perfect score add maths 2011 module 1 - module 5

8/3/2019 Perfect Score Add Maths 2011 Module 1 - Module 5

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BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH

DAN SEKOLAH KECEMERLANGAN


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Section A [ 40 marks ]

Answer all question

Diagram 1

1. Diagram 1 shows the function : 1 , 0m

h x xx

, where m is a constant.

Find the value ofm.

Answer :

2. Diagram 2 shows the graph of the functionf(x) = |23x|, for the domain 2x n.

y

MODULE 1


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3. The functions fand g are defined by6

( ) , 11

f x xx

and g(x) = kx + 10, where kis a

constant. Find

(a) the value of k if 1 1( 2)2

f g

(b) g2(x).Answer :

4. The quadratic equationx2

+ 2x =pxp2, wherep is a constant, has two different roots.

Find the range of the values ofp.

Answer :


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6. Find the range of values ofx where 2x (2x 5)(x + 3).

Answer :

7. Solve the equation 2 19 243(27 )x x .

Answer :


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10. In a geometric progression, the second term is 18 and the sum to infinity is 72.

Find the fifth terms

Answer :

Diagram 11

11. In Diagram 11, PQR is a triangle and PQS is a sector of a circle with centre P.

Given PQ = QR = 6 cm and PQR =2

3 rad. Using = 3.142, find

(a) the area, in cm2, of the shaded region.

(b) the perimeter, in cm, of the shaded region.

Answer :


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13. Two vectorsa andb are given as a = ki9j and b = i + (k+6)j where kis a constant.

The vectorsa and b are parallel. Find the value ofk.

Answer :

14. The pointsA(1,p),B(2,1) and C(4, 5) are collinear. Find the value ofp.

Answer :

15. The points P(1,2), Q(3, k) andR(7, 22) lie on a straight line. Point Q divides PR in the

ratio m : n.

(a) Find the ratio m : n.

(b) Find the value ofk.

Answer :


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17. Diagram 17(a) shows a curvey = 2x2 + 3. Diagram 17(b) shows the straight line graph

obtained wheny = 2x2 + 3 is expressed in the linear form Y= mX+ 3.

Find the value ofm and k.

Answer :

18 Solve the equation 3 sin 2x 4 sin x = 0 for 0 x 360

Diagram 17(a) Diagram 17(b)

22 3y x

(1,7)

(k,11)


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20. The diagram 20 shows a curvex = 4y2 and a straight liney = k.

Diagram 20

If the area of the shaded region is 36 unit, find the value ofk..

Answer

21. A cubic ice block with sides ofx cm, melts at a rate of 0.81 cm3 per second.

Find the rate of change ofx when the volume of a cubic is 27 cm3

Answer :


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23. A three-digit number is to be formed from the digits, 1, 2, 3, ..., 9. How many different

numbers can be formed

(a) if there is no restriction?

(b) if the number must end with an odd digit and grater than 800 ?

Answer :

24. The probability that a seed will grow is 23

. If Hassan plants 5 seeds, find the probability

that

(a) 4 seeds will grow.

(b) all the seeds will not grow.

Answer :


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Answer all questions

1 A functionf is defined by 5,5

1:

xxxxf .

Find

(a) the image of k3 ,

(b) the object that has image of 2.

Answer:

2Given that 0,

5

35:)(

p

p

xxxf and 0,

62:1

q

q

xxf , wherep and q are

constants , find the value ofp and ofq.

Answer:

MODULE 2


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4The roots of the equation 82 xx are

3

2and

5

1 . Find the values of and .

Answer:

5 A quadratic function 0)32(6)31()( 2 kkxxkxf , find the range ofkif the graph

)(xf is always positive.

Answer:

6 Diagram 6 shows the graph of the curve bxaxf 2)1()( , where a and b are constants.

)(xf

2


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7 Find the range of values of x for 0413 xy and 212 xy .

Answer:

8. Solve the equation .932 4 xxx

Answer:

9 Solve the equation 130loglog4 xx . Give your answer correct to four significant figures.

Answer:


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11 The thn term of an arithmetic progression , nT , is given by nTn 714 . Find the sum of the

n terms of the progression.

Answer:

12 The sum of the first two terms is 30 and the third term exceeds the first term by 15. Find(a) the common ratio ,

(b) the fifth term.of the progression.

Answer:

13It is given that 2.0......280808.0

q

p+ r, where p, q and rare the constants.

State the value ofp , q and r.

