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Prelim Standard Grade 2008
C1 Fast Track _____________________________________________ Knightswood MATHEMATICS Secondary Standard Grade School Credit Level Prelim Exam 2008 Paper 1 (non-calculator) Time: 55 minutes Answer as many questions as you can. In this paper good thinking is looked for as well as correct answers. Your working gives an indication of your thinking so SHOW YOUR WORKING CLEARLY. You may not use a calculator. Square ruled paper is available. Give all answers to 1 decimal place unless otherwise stated. Formulae List −b ! b 2 − 4ac The roots of ax 2 + bx + c = 0 are x = 2a The Sine Rule: a = b = c sin A sin B sin C 2 2 2 Cosine Rule: a 2 = b 2 + c 2 − 2bc cos A or cos A = b + c − a 2bc Area of triangle: A = 1 ab sin C 2 Trigonometric Relationships: sin x sin 2 x + cos 2 x = 1 cos x = tan x, (¨ x) 2 Standard Deviation: s = ¨(x − x) 2 = ¨ x2 − n n−1 n−1 Based on a publication by P&W 2008/09 KU RE 1. Evaluate 70.1 − 1.65 % 30 2 2. Evaluate 22 −14 2 3 7 3. A is related to a and b by the formula A = 3a 2 − 2b 2 Calculate the value of A when a = 4 and b = −5 2 4. The charities committee of Kent High School holds a lottery to raise funds. The numbers 1 to 25 are used. What is the probability that the first number drawn will be a prime number? 2 5. A knitting shop for wool is closing down. It has this sign in the window. Closing Down Sale 40% off original cost Jill buys knitting wool which costs £42 in the sale. What was the original cost of the wool? 3 6. x Solve the equation 2 = 3(x − 10) 3 7. a) Factorise 2x 2 + 5x − 12 1 b) Hence simplify 2x 2 + 5x − 12 2x 2 − 3x 2 Y 8. The sketch opposite shows the line with equation y = 2x − 4. a) Write down the coordinates of 0 B points A and B. X 2 b) Write down the gradient of the line. 1 A Based on a publication by P&W 2008/09 KU RE 9. In the diagram, N N The bearing of B from A is 110° The bearing of A from C is 034° Angle ACB is 18° 110° A B Find;- N a) The angle CAB 2 b) The bearing of C from B 2 ° 34° 18 C 10. Two identical parabolas are used as a logo for a fast food outlet. They can be represented on a coordinate diagram as shown below. The y-axis is a line of symmetry. Healthy Munch Good food fast! C and E are turning points. y The equation of parabola 1 is y = 6x − x 2 E C Parabola 2 Parabola 1 a) Find the coordinates of B and C. 3 b) Find the coordinates of D and E. 2 c) Write down the equation of parabola 2. 2 D O B x Based on a publication by P&W 2008/09 KU RE 1 1 −1 11. Expand the brackets and simplify x (x − x 2 2 2 ) 2 12. A family of 2 adults and 3 children spend a day at a theme park. The total cost of the tickets is £74. a) Let a stand for an adult ticket and let c stand for a child’s ticket. Write down an algebraic equation to illustrate this information. 1 b) Another family of 1 adult and 4 children spend a day at the theme park. They are charged £67. Write down another equation in a and c to illustrate this information. 1 c) Calculate the cost of:- i) an adult ticket ii) a child’s ticket 3 13. Four identical placemats are put on a circular table, centre O, as shown below. A B 20 cm O D C E The mats touch at A, B, C and D formaing a square ABCD of side 20cm. a) Calculate the length of OC leaving your answer as a surd in its simplest 3 form. b) If C is the midpoint of the radius of the circle OE, show that the area of the circle is exactly 800( cm². 3 [End of Question Paper] 22 22 Based on a publication by P&W 2008/09 Credit paper 1 - Fast Track Marking scheme 2008/09 Knightswood Secondary No. Give 1 mark per bullet point Illustrations for awarding marks KU RE 1 Answer: 20.6 applying BODMAS rule 1.65 % 30 solution 70.1 − 49.5 = 20.6 2 2 2 Answer: 1 21 56−33 impriper fractions with common 21 denominator 2 answer as a proper fraction 1 21 or any other acceptable method 2 3 Answer: -2 substitution 3 % 16 − 2 % 25 solution -2 2 9 4 Answer: P(prime) = 25 list of primes less than 25 2,3,5,7,11,13,17,19,23 9 probability 25 2 5 Answer: £70 percentage that £42 represents 60% = £42 process data 42 + 60 % 100 solution £70 3 6 Answer: x = 12 begin to process data x = 6(x − 10) further processing x = 6x − 60 solution x = 12 3 7a) Answer: (2x − 3)(x + 4) factorise (2x − 3)(x + 4) 1 7b) Answer: x+4 x factorise denminator x(2x − 3) x+4 cancel x 2 8a) Answer: A(0,-4) B(2,0) coordinates of A A(0,-4) coordinates of B B(2,0) 2 8b) Answer: m = 2 stating the gradient m=2 1 9a) Answer: 104° alternate angle to øNCA 34° supplement to bearing from A 70° to B or any other valid method 2 9b) Answer: 232° find 3rd angle of ¡ABC angle ABC = 58° bearing 360°-(58°+70°) or any other valid method 2 Based on a publication by P&W 2008/09 Credit paper 1 - Fast Track Marking scheme 2008/09 Knightswood Secondary No. Give 1 mark per bullet point Illustrations for awarding marks KU RE 10a) Answer: B(6,0) C(3,9) find roots of the function x = 0, x = 6 x coordinate of turning point x=3 y coordinate of turning point y=9 3 10b) Answer: D(-6,0) E(-3,9) recognise by symmetry D(-6,0) recognise by symmetry E(-3,9) 2 10c) Answer: y = −6x − x 2 x term becomes negative -6x x 2 term remains negative −x 2 2 11 Answer: x − 1 law of indices x1 − x0 simplifies x−1 2 12a) Answer: 2a + 3c = 74 algebraic equation 2a + 3c = 74 1 12b) Answer: a + 4c = 67 algebraic equation a + 4c = 67 1 12c) Answer: adult = £19, child = £12 2a + 8c = 134 form system of equations 2a + 3c = 74 solve for c c = 12 solve for a a = 19 3 13a) Answer: x = 10 2 isosceles right angled triangle x 2 + x 2 = 20 2 use Pythagoras 2x 2 = 400 solution x = 10 2 3 13b) Answer: Area = 800( radius = 2 X OC radius = 20 2 area formula area = ((20 2 ) 2 simplification of solution 800( 3 Total 22 22 Based on a publication by P&W 2008/09