5

SULIT

MatematikTambahanKertas 2Oktober 2010 2 jam

SMK SULTAN SALAHUDDIN ABDUL AZIZ SHAHSHAH ALAM, SELANGOR

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PEPERIKSAAN POST PERCUBAANSIJIL PELAJARAN MALAYSIA 2010

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MATEMATIK TAMBAHANKERTAS 2Masa : Dua Jam Tiga Puluh Minit

===============================================================JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Arahan :1.Kertas soalan ini mengandungi 3 bahagian : Bahagian A, Bahagian B dan Bahagian C 2.Jawab semua soalan dalam Bahagian A, empat soalan daripada Bahagian B dan dua soalan daripada Bahagian C.3.Rajah yang mengiringi masalah dalam kertas soalan ini dimaksudkan untuk memberi maklumat yang berguna bagi menyelesaikan masalah. Rajah tidak dilukiskan mengikut skala kecuali dinyatakan.4.Jawapan hendaklah ditulis pada kertas tulis yang disediakan.5.Semua kaedah penyelesaian mesti ditunjukkan dengan jelas. Anda mungkin kehilangan markah jika langkah-langkah penting tidak ditunjukkan dengan teratur.6.Markah yang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkan dalam kurungan.7.Senarai rumus dan jadual taburan normal N(0,1) disediakan di halaman akhir.8.Penggunaan kalkulator saintifik yang tidak boleh diprogramkan adalah dibenarkan.------------------------------------------------------------------------------------------------------------Kertas soalan ini mengandungi 10 halaman bercetak.

[ Lihat SebelahSULIT3472/2Section A[40 marks]

Answer all questions.

1.Solve the following simultaneous equations :

3 x2 + y2 = 28

3 x + y = 8[5 marks]

2.Diagram shows the curve of a quadratic function = p ( x + q )2 + k

point (-2,4) is a turning point of the graph. y

(0 , 22)

(-2 , 4)

0x Diagram 2

Find the values of p , q and k

(b)the equation of the curve when the graph is reflected along the x- axis

(c)determine the range of values of x if f( x ) 17

3.Diagram 3 shows a series of circles. The total circumference of the first five circles are 60 cm . The lengths of diameter of circles is 2 cm more than the previous circle.

Diagram 3

(a)Find the diameter of the smallest circle.[3 marks]

(b)Calculate the number of circular rings that can be made by using a piece of wire with length of cm

[4 marks]

4.(a)Prove that = cos x

(b) Sketch the graph of y = - | cos x | + 1 for [2 marks] (c ) Hence by drawing a suitable straight line on the same axis, find the number of solutions satisfying the equation

2 | cos x | = x for 0 x2 [6 marks]

5.Tables 5 shows the marks obtained by 40 students in a class. MarksNumber of Students41 - 45646 - 501051 55K56 60H61 - 654

Table 5

Given that the median marks is 52. 167, find the values of h and k. Hence state the modal class.[6 marks]

6.In Diagram 6, K L M N is a parallelogram . PRL and KRQ are straight lines, KP= 2PN and NQ : NM = 1: 4 M Q N

R PDiagram 6

L K

= 8 and = (a)Express in terms of and

(i)(ii) [3 marks]

(b)Given = and = b Express vector in terms of(i) , and (ii)b , and

(c) Hence, find the values of a and b[4 marks]

Section B

[40 marks]

Answer any four questions from this section.

7. Diagram 7(a) shows part of the curve y y= 9 x2. The straight line intersects the y- axis at ( 0, k) and intersect the x-axis at ( 6,0)(0,k)

Y = 9 x2

(6,0)0

x

Diagram 7a

(a) Given that the area of the shaded region is 33 unit2. Find the value of k.[5 marks]

(b) Diagram 7(b) shows parts of the curve x = y2 . The curve intersect the

straight line x = 4 at AX = y2 yA

x 0

Diagram 7b

Calculate

(i) as the coordinates of A the volume generated in terms of , when the shaded region is revolved through 360 about the y- axis .

