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My Dream Car

In: Other Topics

Submitted By lyrickiddkevii
Words 998
Pages 4
Answer TWO questions in this section.
Page l0
( lmark)
( 2 marks)
( lmark )
( 2 marks)
( 2 marks)
9. (a) Simplify
(i) * *
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
(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
(ii) o1234a20F 2008
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.
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.
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
11. (a)
Page 12
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.
( 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
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.
(i) the size of angle RSZ
(ii) the size of angle RZS
(iii) the bearing of R from T.
(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
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)
(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

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