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REVISION EXERCISE[ckgubid/AMF5/W9/Tue/KYRHG] Name:

1. Solve the simultaneous equation 32 yx and 52 22 yxyx . Give your answer correctto two decimal places.

2. Solve the equation )243(279 x12x .3. Solve the equation 12)(xlogxlog 44 .4. Solve the equation xlog25xlog 24 . Ans: (1) 6 (2)

3

8(3)

9

4

5. The triangle with vertices A(4, 3), B(1, 1) and C(t, 3) has an area of 11 unit2.Find the possible values oft. [Ans: t= 0, 22]

6. The points P(3,p), B(1, 2) and C(9, 7) lie on a straight line. If P divides BC internally in theratio m : n, find

(a)m : n,(b)the valuye ofp. [Ans: (a) 2 : 3 (b)p = 4]

7. Given two straight lines 134

kyx and 3y = kx 8 are perpendicular to one another. Find

the values ofk. [Ans: k= 2 ]

8. The point A is (1, 3) and the point B is (4, 6). Point Q moves such that QA : QB = 2 : 3.Find the equation of the locus of point Q. [Ans: 5x

2+ 5y

2+ 14x + 102y54 = 0]

9. The sum of the first n terms, nS of an arithmetic progression is given by nnSn 434

1 2 .

Find the 10th

terms.

10. Given that 1,3 mm and 16 m are three consecutive terms of a positive geometricprogression. Find

(a) the value ofm,(b) the sum of the first 6 terms of this GP.

11. The value of a car decreases yearly by 10% of its value in the previous year. If a new car wasbought in the year 2000 at a price of RM80 000, calculate its value in the year 2010.

12. Given qp 1.0.....1272727,0 , where q is a recurring decimal, express p as a fraction inits simplest form.

13. Two variables, x and y are related by the equation xx

y 53 . Given that y decreases at a

rate of 7 units per second, find the rate of change ofx whenx = 3.

14. A cylinder has a fixed height of 10 cm and a radius of 5 cm. If the radius decreases by 0.05cm, find, in terms of ,

(a) the approximate change in volume of the cylinder,(b) the final volume of the cylinder.

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15. Diagram 1 shows a straight line obtained when the equation xkx

hy is converted

linear form.

Diagram 1

Find the values ofh and k.

16.

Diagram 2

Diagram 2 shows part of a straight line graph obtained by plotting y against 2x , Find thevalue ofx wheny = 85.

17. Table 1 shows values of two variables,x andy, obtained from an experiment. The variablesxandy are related by equation q

yx

p4

1 , such thatp and q are constants.

x 1.5 2.5 3.0 4.5 6.0 8.5

y 0.60 0.66 0.68 0.72 0.74 0.75

Table 1

(a) Plot the graph of

y

xagainstx byusing a scale of 2 cm to 1 unit on both axes. Hence

draw the best fit line. [4 marks]

(b) Use your graph in (a) to find the value of

(i) p,

(ii) q,

(iii) y when 8x .

xy

)4,6(

)9,1(

xO

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18.Items Price Index Weightage

2005 2006

Cheese 115 125 5

Flour 104 112 4

Butter 120 130 x

Creamer 102 110 y

Wages 112 126 3

Table above shows the price indices as well as the respective weightages for the ingredientsused in making a cheese cake which is sold in a hotel. The price indices shows are based on

the year 2004.

(a)Given that the composite index for the years 2005 and 2006 based on 2004 are 109.85and 119.55 respectively, calculate the values ofx andy.

(b)Calculate the composite index of making a cheese cake in the year 2006 based on theyear 2005.

(c)Calculate the increase in wages from the year 2005 to 2006 if the wages charged formaking a cheese cake in 2005 was RM20.

[Ans: (a)x = 3,y = 5 (b) 108.83 (c) RM2.80]