[5 marks]

8. Table 8 shows the values of two variables x and y obtained from an experiment x2. It is known that x and y are related by the equation y=ab where a and b are constants.X1.01.52.02.52.73.0y1.82.263.114.696.027.74Table 8

(a)Plot log10 y against x2 by using scale of 2 cm to 1 unit on the x- axis and 2cm to 0.2 units on the y-axis . Hence draw the line of best fit.[5 marks](b)Use your graph from 8(a) to find the values of

(i)a

(ii)b

[5 marks]

9.Diagram 9 shows two circles. The larger circle has center P and radius 10 cm. The circles touch at point x. The straight line AB is a common tangent to the circles at point A and B.

P

X Q 710

A B Diagram 9

(Use = 3.142)Given that < APQ = radian

(a)show that = 1.39 rad (to two decimal places).[2 marks](b)calculate the length, in cm, of the minor arc BX[3 marks](c)calculate the area, in cm2, of the shaded region,[5 marks]

10.Solution by scale drawing is not accepted.Diagram 10 shows a triangle PQR. Point S lies on PQ. y P (5.k)

S (2,3)

x 0 R(4,0)

Q

Diagram 10

(a)A point M moves such that its distance from S is always 5 units. Find the equation of the locus of M.[3 marks]

(b)It is given that point P and Q lie on the locus M. Calculate(i)the value of k [2 marks]

(ii)the coordinates of Q [2 marks]

(d)Hence, find the area, in unit2, of triangle PQR.

[3 marks]

11.(a)A students is considered pass the test when ever five of ten questions are being answered correctly. If 9 students are chosen at random, calculate the probability that.(i)Exactly 3 students pass the test.

(ii)More than 2 students pass the test

[5 marks]

(b)The height of students in School X are normally distributed with a mean of 150 cm and a standard deviation of 10 cm.(i)Height exceeds 170 cm are classified as tall. It is found that 57 students are tall. Find the total enrolment of the school.

(ii)If 35% of the students are categorized as short. What is the height which is still short?

[5 marks]

Section C

[20 marks]

Answer any two questions from this section.

12.A particle moves along a straight line from a fixed point O. Its velocity, Vms-1, is given byV = 15t - 3t2, where t is the time, in seconds, after leaving the point O,(Assume motion to the right is positive)

Find

(a)the maximum velocity of the particle[3 marks]

(b)the distance travelled during the fourth second.[3 marks]

(c)the value of t when the particle passes the point O again[2 marks]

(d)the time between leaving O and when the particle reverses its direction of motion.[2 marks]13.Diagram 13, is a bar chart indicating the weekly cost of items P, Q, R, S and T for the year 2006. Table 13 shows the prices and the price indices for the items.

Weekly cost (RM) 33 ------------------------------

30 ---------------

24 -----------------------

15 ---- 12 -----------------------------------------

Items 0 P Q R S T

Diagram 13

ItemsPrice in 2006(RM)Price in2008 (RM)Price Index in 2008 based on 2006PX0.70175Q2.002.50125R4.005.50YS6.009.00150J2.5Z120Table 13

(a)Find the value(i) x(ii) y(iii) z[3 marks]

(b)Calculate the composite index for the items in the year 2008 based on the year 2006.[3 marks]

(c)the total monthly cost of the items in the year 2006 is RM456. Calculate the corresponding total monthly cost for the year 2008.

[2 marks]

(d)The cost of the items increases by 30% from the year 2008 to 2010. Find the composite index for the year 2010 based on the year 2006.

[2 marks]

14.Use graph paper to answer this question.A bakery shop produces two types of cake, P and Q. Each type of cake is made by using two ingredients flour and butter. Table 14 shows the masses of the ingredients to make two types of cakes.

CakeMass (g)Mass (g)

FlourButterP100100Q400200

Table 14

The bakery shop produces x cakes P and y cakes Q. The making of cakes per day based on the following constraints.

I:the minimum mass of flour used is 8kgII:the maximum mass of butter used is 9kgIII:the number of cake P produced is not more than the number of cake Q.

(a)Write three inequalities, other than and which satisfies all the above constraints.(b)Using a scale of 2 cm to 10 cakes on both axes, construct and shade the region R which satisfies all the above constrains.(c)Use your graph in 14(b), to find

(i)the minimum number of cakes Q, if 15 of cakes P are produced per day.(ii)the maximum profit per day if the profit of each cake P and Q is RM12 and RM9 respectively.

15.Diagram 15 shows quadrilateral ABCDE.Given BCD is a straight line.