x[1 (1 i ) n ]if ' ( x) limd ( x 2 x1 ) 2 ( y 2 y1 ) 2y y1 m( x x1 )y mx c x a 2 y b r22 x1 x2 y1 y 2 ;22 My y1m 2x 2 x1abc sin A sin B sin CIn ABC:a 2 b 2 c 2 2bc. cos A1area ABC ab. sin C2sin sin . cos cos .sin cos cos . cos sin . sin cos2 sin 2 cos 2 1 2 sin 2 2 cos2 1 𝑥𝑥̅ 𝑛P( A) n( A)n S yˆ a bxPage 10 of 10m tan sin sin . cos cos .sin cos cos . cos sin . sin sin 2 2 sin . cos 2n 2 x x i 1inP(A or B) P(A) P(B) – P(A and B)b x x ( y y ) (x x)2November 2018

Mathematics: Paper 1 Time: 3 hours Marks: 150 Instructions and Information: Read the following instructions carefully before answering the questions. 1. This question paper consists of 9 questions. Answer ALL the questions. 2. Clearly show ALL calculations, diagrams and graphs that you have used in determining your answers. All working should be shown in its proper place. 3. Answers only will .