Answer:


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15The variablesx andy are related by the equation

x

nxmnxy , where m and n are

constants. A straight line is obtained by plotting y againstx

1and passes through the points

)8,0( and )4,2( . Find the value ofm and n.

Answer:

16 Diagram 16 shows a trapezium with PS and QR are parallel.

Diagram 16

P S

Q R

T


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17Given that

2

3

~u and

t

sv~

, where s < 0 and t< 0. If 5~

v and

2

232~~

svu

, find the values ofs and oft.

Answer:

18 It is given that mcos , where oo 360270 . Find

(a) tan

2sin)(

b

in terms ofm.Answer:

19 Diagram 19 shows the sector OAB of a circle center O and radius 12 cm.


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20It is given that

rry

4 and .43 2 xxr

(a) Expressdx

dy in terms ofx ,

(b) Ifx decreases from 1 to 0.98, find the approximate value ofy.

21

Given 2

1

4)(3 dxxf , find

(a) 1

2

)(5 dxxf ,


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22 BagA contains m green balls and 2 blue balls. BagB contains 4 green balls and 8 blue balls.One ball is randomly chosen from each bag. The probability of getting one green ball and one

blue ball is95 . Find the value ofm.

Answer :

23 A set of 16 numbers 16321 ,........,,, xxxx , has a variance of 56 and it is given the sun of the

squares is 9201 . Find

(a) the mean ,


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24 Diagram 23 shows 6 letter cards to be arranged in a row.

C H A N T E K

Diagram 23

Calculate the number of different arrangements of all letter cards if

(a) the first two cards must be consonants ,

(b) all the vowels must be together.

Answer:

25 Given thatX~N(8.0 , 25.0 ) and %85)( kXP .

Find


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MODULE 3

1. Diagram 1 shows that mapping fromx toy is defined as f(x) = ax2 and mapping fromy toz is defined asg(y) = 12

y b.

Diagram 1

Find

(a) the values ofa and b,(b) a function that expresses mapping from x to z.

[ 3 marks]

Answer:

2. Function m is defined as m : x 5 3x. Ifp is another function and mp is defined

as mp : x1 3x2, determine functionp. [3marks]


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4. Straight line y = mx + 1 is tangent to the curve x2

+ y2 2x + 4y = 0. Find the possible

values ofm

Answer :

5 In the the diagram above, point (2, 3) is the turning point on the graph which has

equation of the form y =p(x + h)2 + k.

y

(0, 23)

(2, 3)

xO

Find the,

(a)values ofp, h and k,(b) equation of the curve formed when the graph as shown is reflected at the x-axis.

Answer


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7. Givenx

log 4 = u andylog 2 = w . State 4log x

3y in term ofu and/or w

Answer :

8. Solve the simultaneous equations 2m 1

x 32k+ 2

= 16 and 53m

x 1253 k

= 1,

where m and kare constants.

Answer :

9. Given 14, 11, 8, ........ is a arithmetic progression. Find,

(a) the number of term which is 97.

(b) the sum of tenth successive terms after 97.

Answer :


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11. Diagram 11 shows the graph1

yagainst x2. (1, 5) and (3, 9) are two points lie on the

straight lineAB with equation1

y=px2 + n , wherep and n are constants.

1

y

B

(3, 9)

A (1, 5)

O x2

Diagram 11

(a) Find the values ofp and n.

(b) Findy if givenx = 2

Answer :


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13 Diagram 13 shows the semi circle PQR with centre O and sector QSTwith centre S.

Given ST= 5 cm, OR = 4 cm and the arc length QT= 4.5 cm.

P S O

Diagram 13

Find,

(i) QST in radian,(ii) area of the shaded region.

Answer

14 Gi 2 3 d3

Fi d

T

Q

R


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15. Evaluate2 3 3

3 21

2 ( )( )x x

x

dx

Answer

16. Given kx2x is the gradient function for a curve such that kis a constant.

y 5x + 7 = 0 is the equation of tangent at the point (1, 2) to the curve.Find,

(a) the value ofk,(b) the equation of the curve

Answer :


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18.(a) Ifx = 2ij and y = i + 3j, find the value ofp if 2px + 3y is parallel to they-axis

P

R S

Q

r s

O

(b) The diagram above shows

OR = r,

OS = s,

OP and

PQ are drawn in the square

grid. Express in terms of r and s.

(i) OP (ii) PQ .

