MATHEMATICS Standard Grade - Credit Level

Transcription

1 Prelim Examination 008 / 009 MATHEMATICS Standard Grade - Credit Level Paper I Time allowed - minutes Read Carefully. Answer as many questions as you can.. Full credit will be given only where the solution contains appropriate working.. You may not use a calculator Pegasys 008

2 KU RE. Evaluate kq P r Change the subject of the formula to r.. Factorise fully x 0x 6.. Sparks Electrical are having their annual clearance sale where everything is reduced by 0%. A Flat screen TV cost 80 in the sale. How much did the TV originally cost?. Express as a single fraction in its simplest form. x x Pegasys 008

3 KU RE 6. Does the point (0,0) lie on the line shown below? [You must show working] y 8 (, 6) x 7. (a) Simplify 7a b a b (b) If a = and b =, find the value of the expression in part (a). 8. cm cm A cm (a) Write down the value of tan A from the triangle above. (b) Hence, evaluate tan A. tan A Pegasys 008

4 KU RE 9. When two numbers (x and y) are added together the answer is. When the same two numbers are multiplied together the answer is 8. By creating a system of equations and solving them, find the two numbers. 0. A sequence of numbers is 7, 9, 7,.. Numbers from this sequence can be written in the following way : st term : 7 = nd term : 9 = rd term : 7 = (a) Write down a similar expression for the th term. (b) Hence or otherwise find the n th term in its simplest form.. The diagram shows part of the graph of the function y x x 6. The graph cuts the x axis at the points P and Q. Find the distance PQ. y P O Q x END OF QUESTION PAPER Pegasys 008

5 Credit Level Prelim 008/009 Marking Scheme - Paper Give mark for each Illustration(s) for awarding each mark. ans: 8 KU 0 0 = 6 know order of calculations calculations correct answer. ans: kq r KU P remove fraction manipulate formula solve for r Pr kq kq r P answer. ans: x x KU extract common factor attempt to factorise trinomial complete factorisation x x x x. ans: 800 KU correct strategy uses correct ratio calculations correct 60% = answer. ans: Pegasys 008 x x x KU x x x x x x KU

6 common denominator correct numerator simplify fraction Give mark for each Illustration(s) for awarding each mark 6. ans: Yes RE correct strategy find equation of line sub point into line conclusion m y x 8 y 08 0 (0, 0) lies on the line 7.(a) ans: 7a b KU convert sq root to a power simplify a s simplify b s b b a b 7.(b) ans: 6 KU substitutes correctly correctly evaluates expression 7 answer 8.(a) ans: correct Tan ratio KU tan A (b) ans: Pegasys substitute correctly subtract fractions correctly KU answer 7

7 divide fractions correctly Give mark for each Illustration(s) for awarding each mark 9. ans: 6 and 8 RE creates both equations substitutes attempts to solve equations successfully solves equations x y, xy 8 y x x x 8 x x 8 0 x 8x (a) ans : RE state answer answer 0.(b) ans: n + n + RE generalise pattern attempts to simplify completes simplification n n n n n n answer. ans : PQ = units RE knows to make function equal to 0 factorises solves finds distance x x 6 0 ( x )( x ) 0 x, x PQ = units Pegasys 008

8 Total: KU RE 6 Standard Grade Credit Paper I - Marks Grid 008/009 Question Number KU RE 6 7(a) 7(b) 8(a) 8(b) 9 0(a) 0(b) Total / /6 Pegasys 008

9 Prelim Examination 008 / 009 MATHEMATICS Standard Grade - Credit Level Paper II Time allowed - 80 minutes Read Carefully. Answer as many questions as you can.. Full credit will be given only where the solution contains appropriate working.. You may use a calculator Pegasys 008

10 FORMULAE LIST The roots of b b ac ax bx c 0 are x a Sine rule: a b c sin A sin B sin C Cosine rule: b c a a b c bccos A or cosa bc Area of a triangle: Area ab sin C Standard Deviation: s ( x x ) n x n ( ) n x Pegasys 008

11 KU RE. During the 00 Athens Olympic games the BBC recorded audience figures for different events people watched Paula Radcliffe compete in the marathon people watched Kelly Holmes win in the 800 metres. (a) How many more people watched the marathon than the 800 metres? Answer in scientific notation. (b) Express this as a percentage of the 800 metres audience to the nearest percent.. Solve the inequation ( x) + 7 x 6, where x is a whole number.. Last year, for a Mathematical Competition the organisers bought 0 medals and 8 trophies for 8.0 Let m be the price of a medal and t the price of a trophy. (a) Write down an equation in m and t to illustrate this information. This year they bought in medals and trophies which cost them 0% more than last year. (b) Write down an equation in m and t to illustrate this information. (c) Assuming that the cost of a medal and a trophy remained the same for both years, find algebraically the cost of medal and trophy. Pegasys 008

