bukit merah_prelim2011_am_4e5n_p1.doc

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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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2

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

[Turn Over


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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

bukit merah_prelim2011_am_4e5n_p1.doc

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