Answer :


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20. Rashid and Rudi compete in a badminton game. The game will end when any of the

players has won two sets. The probability that Rashid will win any one set is5

3.

Calculate the probability that

(i) the game will end in only two set,

(ii) Rashid will win the competition after playing 3 sets.

Answer :

21. Diagram 21 shows 5 letters and 3 numbers.

A B C D E 6 7 8

Diagram 21A code is formed by using the above letters and numbers.

Each code must consists of 3 letters follows by 2 numbers.How many codes can be formed if no letter or number is to be repeated for each code.

Answer :


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23. Mean of the list of numbers x 2,x + 4, 2x + 5, 2x 1,x + 7 andx 3 is 7.Find,

(a) the valuex,

(b) the variance.

Answer

24. GivenX~ B (4,6

1) . Table 24 shows the probability distribution of the random variable,X.

x 0 1 2 3 4P(X= x) 0.4823 k 0.1157 0.0154 0.0008

Table 24Find

(a)The value of k(b)P (X> 1)Answer


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MODULE 4

Time: Two hours and thirty minutes

Section A

[40 marks]Answer all questions

1. Solve the simultaneous equations3

x+

y

2= 4 , 6 3x y

[5 marks]

2. The curvey = k(x22x3) cuts they-axis at the point (0, 15).

(a) Find the value ofk. [2 marks]

(b) By using the method of completing the square, find the coordinates of

maximum point of the curve.

[3 marks]

3. A straight line 0103 xy is normal to a curve 1912423

xxxy at pointA.

Find

(a) the coordinates of pointA, [6 marks](b) the equation of tangent at pointA. [2 marks]

4. A circle is divided into n sectors such that the angle subtended by each sector at the

centre of the circle forms an arithmetic progression Given that the smallest angle and the


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6. Diagram 6 shows,ABCD is a quadrilateral.AED andEFCare straight lines.

BA

C F E

D

It is given that AB 20x, AE 8y, DC= 25x24y, AE = AD

andEF=

5

3EC.

(a) Express in terms ofx and/or y:(i) BD

(ii) EC [3 marks]

(b)Show that the points B, F and D are collinear. [3 marks](c) If |x | = 3 and |y | = 2, find | BD |. [2 marks]

Diagram 6


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(a) Plotxy againsty by using a scale of 2 cm to 0.5 unit on they-axis and 2 cm to 1 unit tothexy-axis.

Hence, draw the line of best fit.

(b) Use your graph from (a) to find the values ofa andb.(c) Find the value of the gradient of the straight line obtained when 1

yis plotted againstx.

[10 marks]

8. Diagram 8 shows the straight liney=3x intersecting the curvey = 4 x2 at point P.

Find(a) the coordinates ofP, [3 marks](b) the area of region which is bounded by the line y = 3x the curve y = 4 x

2and the x-axis

P

RDiagram 8

y=3x

y = 4 x2

0

y

x


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Diagram 9 shows, P(6,3), Q(4,7) andR(3,1) are the mid-points of the sides of triangleABC.

(a) Calculate the gradient of the line that passes through P and Q. [ 2marks]

(b) Find the equation ofAB [ 2marks]

(c) Calculate the area, in unit2

, of triangleABC. [ 3marks]

(d) A point Tmoves such that its distance from pointA is always the same as its distance

from point C. Find the equation of the locus of T. [ 3marks]

10. Diagram 10 shows a squareABCD with sides 5 cm in length.APCis a sector with its

centre at B andABCis a semicircle.

A

B

C

D

P

QR

Diagram 10


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11. (a) An insurance saleman sells policies to 5 men of identical age and in good health.According to his companys records, the probability that a man of this particular

age will be alive in 20 years time is32 . Find the probability that in 20 years time,

the number of men still alive will be

(i) exactly two,(ii) at least one.

(iii) expected value

[ 5marks](b) The mean mark for 400 candidates in an examination was 42 . If the marks were

normally distributed with standard deviation of 24 , find

(i) the passing mark if 90% of the candidates pass(ii) the number of candidates with grade A if a candidate must get 80 marks and above

for grade A.

[ 5marks]

SECTION C

[20 marks]

Answer two questions from this section

12. A particle moves in a straight line and passes through a fixed point O. Its velocity,

v ms 1 , is given by 562 ttv , where tis the time, in seconds, after leaving O .[Assume motion to the right is positive.]


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13. Diagram 13 shows a quadrilateralABCD such that ABCis acute.

