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Prelim Standard Grade 2008

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_____________________________________________
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

				
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