Free Essay

My Dream Car

In: Other Topics

Submitted By lyrickiddkevii
Words 998
Pages 4
2008
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I
SECTION II
Answer TWO questions in this section.
RELATIONS, FUNCTIONS AND GRAPHS
Page l0
( lmark)
( 2 marks)
( lmark )
( 2 marks)
( 2 marks)
9. (a) Simplify
(i) * *
(ii)
t'xt+)f
35
oibi*J"ut.
If"flr) = ?-x- 3, find the value of
(i) fl2)
(ii) ,f-t(o)
(iii) f-'f(z) f o)
(c) The temperature, K, of a liquid t minutes after heating is given in the table belowt
(time in minutes) 0 10 20 30 40 50 60
K
(Temp. in "C) 84 6l 4D 29 27 26 25
Using a scale of 2 cm to represent 10 giggkon the horizontal axis and a scale of 2 crn to represent l0 degrees on the vertical axis, construct atemperature-time graph to show how the liquid cools in the 60 minute interval'
Draw a smooth curve through all the plotted points.
Use your graph to estimate
( 4 marks)
a) the temperature of the liquid after 15 minutes
b) rhe rate of cooling of the liquid at t = 3o minutes. ( 3 marks)
Total 15 marks
(i)
(ii) o1234a20F 2008
GO ON TO TIIE NEXT PAGE
.-
\
10.
Page 11
(a) Solve the following pair of equations forx and y: y + 4x=27 ry + x=40 ( 6marks)
(b) The shaded area in the diagram below shows the solution of a set of inequalities in
.r and y. The variable x represents the number of boys in a cricket club and y represents the number of girls in the cricket club.
20
J= + x+tZ
Use the graph above to answer the questions which follow.
(i) State, using arguments based on the graph, whether the cricket club can have as members:
a) 10 boys and 5 girls
b) 6 boys and 6 girls. ( 2marks)
Write down the set of THREE inequalities that define the shaded region.
( 4 marks)
A company sells uniforms for the club and makes a profit of $3.00 on a boy's uniform and $5.00 on a girl's uniform.
(ii)
(iii)
a)
b)
Write an expression inx andy thatrepresents the total profit made by the company on the sale of uniforms.
Calculate the minimum profit the company can make. ( 3marks)
Total 15 marks
GO ON TO TI{E NEXT PAGE
0r234020tF200,8
\rr
11. (a)
Page 12
GEOMETRY AND TRIGONOMETRY
In the diagram below, not drawn to scale, PQis atangent to the circle, centre O. PR is parallel to OS and angle SPR =26".
Calculate, grying reasons for your answer, the size of
(i) angle PTS
(ii) angle RPQ.
(i)
(ii)
(iii)
(iv)
( 2 marks)
( 2 marks)
O) In the diagram below, not drawn to scale, O is the centre of the circle of radius 8.5 cm and AB is a chord of length 14.5 cm.
Calculate the value of I to the nearest degree. ( 3 marks)
Calculate the area of triangle AOB. ( 2 marks)
Hence, calculate the area of the shaded region. [Use n = 3.14f. ( 3 marks)
Calculate the length of the major arc AB. ( 3 marks)
Total 15 marks
01234020F' 2008
GO ON TO THE NEXT PAGE
-.1
I
I
i
12. A ship leaves Port R, sails to Port S and then to Port Z.
The bearing of S from R is 112o.
The bearing of Zfrom S is 033'.
The distance RTis 75 km and the distance RS is 56 km.
Page 13
( lmark)
( 2 marks)
( lmark)
( lmark)
( Lmark)
( 3 marks)
( 2 marks)
(a) Draw a diagram showing the journey of the ship from R to S to f.
Show on your diagram
(i) the North direction
(ii) the bearings 112o and 033o
(iii) the points R, S and T
(iv) the distances 75 km and 56 km.
Calculate
(i) the size of angle RSZ
(ii) the size of angle RZS
(iii) the bearing of R from T.
o)
(c) The ship leaves Port T and travels due west to a point X which is due north of R.
(i) ShowonyoudiagramthejoumeyfromZtoX. ( lmark)
(iD Calculate the distance 7X. ( 3 marks)
Total 15 marks o1234020tF 2008
GO ON TO THE NEXT PAGE v VECTORS AND MATRICES
13. The position vectors of A and B relative to the origin are a and D respectively.
The point P is on OA such that OP =2PA.
The point M is on BA such that BM = MA.
(a) Copy the diagram and complete it to show the points of P and M.
(b) OB is produced to N such that OB = BN.
(i) Show the position of N on your diagram.
(ii) Express in terms of c and D the vector
"
l,i, pi, ura pfr.
(c) Use a vector method to prove that P, M and. N are collinear.
(d) Calculate the length of AN if
A= /o\ , =(l
[/ *o
Page 14
( 2marks)
( lmark)
( 5 marks)
( 4 marks)
( 3 marks)
Total 15 marks o123N20tF2008 GO ON TO TI{E NEXT PAGE ta' t4. (a) X and f are two matrices where
(-z o\ (q X- I landl=l -l\l. [5 t) t3 7)
Evaluate f + V.
(r 2\
Thematrix | . ^ | maps QQ,2)toQ'(5,7). \l 3)
Find the 2x2manix which maps Q' back to Q.
Page 15
( 4 marks)
( 2marks)
(b)
(c) The vertices of triangle DEF are
D(5, 12), E(2, 7) and F(8, 4).
(i) Triangle DEF undergoes an enlargement with centre, O, andscale factor, ft. Its image \s AEF where
D (5,12) + D'(7.5, l8).
a) Determine the value of ft.
b) Hence write down the coordinates of E" and F' . ( 4marks)
(iD D'gF undergoes a clockwise rotation of 90o about the origin.
a) Determine the 2 x 2 matrix that represents a clockwise rotation of 90o about the origin.
b) Determine the coordinates of D'E'F', the image of D'EF, under this rotation. c) Deterrnine the 2 x 2 marix that maps triangle DEF onto triangle D'E'F'.
( 5 marks)
Totsl 15 marks
EI\D OF TEST
oL234020tF2W8

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