GANSBAAI ACADEMIA. L. Havenga A. van Wyk

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1 MATHEMATICS Grade 1 EDUCATOR MODERATOR GANSBAAI ACADEMIA L. Havenga A. van Wyk EXAM P1 June 014 Total: 150 Time: 3 hours INSTRUCTIONS 1. This question paper consists o 11 questions. Answer ALL questions.. Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in determining the answers. 3. An approved scientiic calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 4. I necessary, answers should be rounded o to TWO decimal places, unless stated otherwise. 5. Number your answers correctly according to the numbering system used in this question paper. 6. Diagrams are not necessarily drawn to scale. 7. It is in your own interest to write legibly and to present your work neatly. QUESTION 1 PAPER Solve or x correct to two decimal places, i necessary: x x 4 3 (3) 3 x x 3 x 6x x (5) x 15 (4) 1. Solve simultaneously x and y: x3y 5 and xy (7) y I ( x) 4x and g( x) x, determine ( g (9)). (3) 1.4 Simpliy without using a calculator: (4) [6] 1

2 QUESTION Consider the series: How many terms are in the series? (3).1. Write the series in sigma-notation. ().1.3 Calculate the value o the series. (). Consider the ollowing sequence: ; 5; ; 9; ; 13; ; 17;... Calculate the sum o the irst 100 terms o the sequence. (4) QUESTION 3 3. Given the series: (3) (3) (3) (3) k 3.1 Show that the series will converges. () 3. Calculate the sum to ininity. () 3.3 Calculate the sum o the irst 7 terms o the series. (3) 3.4 Use your answers rom 3. and 3.3 to calculate the ollowing: [11] 8.(3) n (3) n8 [10] QUESTION 4 6; 5 x; 6 and 6x are the irst our terms o a quadratic sequence. 4.1 Calculate the value o x. (4) 4. Hence, determine a ormula or the n th term o the sequence. (4) [8]

3 QUESTION Calculate the annual compound interest rate that will have the same outcomes over three years at a simple interest rate o % per year. (5) 5. Thuso is a young armer. He has just bought his irst tractor or R Due to inlation, the value o the tractor depreciates at a rate o 7% p.a. on a reducing balance. Thuso knows that he will have to replace the tractor in our years time. The price o a new tractors appreciates at 9% per annum Calculate the scrap value o his tractor ater our years. () 5.. Determine the cost o a new tractor in our years time. () 5..3 He plans to trade in the old tractor ater our years. In his budget, he makes provision or R unorseen expenses that might occur during the transaction. How much money will he need in the sinking und in our years time? () 5..4 Thuso immediately starts to pay equal monthly payments into the sinking und. The und earns interest at 9% per annum, calculated monthly. His last payment is made at the end o the our-year period. How much does he pay every month? (3) [14] QUESTION 6 The ollowing equations are represented graphically. x ( ) ( x ) 9 AND D is the turning point o ( x ). g x mx k 3

4 6.1 Write down the range o. () 6. Calculate the coordinates B, the intercept o. (3) 6.3 Calculate the values m and k. () 6.4 Calculate the distance rom E to F, where E and F lies on the symmetry axis o. (3) 6.5 Determine the equation o the tangent to the curve and goes through C. (3) [13] QUESTION 7 a Given ( x) q. The point A (, 3) is the intersection asymptote o x p. The graph o goes through x axis at (1; 0) D is the y -interception o. 7.1 Write down the equations o the asymptote o. () 7. Determine the equation o. (4) 7.3 Write down the coordinate o D. () 7.4 Write down the equation o g, i g is n straight line that connects A and D. (3) 7.5 Write the coordinates o the other intersections o and g. (4) [15] 4

5 QUESTION 8 h x The graph x a is outlined below. 1 A 1; is a point on the graph h. y h A(-1; ½) O Q x 8.1 Explain why the coordinates o Q is Q 0;1. () 8. Calculate the value o a. () 8.3 Write down the equation o the inverse unction, -1 h, in the orm o y... () Draw a graph on DIAGRAM SHEET 1 o h. Show on the graph the coordinate o the two points that lies on this graph. (3) 8.5 Read rom your graph the values o x which log x 1. () [11] QUESTION Calculate x using the irst principle x x 9. Evaluate: D x 1. (4) 4 x x 8 (3) dy dx i 5 3 x y 7x x (4) d dx 9..3 ( x) g( x) i and g( x) x 1 (3) 3 ( x) 3x x [14] 5

6 QUESTION 10 3 The graph o x x ax bx c is sketched below. The x -intercept are indicated Determine the values o a, b and c. (4) 10. Calculate the x -coordinate o A and B, the turning point o. (5) 10.3 For which values o x be x 0? (3) [1] QUESTION A eeding scheme conducted a survey about the preerences or mutton, bee and chicken among 150 learners at a school. The indings are as ollows: 54 eat mutton 75 eat chicken 66 eat bee 6 eat all three types 30 do not eat any meat at all 3 eat chicken and bee but not mutton 16 eat mutton and bee but not chicken x number o learners eat chicken and mutton but not bee Represent the results in a Venn diagram. () How many learners eat mutton only? () What is the probability that a learner, i randomly selected, would eat only two types o meat? () 6

7 11. In July 01, the Western Cape government started a campaign against people using a cell phone while driving a vehicle. Cell phones are coniscated and returned to the owner upon paying a ine. This action is based on their assumption that speaking on a cell phone is more likely to contribute to an increase in the number o accidents. The Grade 11 learners o a private school conducted a survey among 650 drivers in their area to test this assumption. The results o the survey are captured in the ollowing table. Involved in accidents Never involved in accidents Total Drivers using cell phones while driving Drivers not using cell phones while 444 driving Total Copy and complete the table. (3) 11.. Use the table to determine the ollowing probabilities: a) P(drivers never involved in accidents) (1) b) P(drivers using cell phones while driving or drivers never involved in accidents) () c) P(drivers using cell phones while driving and involved in accidents) (1) Contrary to the government s belie, most o the public argue that using cell phones while driving and being involved in accidents are two independent events. Which perception is supported by the survey? (3) [16] TOTAL: 150 7

8 DIAGRAM SHEET 1 NAME AND SURNAME:.. 8