Pakej Percutian Pelajar 2009

PAKEJ PERCUTIAN PELAJAR 2009 SMKA SIMPANG LIMA

MATEMATIK TAMBAHAN TINGKATAN 4 ________________________________________________________________________ _ GURU : MOHD SAFARIN MAT RAJULI NAMA :…………………………………………………………………. TINGKATAN :…………………………………………………………. ARAHAN: 1. SILA JAWAB SOLAN YANG DIBERIKAN SEMASA CUTI PERSEKOLAHAN 2. JAWAPAN YANG DIBERIKAN ADALAH SEBAGAI SEMAKAN SAHAJA. PELAJAR PERLU MENULIS JALAN PENGIRAAN BAGI SETIAP SOALAN. 3. IBU BAPA/ PENJAGA PERLU MEMANTAU PARA PELAJAR AGAR KERJA YANG DIBERIKAN SIAP SEPENUHNYA. IBU BAPA/PENJAGA PERLU MENURUNKAN TANDATANGAN DI BAWAH INI SEBAGAI PENGESAHAN. SELAMAT MENJAWAB DAN SELAMAT BERCUTI.

DENGAN INI SAYA …………………………………………………………………………… …… IBU BAPA/PENJAGA* KEPADA …………………………………………………………… TINGKATAN …………………….. MENGESAHKAN BAHAWA PELAJAR INI TELAH MELAKSANAKAN TUGASAN YANG DIBERIKAN DENGAN JAYANYA.

…………………………………………………………………. ( )

YEAR END REVISION EXERCISE FORM 4 ADDITIONAL MATHEMATICS PAPER 1 The relation which maps set P = {1, 2,3} to set Q = {4,8,12} is defined by the ordered pairs {(1, 4), (2,8), (2,12), (3,12)} . State the images of 2, (b) the object of 4. 1 (a)

2

Given that g −1 ( x ) = 8 − 5 x, find g (−2).

3

Given that f : x → (a) (b)

4 5

x−3 , x ≠ k , find 2− x the value of k , the value of f (1) .

3 −1 Given that f ( x) = ax + 2, and f ( x ) = b − x. Find the value of a and of b. 2 2 2 Find the values of p, given the quadratic equation 9 x + 1 = x has two real and p equal roots. A

G i 6 Solve the quadratic equation 8 x + 5 = x(3 x + 2) . Give your v answer correct to four significant figures. e n 7 Given that quadratic equation x(3 x − p ) = 2 x − 3 has no roots, find the range of values of p. t h a 8 Find the range of values of x for which x( x + 3) ≤ 18 . t 2 9 Given f ( x) = 3( x −1) + 5 . Determine whether f ( x ) has maximum or O minimum value and state its value. A B 10 Find the range of values of k if f ( x ) = 4 x 2 − kx + 1 is always positive. a 1 n x+2 11 Solve the equation 16 = . 3− x d 64 12 13 14

Solve the equation log 3 ( y + 2 ) = 1 + log3 ( y − 4 ) .

O D C

 xy 2  Given that x = 3m and y = 3n , express log 3   in terms a of m and n.  27  r e Point Q(2, 7) divides the line joining P(−2, 1) and R(4, 10) internally in the ratio t w o s t r

i g h t

m : n. Find the ratio m : n. 15

The vertices of a triangle are P(2, 5), Q(k, 1) and R(3, 4). l Given that the area of the 2 triangle is 6 unit , find the values of k. i

n 16 Given points P, Q(0, −3), R(4, −1) and S(6, 3), where P ise the midpoint of RS. Find the equation of a straight line which passes through P and s is parallel to the straight line QR. . 17 A set of data consists of five numbers. The sum of the number is 95 and the sum of O the squares of the numbers is 1845. Find, D (a) the mean, (b) the standard deviation. = 18 19

A set of five numbers has a mean of 15. When a number, 5 m is added to the data, the new mean is 18. Find the value of m. c m Given that the mean of a set of data 4, 5, 7, 3, 7 and m is 5. Find, (a) the value of m, , (b) the variance of the set of data.

D 20 Diagram 1 shows two sectors with center O. Given that C OAB and ODC are two straight lines. OD = 5 cm , DC = 2 cm and ∠AOD = 0.6 rad , find the area, in cm 2 , of the shaded region. = 2

B

c m O

0.6 rad

a n d

5 cm

21

D A 2cm ,C A Diagram 1 f i n Diagram 2 shows a right-angled triangle OAT and a sector d AOB. A

t h e

10 cm 1.2 rad O

B Diagram 2

a r e a o f t h e s

T

[Use π = 3.142 ] Calculate the area, in cm2, of the shaded region.

