MATHEMATICS: PAPER I. 4. You may use an approved non-programmable and non-graphical calculator, unless otherwise stated.

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1 GRADE 11 EXEMPLAR PAPERS NOVEMBER 007 MATHEMATICS: PAPER I Time: 3 hours 150 marks Instructions to candidates 1. This eamination consists of 9 pages.. Read the questions carefull. 3. Answer all the questions on the question paper. 4. You ma use an approved non-programmable and non-graphical calculator, unless otherwise stated. 5. Round off our answers to two decimal digits where necessar. 6. All the necessar working details must be clearl shown. 7. It is in our own interest to write legibl and to present our work neatl. PLEASE TURN OVER

2 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page of 9 QUESTION 1 Simplif: 4 + (1) K (3) R 4 marks QUESTION Solve for : 5 = 6 () K 6 + = (correct to decimal places) (5) R and represent our solution graphicall. (5) R (d) < 4 (3) R (e) p 4 = 0 (b completing the square). (5) C 0 marks

3 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page 3 of 9 QUESTION 3 Wooden ice-cream sticks are joined using split-pins to create the following pattern : Complete the table b filling in the missing values. Number of diamond shapes formed Number of split pins Number of icecream sticks n (4) K () R 6 marks QUESTION 4 An advertisement advertises a mirror of dimensions,3 m b 1,5 m. This means that the actual length of the mirror could be,5 m length <,35 m. Write down the possible measurements of the width of the mirror. (),3 m Hence calculate the minimum possible area of the mirror. (correct to decimal places.) (3) 1,5 m 5 marks PLEASE TURN OVER

4 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page 4 of 9 QUESTION 5 A gift shop sells boes of chocolates and bunches of flowers per da subject to the following constraints In the diagram a graphical representation with the feasible region shaded, is given Bunches of flowers B C 5 A D Boes of chocolates Determine the coordinates of vertices A, B, C and D. (8) R The shopkeeper makes a profit of R10 on a bo of chocolates and R0 on a bunch of flowers. (d) Write down an equation that will represent the profit for the da. How man boes of chocolates and bunches of flowers should be sold ever da to make a maimum profit? What is this maimum profit? Near Valentine's da flowers become ver epensive and the shopkeeper finds that whilst he still makes R10 profit on a bo of chocolates, he now makes no profit on a bunch of flowers. Subject to the above constraints, how man boes of chocolates and bunches of flowers should he now sell to make a maimum profit? () R (3) R () C 15 marks

5 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page 5 of 9 QUESTION 6 Refer to the figure. The graphs of f () = and g () = + 10 are drawn (not to scale). A and B are the -intercepts and C is the -intercept of f (). G is the turning point of f (). A is the -intercept and D is the -intercept of g (). Use the sketch to answer the following questions: G C g () = + 10 F H D E J A 0 B K f () = L Determine the coordinates of A, B, C and D. (5) K Hence write down for which values of, f () > 0. () R Determine the coordinates of E one of the points of intersection of f () and g (). (4) R (d) Determine the equation of the ais of smmetr of f (). () R (e) Determine the length of GH if GH is parallel to the -ais. (5) R (f) If JL = 60 units, determine the length of OK. (5) C 3 marks PLEASE TURN OVER

6 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page 6 of 9 QUESTION 7 Circle the number of the equation which best describes the sketch graph alongside: 1 (1) = sin 0 () = cos (3) = cos (4) = sin () R (1) = + () = (3) = ( + ) (4) = ( ) 0 () R (1) = 3 1 () = 3 + (3) = (4) = + () R (d) (1) =. 3 () = 3 + (3) = 3 + (4) = 3. 0 () R 8 marks

7 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page 7 of 9 QUESTION 8 Refer to the diagram A hunter is standing on a 6 m high cliff. He shoots an arrow at a bird fling 15 m above the ground. The height of the arrow above the ground (in m) for the time that the arrow is in the air (in s) is given b the equation h = 5 t + 13 t m 6 m Is it possible for the hunter to hit the bird? Show all working. ground 5 marks QUESTION 9 Given A () = 3 4 Determine the value(s) of for which: A () = 0 (1) K A () undefined () K A () 0 and Real () R (4) P 9 marks PLEASE TURN OVER

8 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page 8 of 9 QUESTION 10 Michael invests R in a savings account. The interest rate for the first 4 ears is 8% p.a. compounded monthl, thereafter the interest rate is changed to 9% p.a. compounded semi-annuall for the net 5 ears. Determine the amount of mone that Michael had in his savings account at the end of this period. (6) C Leigh-Anne is saving for universit and decides to put her mone into a fied deposit paing 10% per annum compounded annuall. She starts her savings with R After 3 ears she deposits another R A final deposit of R is made 8 ears after the initial deposit. How much mone is accumulated in the fied deposit at the end of 10 ears? (6) C Our atmosphere contains ozone which protects the earth from the harmful effects of the sun's radiation. When chloroflurocarbons are released into the atmosphere the destro the ozone in the atmosphere. It is estimated that 0,% of the ozone laer is being lost each ear. If we continue at this rate, it is predicted that in ears we will have destroed half of the ozone laer. Determine, to the nearest decade, how long it will take to have destroed half of the ozone laer. (4) P 16 marks QUESTION 11 Refer to the figure. The graph of to scale). = f () with minimum turning point A ( ; - 9) is drawn (not Write down the co-ordinates of A if = f () becomes: = f () () C = f () + 3 () C f() = f ( + 3) () C (d) = f ( + 3) + 3 () C 0 A (;- 9) 8 marks

9 GRADE 11: EXEMPLAR: MATHEMATICS: PAPER I Page 9 of 9 QUESTION 1 Simplif: (write all answers with positive eponents) a 3n n 4. a (3) R 54 n ( 3 18 n 1 ) n n n+ 1 8a ( a 3 18a ) (7) C (4) P 14 marks QUESTION 13 Pete is driving his remote controlled car at the local track. Once he has set the throttle, he starts to take note of the how far the car is from the starting line (in cm) at a particular time (in seconds) and records his measurements. His results are presented in the table below. time (seconds) distance from start line (in cm) Assume the pattern continues. If the throttle setting and all other conditions remain the same, complete the table for the net 3 seconds. (6) P If it is given that the relationship between the distance the car travels (d) in a particular time (t) is an equation of the form d = a t + b t + c (1) Write down the value of c (the distance travelled when t = 0 seconds). () Determine the value of a and b and hence the equation of motion of this remote controlled car. Hence (or otherwise) determine how far from the starting line the car is after 10 seconds. (1) K (4) C () R (d) What is the average speed of the car in the first 3 seconds? Give our answer in metres per minute (m/min). () K () R 17 marks Total: 150 marks