WEDNESDAY, 4 MAY 1.30 PM 2.25 PM. 3 Full credit will be given only where the solution contains appropriate working.

Transcription

1 C 500/405 NATIONAL QUALIFICATIONS 0 WEDNESDAY, 4 MAY MATHEMATICS.0 PM.5 PM STANDARD GRADE Credit Level Paper (Non-calculator) You may NOT use a calculator. Answer as many questions as you can. Full credit will be given only where the solution contains appropriate working. 4 Square-ruled paper is provided. If you make use of this, you should write your name on it clearly and put it inside your answer booklet. LI 500/405 6/0 *500/405*

2 FORMULAE LIST ± 4 The roots of ax + bx + c = 0 are x = ( b b ac a ( Sine rule: a = b = c sin A sin B sin C Cosine rule: a = b + c bc cos A or cos A = b + c a bc Area of a triangle: Area = ab sin C Standard deviation: ( x x) x ( x) / n s = =, where n is the sample size. n n [500/405] Page two

3 . Evaluate Factorise fully m 8.. Given that f(x) = 5 x, evaluate f( ). 4. Solve the equation x + = x 5. [Turn over [500/405] Page three

4 5. Jamie is going to bake cakes for a party. He needs 5 of a block of butter for cake. He has 7 blocks of butter. How many cakes can Jamie bake? 6. A driving examiner looks at her diary for the next 0 days. She writes down the number of driving tests booked for each day as shown below. Number of tests booked Frequency (a) Find the median for this data. (b) Find the probability that more than 4 tests are booked for one day. [500/405] Page four

5 7. (a) Brian, Molly and their four children visit Waterworld. The total cost of their tickets is 56. Let a pounds be the cost of an adult s ticket and c pounds the cost of a child s ticket. Write down an equation in terms of a and c to illustrate this information. (b) Sarah and her three children visit Waterworld. The total cost of their tickets is 6. Write down another equation in terms of a and c to illustrate this information. (c) (i) Calculate the cost of a child s ticket. (ii) Calculate the cost of an adult s ticket. [Turn over [500/405] Page five

6 8. A square, OSQR, is shown below. Q is the point (8, 8). y T S P Q (8, 8) O R x The straight line TR cuts the y-axis at T (0, ) and the x-axis at R. (a) Find the equation of the line TR. The line TR also cuts SQ at P. (b) Find the coordinates of P (a) Simplify a a 4. (b) Solve for x, x + 8 = 4. [500/405] Page six

7 0. In triangle ABC AC = 4 centimetres BC = 0 centimetres angle BAC = 50 A 50 4cm C B 0 cm Given that sin 0 =, show that sin B = F varies directly as s and inversely as the square of d. (a) Write down a relationship connecting F, s and d. (b) What is the effect on F when s is halved and d is doubled?. The sums, S, S and S 4 of the first, and 4 natural numbers are given by: S = + = ( ) = S = + + = ( 4) = 6 S 4 = = (4 5) = 0 (a) Find S 0, the sum of the first 0 natural numbers. (b) Write down the formula for the sum, S n, of the first n natural numbers. [END OF QUESTION PAPER] [500/405] Page seven

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9 C 500/406 NATIONAL QUALIFICATIONS 0 WEDNESDAY, 4 MAY.45 PM 4.05 PM MATHEMATICS STANDARD GRADE Credit Level Paper You may use a calculator. Answer as many questions as you can. Full credit will be given only where the solution contains appropriate working. 4 Square-ruled paper is provided. If you make use of this, you should write your name on it clearly and put it inside your answer booklet. LI 500/406 6/0 *500/406*

10 FORMULAE LIST Sine rule: ± 4 The roots of ax + bx + c = 0 are x = a = b = c sin A sin B sin C ( b b ac a ( Cosine rule: a = b + c bc cos A or cos A = b + c a bc Area of a triangle: Area = ab sin C Standard deviation: ( x x) x ( x) / n s = =, where n is the sample size. n n [500/406] Page two

11 . Olga normally runs a total distance of 8 miles per week. She decides to increase her distance by 0% a week for the next four weeks. How many miles will she run in the fourth week?. Expand and simplify (x + )(x 5x + 4).. Solve the equation x + x 7 = 0. Give your answers correct to significant figures A car is valued at 780. This is 6% less than last year s value. What was the value of the car last year? [Turn over [500/406] Page three

12 5. A spiral staircase is being designed. B C. m 4 A Each step is made from a sector of a circle as shown. The radius is metres. Angle BAC is 4. For the staircase to pass safety regulations, the arc BC must be at least 0 9 metres. Will the staircase pass safety regulations? 4 6. Two rectangular solar panels, A and B, are mathematically similar. Panel A has a diagonal of 90 centimetres and an area of 400 square centimetres. A 90 cm B 5 cm A salesman claims that panel B, with a diagonal of 5 centimetres, will be double the area of panel A. Is this claim justified? Show all your working. 4 [500/406] Page four

13 7. ABCDE is a regular pentagon with each side centimetre. Angle CDF is 7. EDF is a straight line. B cm cm A C cm cm 7 E cm D F (a) Write down the size of angle ABC. (b) Calculate the length of AC. 8. A pipe has water in it as shown. A B A O r B 5cm 8 cm The depth of the water is 5 centimetres. The width of the water surface, AB, is 8 centimetres. Calculate r, the radius of the pipe. [Turn over [500/406] Page five

14 9. A flower planter is in the shape of a prism. The cross-section is a trapezium with dimensions as shown. 68 cm 0 cm 4 cm 0 cm cm (a) Calculate the area of the cross-section of the planter. (b) The volume of the planter is 56 litres. l centimetres Calculate the length, l centimetres, of the planter. 0. Tom and Samia are paid the same hourly rate. Harry is paid more per hour than Tom. Tom worked 5 hours, Samia worked 8 hours and Harry worked hours. They were paid a total of 49. How much was Tom paid? [500/406] Page six

15 . Paper is wrapped round a cardboard cylinder exactly times. The cylinder is 70 centimetres long. 70 cm The area of the paper is 000 square centimetres. Calculate the diameter of the cylinder. 4. Part of the graph of y = 4 sin x is shown below. y P O Q R 60 x y = 4 sin x The graph cuts the x-axis at Q and R. P is the maximum turning point. (a) Write down the coordinates of P. (b) Calculate the x-coordinates of Q and R. 4 [Turn over for Question on Page eight [500/406] Page seven

16 . The diagram shows the path of a flare after it is fired. The height, h metres above sea level, of the flare is given by h = t t where t is the number of seconds after firing. h h = t t O t Calculate, algebraically, the time taken for the flare to enter the sea. 4 [END OF QUESTION PAPER] [500/406] Page eight