Additional Mathematics Camp 2013

7/29/2019 Additional Mathematics Camp 2013

1/12


2/12

ALGEBRA

1. x =2 4

2

b b ac

a

2. ama

n= a

m + n----pan-pen

3. ama

n= a

mn----pan-pen

4. (am)n = a

mn

5. logamn = loga m + loga n-----pan-pen

6. logan

m= loga m loga n -----pan-pen

7. logamn

= n logam-----kuda pan

8.log

loglog

ca

c

bb

a= ---- kuda

9. ( 1)n

T a n d = + ------- kaki atok gbai

10. [2 ( 1) ]2n

n

S a n d = +

11.1n

nT ar =

12. nS =1

)1(

r

ran

=r

ran

1

)1(, 1r

13.

S =r

a

1, | r| < 1

KALKULUS

1. y = uv,dx

dy= u

dx

dv+ v

dx

du-----sida

2. y =v

u,

dx

dy=

2v

dx

dvu

dx

duv

3.dx

dy=

du

dy

dx

du----3p/u

4. Area under a curve

=

b

a

y dx or = b

a

dyx

5. Volume generated

= b

a

dxy2 or = b

a

dyx2

STATISTIK

1. x =N

x----tiada f

2. x =

f

fx

3. =N

xx 2)(=

22

)(x

xN

tiada f

4. =

f

xxf 2)(=

22

)(fx

xf

5. m = CLmf

FN

+

21

6. I =0

1

Q

Q 100-2 thn

7. I =

i

ii

W

IW----fungsi gubahan

8. rn P =

!)(

!

rn

n

9. rnC =

!!)(

!

rrn

n

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

11. )( rXp = = rnrrn qpC , p + q = 1

12. Mean /Min = np

13. = npq

14. Z =

X

-3 thn

=0

> 0

Paksi-y

Paksi-x

1

1

4Q N=

3

3

4Q N=


3/12

GEOMETRI

1. Distance = 2212

21 )()( yyxx +

2. Midpoint

(x,y) =

++

2

,

2

2121 yyxx

3. A point dividing a segment of a line

(x,y) = 1 2 1 2,nx mx ny my

m n m n

+ +

+ +

4. Area of triangle /Luas segi tiga

)()( 3123121332212

1yxyxyxyxyxyx ++++

5. r = 22 yx +

6. r =22

yx

yx

+

+ ji

TRIGONOMETRI

1. Arc length, s = r

2. Area of sector =2

1 2r

3. AA 22 cossin + = 1

4. A2sec = A2tan1 +

5. A2cosec = A2cot1 +

6. sin 2A = 2 sinA cosA

7. cos 2A = cos2A sin

2A

= 2 cos2A 1

= 1 2 sin2A

8. )(sin BA = sinA cosB cosA sinB

9. )(cos BA = cosA cosB m sinA sinB

10. )(tan BA =BABA

tantan1tantan

m

11. tan 2A =A

A2

tan1

tan2

12.A

a

sin=

B

b

sin=

C

c

sin

13. a2

= b2

+ c2 2bc cosA

14. Area of triangle = 2

1

ab

sinC

FORMULA TAMBAHAN

1. x2

(SOR)x + POR = 0 2b c

xa a

+ = 0

2. f(x) =

2 2

2 4b ba x ca a

+ +

3.100

X YZ

=

Z

Year C

X

YearA

Y

Sila t2

Vektor unit

SiLa

Anak Panah


4/12

A FUNCTIONS

1. Given thatf(x) = 3 4x + and fg(x) = 6x + 7, SPM 2012Find (a) fg(4)

(b) g(x) , [4 marks]

2. Given the function h(x) =6

x,x 0 and the composite function hg(x) = 3x, SPM 2004

Find (a) g(x) ,

(b) the value ofx when gh(x) = 5 . [4 marks]

3. Given the functions : 4h x x m + and 15

: 28

h x kx

+ , where m and k

are constants , find the value ofm and ofk. [3 marks]

