8/13/2019 METHODIST KL 2013 M1(Q&A)

1/12

1 | 4

SEKOLAH MENENGAH KEBANGSAAN LAKI-LAKI METHODIST, KL

Section A

[45 marks]

Answerallquestions in this section.

1. Show that the polynomial 241072 23 xxx has 2x as a factor. [2 marks]Hence determine the set of values of x so that 63241072 23 xxxx . [6 marks]

2. Expand 31)31( x in ascending powers of x up to and including the terms in 5x . State the range of validityfor this expansion. [4 marks]

By taking8

1x , find 3 5 correct to 3 decimal place. [3 marks]

3. Given

P=

112

121

211

(a) Find Rso that R= P24PI, [3 marks](b) Show that PR+ 4I= 0. [2 marks]

4. The curve C has equation054916

23

xyxy

(a) Finddx

dyin terms of x and y . [4 marks]

(b) Find the coordinates of the points on C where 0dx

dy. [5 marks]

5. Sketch the curve 29 xy , stating the coordinates of the turning points and of the intersections with theaxes. [3 marks]

The finite region bounded by the curve and thex-axis is denoted byR.

(a) Find the area ofR. [2 marks](b) Hence or otherwise find 90 .9 dyy [2 marks](c) Find the volume of the solid of revolution obtained whenRis rotated through 180oabout they-axis.

[2 marks]

6. Solve the differential equation).1)(1(2

222yx

dx

dyyx

given that 1y when 1x . [6 marks]

8/13/2019 METHODIST KL 2013 M1(Q&A)

2/12

2 | 4

Section B

[15 marks]

Answeranyone question in this section

7. During the schools family day, U6A offers three sales packages A, B and C for spaghetti, hot-dogs andcupcakes. The number of each item and the offer price for each package are shown in the following table.

Sales Package Number of plates of

spaghetti

Number of hot-

dogs

Number of

cupcakes

Offer price (RM)

A 4 2 2 28

B 3 4 3 30

C 2 4 2 24

By representing the prices of a plate of spaghetti, a hotdog and a cupcake asx,yandzrespectively, obtain

the simultaneous equation representing the information above. [3 marks]

By applying the Gaussian elimination, find the price of a plate of spaghetti, a hotdog and a cupcake

respectively. [12 marks]

8. Expressrr

ur2

22

in partial fractions. [3 marks]

Using the results obtained,

(a) show that 222)2(

12

111 rrrr

ur . [3 marks]

(b) show that

n

r

rnn

u1

,2

1

1

1

2

3and determine the values of

1rru and ).

3

1(

1

1

rrr

u

[9 marks]

8/13/2019 METHODIST KL 2013 M1(Q&A)

3/12

3 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

4/12

4 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

5/12

5 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

6/12

8/13/2019 METHODIST KL 2013 M1(Q&A)

7/12

7 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

8/12

8 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

9/12

9 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

10/12

10 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

11/12

11 | 4

8/13/2019 METHODIST KL 2013 M1(Q&A)

12/12

12 | 4