5.2 cm

9.8 cm

9.5 cm

(a) Calculate

(i) ABC,(ii) ADC,(iii) the area, in cm2, of quadrilateralABCD. [8 marks]

(b) A triangle ABC has the same measurements as those given for triangle ABC, that is,

AC= 12.3 cm, CB= 9.5 cm and BAC= 40.5, but which is different in shape totriangleABC.

(i) Sketch the triangleABC

,(ii) State the size ofABC. [2 marks]

14. A furniture workshop produces tables and chairs. The production of tables and chairsinvolve two processes , making and shellacking. Table 14 shows the time taken to make

and to shellack a table and a chair.

Product Time taken (minutes)

Making ShellackingTable 60 20

Chair 40 10

bl 14

A

C

D

B

40.5

12.3 cm Diagram 13


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15. Diagram 15 shows the bar chart for the monthly sales of five essential items sold at asundry shop. Table 15 shows their price in the year 2000 and 2006, and the

corresponding price index for the year 2006 taking 2000 as the base year.

ItemsPrice in the

year 2000

Price in the

year 2006

Price Index for the year2006 based on the year

2000P x RM2.50 125

Q RM1.60 RM2.00 125

R RM0.40 RM0.55 y

S RM0.80 RM1.20 150

T RM2.00 z 120

TABLE 15

(a)Find the values of(i) x, (ii) y, (iii) z. [ 3 marks]

Sugar

Rice

Salt

Cooking Oil

Flour

10 20 30 40 50 60 70 80 90 100units

Diagram 2DIAGRAM 15

P

Q

R

S

T


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Section A

( 40 marks )

Answer ALL the question in this section.

1. Solve the simultaneous equations 12 nm and 722 mnnm .

Give your answers correct to four decimal places.

[ 5 marks ]

2.

Diagram 2

Diagram 2 shows a pendulum bulb, with length L cm. The time taken to complete an

oscillation, T s, is given by10

2L

T .

(a) FinddL

MODULE 5


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4. The diagram 4 below shows the first three of an infinite series of cylinders.

The height of each cylinder is 1 cm more than that of the previous cylinder.

(a) Show that the volumes of the cylinders form a progression. Determine whether it

is a geometric progression or an arithmetic progression .

(b) Given that the volume of the forth cylinder is 32 cm and the sum of volumes of the

first four cylinder is 104 cm, find the height and the radius of the smallest cylinder.

[ 8 marks ]

5. Table 5 above shows the performance of 100 students in a test.

Marks


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6. In Diagram 6,AOBEis a quadrilateral.AFB and OFEare straight lines.

Diagram 6

It is given that aOA~

, bOB~

. The point F lies on the straight line AB such that

ABAF

3

1

(a) Find in terms of a~

and/or b~

.

(i) AF (ii)OF

(b) Given OEOF

1and OAmBE

A

E

B

F

O


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Section B

( 40 marks )

7. Solutions to this question by scale drawing will not be accepted.

Diagram shows quadrilateral ABCD . The point A is (4,2 ) ,B is (1,5), C(k, 8) and the

equation ofBCis 2y =x + 10.

.

a) Find the value of k.b) Given that R is the point onBCsuch thatAR is perpendicular to BC

Findthe equation of AR .

O

D(8,4)

R

x

y

DIAGRAM

B ( 1, 5)

C(k,8 )

A(4,2 )

2y = x+10


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8. Use graph paper to answer this question

Siva wishes to determine the density of an object by an experiment. He uses sevencubical blocks of various size. Each block has a square cross section of sidex cm and

constant height 2 cm.

Each block is weighed with a balance. Siva does not adjust the balance to zero reading

before using it. As a result, the readings obtained have errors. Table below shows the

readings obtained.

Side of cross section of

block,x (cm)

3.0 4.0 5.0 6.0 7.0 8.0 9.0

Mass of block,J(g) 18.1 22.8 30.0 38.8 47.5 61.2 74.0

Table 8

Based on the formula, Mass = volume density, Siva obtains the formulaJ= 2x

2k, where J= mass of block,

x = side of cross section of block,k= density of block.

(a)Based on the data shown in Table 8 draw J against x2 using a scale of 2 cm to 10 units onthe x

2 axis and 2 cm to 10 unit on theJ-axis.

(b) From your graph, find

(i) the density of block material,(ii) error in the balance reading.

