```					                                                                                                   C1
Fast Track

_____________________________________________
Knightswood                     MATHEMATICS
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
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.

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:-
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
applying BODMAS rule                 1.65 % 30
solution                             70.1 − 49.5 = 20.6                2
2
56−33
impriper fractions with common        21
denominator
2
answer as a proper fraction           1 21
or any other acceptable method       2
substitution                         3 % 16 − 2 % 25
solution                             -2                                2
9
list of primes less than 25          2,3,5,7,11,13,17,19,23
9
probability                          25
2
percentage that £42 represents       60% = £42
process data                         42 + 60 % 100
solution                             £70                               3
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
x
factorise denminator                  x(2x − 3)
x+4
cancel                                x                                2
coordinates of A                     A(0,-4)
coordinates of B                     B(2,0)                            2
alternate angle to øNCA               34°
supplement to bearing from A          70°
to B                              or any other valid method                  2
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
find roots of the function           x = 0, x = 6
x coordinate of turning point        x=3
y coordinate of turning point        y=9                                     3
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
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
area formula                         area = ((20 2 ) 2
simplification of solution           800(                                    3
Total                                22    22

Based on a publication by P&W 2008/09

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 34 posted: 3/7/2010 language: English pages: 6