12 . The cost, C, of a pizza varies directly as the number of toppings, T, and the square of its diameter, D inches. An eight inch pizza with toppings cost.0. Serena reckons that a sixteen inch pizza with the same toppings should cost 0.0 (double the 8inch cost). Is she correct? [All working should be shown.] KU RE. Solve the following equation giving your answer correct to significant figures. x x Two windows are broken in a block of flats and the owner has hired in a crane to allow him to carry out the repairs. In the two positions shown above the arm of the crane is at its full stretch of m. The diagram below represents the arms of the crane. The lower window is 8m above Pegasys 008

13 the ground and the higher window is 0 6m above the ground. 0 6m x o 8m Find the angle, x o, the crane had to turn through to get to the higher window from the lower window. 7. Solve the following equation sin x where 0 x Shown is a children s swimming toy consisting of a plastic cylinder connected to a handle. KU RE 7cm 8cm The toy is thrown into deep water where it sinks and the swimmer is then encouraged to retrieve it. Pegasys 008

14 To make it easy to pick up, the cylinder is weighted on the underside with a dense material and the upper part filled with water. The sections are separated by a plastic seal. End view of toy Water Seal Dense Material cm 7cm The cylinder has a diameter of 7cm and length 8cm. The depth of the dense material is cm. Calculate the area of seal required to keep the two substances separate. 9. The depth, d metres, of water in a harbour over a hour period starting at 0600 is 0 given by the formula d cos 0t, where t is the number of hours after (a) Write down the maximum and minimum depth of water in the harbour. A pod of whales enters the harbour at 0600 when the water is at its maximum depth. They need to swim in water at least m deep or they become distressed. (b) At what time, to the nearest minute, must the pod leave the harbour to prevent any distress? KU RE 0. The sketch below shows a plot of land purchased to build a house on. 70 o m At present the land is valued 80 per square metre. m 0 o m Calculate the value of the plot shown to the nearest 0. 6 Pegasys 008

15 . Part of the graph of y x x is shown below. y 0 Use iteration to find the value of the negative root of the equation x x 0, correct to one decimal place. Show all steps in your calculation. x End of Question Paper Give mark for each Illustration(s) for awarding each mark. (a) ans: KU subtracts in the correct order answer. (b) ans: % KU know how to calculate % Pegasys 008 calculation correct Credit Level Prelim 008/ % 8 8 answer

16 . ans: 0,,, KU break brackets and collect like terms create positive variable state whole number solution.(a) ans: 0m +8t = 8 0 KU RE state equation.(b) ans: m + t = 70 0 RE calculate new cost state equation.(c) ans: m = 8p & t = RE attempts to solve equations simultaneously correctly solves one variable correctly solves second variable states cost of of each item. ans: No, the price is quadrupled. RE RE state equation introduce change implement change comment on answer Give mark for each Illustration(s) for awarding each mark Pegasys 008 evidence a = b = c = b ac 6

17 . ans: and 0 77 KU know to use quadratic formula identify values of a, b, and c finds discriminant both solutions correct rounding 6. ans: o RE use SOHCAHTOA calculate first angle calculate second angle calculate missing angle 7. ans: o, 6 9 o KU solves for sinx o identifies quadrants states solution 8. ans: cm RE interpret information identify right angled triangle calculate missing side state breadth of seal calculate area Pegasys 008

18 Give mark for each Illustration(s) for awarding each mark 9.(a) ans: 8m & m KU state maximum state minimum 9.(b) ans: 099 RE correct strategy attempt to solve equation correctly solve equation state time cos0t cos0t 0t 09, [0 ] t = 6h = hours 9minutes 0. ans: 0 0 6RE 6 correct strategy calculate area of upper triangle calculate second side of lower triangle calculate area of lower triangle calculate total area calculate cost answer 0 A sin m s cos70. ans: KU s = 8m root lies between & / repeated calculations answer 0 A 8 sin 0 8 m 6 C 6 80 leading to answer f, f root lies between and. Pegasys 008

19 Standard Grade Credit Paper - Marks Grid 008/009 Question Number KU RE (a) (b) (a) (b) (c) (a) 9(b) 0 Total / /9 Pegasys 008

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