(c) With the same axes, draw a straight line graph obtained if the balance is adjusted to zero.(d) From your graph find the actual mass of one similar block, which has a square

cross section of side 5.7 cm.


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10. Diagram 10 shows a kite that has axis of symmetry OR .

Diagram 10

Given that APB is an arc of a circle with radius 25 cm and centre O . ANBQ is a semi

circle with centre Nand diameter 30 cm. TQS is an arc with centre R and radius 10 cm.

Given the arc length TQS is 18.75 cm,[use 142.3 ]

Calculate

(a) AOB (b)the area of segment ANBP (c) the area of shaded region

[ 10 marks ]

11 (a) In a survey in a district it is found that 2 out of 5 families have a video recorder


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Section C

( 20 marks )

12. Diagram 12 shows a triangle RTU.

Diagram 12

Given that RST is a straight line and UST is obtuse.

(a) Calculate

(i) UST ,

(ii) the length , in cm, ofRU

[ 4 marks ]


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13. Table 13 shows the price and the price indices of five types of coffees in a shop.

Types of

coffees

Price (RM) per cup Price index for

the year 2011

based on the year

2009

Weightage

2009 2011

P 3.25 3.90 120 5

Q 4.00 4.40 x 1

R 2.75 3.85 140 4S 2.50 y 130 2

T 1.20 1.44 120 1m

Table 13

(a)Find the value of(i) x

(ii) y

(b) The composite index for the price of types of coffees in the year 2011 based on year 2009

is 126. Calculate the value of m .

(c) Given the composite index for the price of the types of coffees increased by 25% from

the year 2007 to 2011. Calculate

(i) the composite index for the price of the types of coffees in the year 2009 based on the

the year 2007.


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14. Diagram 14 shows two fixed points, B and A on a straight line. A particle, P , movesalong the line.

Diagram 14

The particles speed, Vms-1

is given by 42 tV , where t is the time,

in seconds, after passing through the fixed point A . Initially, the particle moves towards

the fixed point B .

[ Assume motion from A to B is negative ]

(a)Find the time interval during which the particle moves towards B .(b)Given that the distance AB is 5 m, determine whether the particle will reach B or not.(c)Calculate the total distance travelled by the particle during the first 6 seconds.(d) Sketch the As against t, for 60 t , given that As is the displacement of the


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15. For this question, use the graph paper provided.

A factory produces model A and model B of a product. In any given day, the factory

produces x unit model A and y unit model B , provided 0x and 0y .

The time taken to produce one unit of model A and one unit of model B is 5 minutes and

4 minutes respectively. The operation of the factory is subject to the following

constraints:

(I) The number of model A does not exceed 60.

(II) The number of model B is more than twice the number of model A by at most 10.

(III) The total time taken to produce model A and model B should not be more than

400 minutes.

(a)Write three inequalities satisfying all the constraints.(b)Construct and shade the region R which is the region of feasible solutions.(c)Use the graph to find:

(i) the range number of units of modelA

that can be produced if 40 units ofmodel B is produced.

(ii) the maximum profit that can be obtained if the profit for one unit of model A

d i f d l i 6 d 3 i l


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SULIT 3472/2The following formulae may be helpful in answering the questions. The symbols given arethe ones commonly used.

ALGEBRA

1 x =a

acbb

2

42

2 am an = a m + n

3 am an = a m - n

4 (am

)n

= anm

5 logamn= log am + logan

6 logan

m= log am - logan

7 log amn = nlog am

8 logab =a

b

c

c

log

log

9 Tn = a + (n-1)d

10 Sn = ])1(2[2

dnan

11 Tn = ar n-1

12 Sn =r

ra

r

rann

1

)1(

1

)1(, (r 1)

13r

aS

1

, r


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STATISTICS

TRIGONOMETRY

1 Arc length, s = r 9 sin (A B) = sinAcosB cosAsinB

1 x = N

x

2 x =

f

fx

3 =

N

xx 2)(=

2_2

x

N

x

4 =

f

xxf2)(

=2

2

xf

fx

5 M = Cf

FN

L m

2

1

6 1000

1 P

PI

71

11

w

IwI

8)!(

!

rn

nP

r

n

9!)!(

!

rrn

nCr

n

10 P(AB)=P(A)+P(B)-P(AB)

11 p (X=r) = rnrr

nqpC , p + q = 1

12 Mean , = np

13 npq

14 z =

x


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[ Lihat sebelah

3472/2 SULIT

VII

perfect score add maths 2011 module 1 - module 5

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