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Bukit Merah Secondary School AM 2011 Prelims Paper 1
1. The gradient function of a curve is ( )( )kxx + 213 , where kis a constant. Given that
the curve has a turning point at ( )5,2 , find the value ofkand hence the equation of
the curve. [4]
2. (a) Solve the equation 0332 = xx . [2]
(b) Sketch the graph of 31 = xy , indicating clearly all the points at which the
graph meets the coordinate axes. [3]
3. (a) Calculate the smallest positive integerp for which the equation01025
2 =++ pxx has real roots. [3]
(b) Calculate the range of values ofm for which ( )1144 2 ++++ xmxx is always
positive for all real values ofx. [3]
4. The diagram, which is not drawn to scale, shows a regionRbounded by the curve
pxxy ++= 32 2 , theyaxis and the line 2+= qxy wherep and q are constants. The
line is also the tangent to the curve at the pointM wherex = 2.
(i) Find the value of p and ofq. [3]
(ii) Find the area of region R. [4]5. (i) Prove the identity x
x
xx tan
sin1
cossec =
+ .
[3]
(ii) Hence solve the equation 7sec5
sin1
cossec3
2 =
+
x
x
xx for
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6. The table shows experimental values of two variablesx andy.
x 0.2 0.4 0.6 0.8 1.0
y 0.44 0.50 0.57 0.68 0.83
It is known thatx andy are related by the equationbx
ay
= where a and b are
constants.
(i) Using graph paper, ploty
1againstx and draw a straight line graph.
[3]
Use your graph to estimate
(ii) the value of a and ofb, [3]
(iii) x wheny =9
5.
[2]
7. (i) Given that ( ) 9206 23 += xpxxxf , find the value ofp for which ( )xf is
exactly divisible by ( )13 x . [2]
(ii) Using this value ofp, factorise ( )xf completely.
Hence, or otherwise, solve the equation ( ) ( )927 = xxf . [6]
8. A curve has the equation ( ) 4643 += xxy .
(i) Expressdy
dxin the form
46 x
kx, where kis a constant.
[3]
Hence
(ii) find the rate of change ofx whenx = 2, given thaty is changing at a constant
rate of 4 units per second, [2]
(iii) evaluate dxx
x 46
94
1.
[3]
9. (a) Given that 152
3
3
1 23 ++= xxxy , show thaty is a decreasing function ofx.[3]
(b) The equation of a curve is
cossin
sin8
+=y . Find the value(s) of , where
BMSS / 4E5N Add Maths Paper1 /Prelim2011
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* * * EndofPaper * * *
Answers (BMSS AMaths Prelim Paper 1)
1 4=k , 7452 23 += xxxy2
(a)5
3=x (b)
3 (a) 8 (b) 80
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BMSS / 4E5N Add Maths Paper1 /Prelim2011