22 Diagram 3 shows a sector BOC with centre O.

O

a d e d r e g i o n B .

0.45 rad

[ 3 m a r k Diagram 3 s ] Given the perimeter of the sector BOC is 24.5 cm, calculate (a) the radius, in cm, of the sector, (b) the area, in cm2, of the sector.

C

15 . r Given that r increases at a constant rate of 0.1 unit per second, find the rate of change of A when r = 2.

23

2 Two variables, A and r, are related by the equation A = 2r −

24

Given that g ( x) =

25

Given that y = x 2 (1 − x) , dy (a) find the value of when x = 1. dx (b) express the approximate change in y, in terms of p, when x changes from 1 to 1 + p, where p is a small value.

1 , evaluate g ′′ (2) . 2(3 − 2 x)

22

3

Part 2 – Year End Revision Exercise, PAPER 2 1

Solve the following simultaneous equations x + 2 y = 4 , x 2 + xy + y 2 = 7

2

Given the function f ( x) =

2( x + 3) , where x ≠ k . Find x −3

(a) the value of k, (b) the positive value of p given that f ( p ) = p, (c)

f −1 ( x).

3

(a) Solve the equation 2 x + 2 x+ 2 = 40 . (b) Given that log a 5 = p and log a 7 = q , express log 35 a in terms of p and q.

4

Solution by scale drawing will not be accepted. Given points A (−3, 6), B (3, 8) and C (3, 0). Find (a) the equation of AB, (b) the equation of straight line that passes through point C and is perpendicular to straight line AB, (c) area of triangle ABC.

5 Score Skor

< 15

< 20

< 25

< 30

< 35

Number of Students Bilangan Murid

10

25

55

75

80

Table 1 Table 1 shows the cumulative frequency distribution for the scores of 80 students in a task. (a) (b) (c)

Construct a frequency distribution table, Without drawing an ogive, find the median score, Calculate the variance of the distribution.

6

Diagram 1 shows a semicircle APBD with centre O, of radius 5 cm and a sector of a circle ACD with centre A.

B

P

A

O Diagram 1

Given that the length of the arc AB is 10 cm, [Use π = 3.142 ] Calculate, (a) ∠AOB, in radians, (b) the area, in cm2, of the shaded region.

C

D

Part 3 – Year End Revision Exercise Diagram 1 shows a triangle ABC. Given ∠ADB is an obtuse angle.

1 .

B 12cm 20° 14cm C

D A

6cm Diagram 1

Calculate (a) ∠ADB , (b) the length, in cm, of BD, (c) ∠DBC , (d) the area, in cm2, of triangle ABC.

2

(a) Diagram 2 shows a trapezium ABCD. Calculate (i)

∠CBD ,

(ii) the length, in cm, of AC.

D

5cm

C

8cm

25° A

10 cm

B

Diagram 2

(b)

JKL is a triangle with side JK of length 10cm. Given that sin ∠KJL = 0.456 and sin ∠JKL = 0.36 , calculate (i) ∠JLK , the area, in cm2, of triangle JKL .

(ii)

3 Food Fish Chicken Rice Meat Prawn

Price Index for the year 2007 based on the year 2006

Weightage, w

110

3

m

2

130

5

105

n

115

1

Table 1 Table 1 shows the price indices and weightage of 5 items of food. Given the composite index of these 5 items in the year 2007 using 2006 as the base year is 117 and Σw = 13. (a)

Calculate the values of m and n.

(b)

Find the price of a kilogram of rice in the year 2007 if its price in the year 2006 is RM12.50.

(c)

Given the expected rate of change in the prices of all the foods from 2007 to 2008 is the same as that from 2006 to 2007. Find (i) (ii)

the composite index number of these foods in the year 2008, using the year 2006 as the base year. the amount to be paid for these foods in the year 2008 if the amount paid for these items in 2006 was RM650.

4 Price (RM)

Material

Price Index

2000

2005

A

40.00

p

130

B

50.00

75.00

q

C

r

80.00

125

D

25.00

45.00

116

Table 2

D A C

B

Diagram 3 Table 2 shows the prices of four types of materials, A, B, C and D , used in building a house in the year 2000 and 2005 with their respective price indices in the year 2005 based on the year 2000. The Diagram 3 is a pie chart representing the relative amounts of the materials A, B, C and D used in building a house. (a) (b)

Find the values of p, q and r. (i) (ii)

(c)

Calculate the composite index for the cost of building a house in the year 2005 based on the year 2000. Hence, calculate the corresponding cost of building a house in the year 2000 if the cost in the year 2005 was RM55,000.

The cost of building a house is expected to increase by 40% from the year 2005 to the year 2010. Find the expected composite index for the cost of building a house in the year 2010 based on the year 2000.