4. Given that : 5 1g x x + and2: 2 3h x x x + , find

(a) g 1 (3) ,(b) hg(x) . [4marks]


5/12

QUADRATIC EQUATIONS/QUADRATIC FUNCTIONS

1. It is Given that 3 and m+ 4 are the roots of the equation 2 ( 1) 6 0x n x+ + = where m and n are

constants. Find the value of m and of n. [3 marks]

2. Solve the quadratic equation )2)(1()4(2 += xxxx . Give your answer correct to

four significant figures. [3 marks]

3. The quadratic equation 4)1( =+ pxxx has two distinct roots. Find the range of

values ofp. [3 marks]

4. Form the quadratic equation which has the roots - 3 and2

1. Give your answer in

the form ,02

=++ cbxax where a , b and c are constants. [2 marks]


6/12

5. Diagram shows the graph of quadratic function f(x) = 3(x +p)2

+ 2, wherep is a constant.

The graphy =f(x) has minimum point (1, q), where q is a constant. State,

(a) the value ofp,(b) the value ofq,

(c) the equation of axis of symmetry. [3 marks]

6. Diagram shows the graph of a quadratic functiony =f(x). The straight liney = 4 is a

tangent to the curvey =f(x).

(a) Write the equation of the axis of symmetry of the curve.

(b) Expressf(x) in the form of (x + b)2

+ c, where b and c are constants. [3 marks]

y

x0

(1, q)

y =f(x)

y

x0

y =f(x)

y = 4

1 5


7/12

INDICES AND LOGARITHM

1. Solve the equation 27 (32x + 4

)= 1 [3 marks]

2. Solve the equation 2 21 log ( 2) logx x+ = [3 marks]

3. If 3 log10x = 2 log10y, findx in terms ofy. [3 marks]

4. Given log2T log4V= 3, express Tin terms ofV. [4 marks]

5. Solve the equation 42x 1

= 7x. [4 marks]

6. Solve the equation 324x

= 48x + 6

. [3 marks]

7. Given log5 2 = m and log5 7 =p, express log5 4.9 in terms ofm andp. [3marks]


8/12

COORDINATES GEOMETRY

1 . Diagram shows the straight line CD which meets the straight line AB at the point D.

Point C lies on they-axis.

(a) Write the equation of AB. [1 marks]

(b) Given 2AD = DB, find the coordinates of D. [2 marks]

(c) Given CD is perpendicular to AB, find they- intercept of CD. [3 marks]

(d) A point P moves such its distance from point D is always 5 units.

Find the equation of the locus of P. [3 marks]

A

(0, 6)

C

y

x

D

B

(9, 0)


9/12

STATISTICS

1. A set of test marksx1,x2,x3,x4,x5,x6 has a mean of 5 and a standard deviation of 1.5.

(a)Calculate,(i) the sum of the marks, x,

(ii) the sum of the squares of the marks, x2. [3 marks]

(b)Each mark is multiplied by 2 and then add 3. Find for the set of marks(i) the mean,

(ii) the variance. [4 marks]

2. A set of data consists of 10 numbers. The sum of the numbers is 150 and the sum of the

squares of the numbers is 2472.

(a) Find the mean and the variance of the 10 numbers. [3 marks]

(c)A different number is added to the set of data and the mean is increased by 1.Find,

(i) the value of the number,

(ii) the standard deviation of the set of 11 numbers. [4 marks]

04P.2.4

3. Table 5 shows the marks obtained by 40 candidates in a test.

Marks Number of candidates

10 - 19 4

20 - 29 x

30 - 39 y

40 - 49 10

50 - 59 8

Table 5

Given that the median mark is 35.5, find the value ofx and ofy. Hence, state the modal class.

[6 marks]


10/12

Differentiation

1 Given thaty = 14x(5-x), calculate the value ofx wheny is a maximum. Hence, find the maximum

value ofy.

2 Given that xxy 52 += . Use differentiation to find the small change iny whenx increases from 3 to

3.01.

3 Differentiate 42 )52(3 xx with respect tox.

4 Two variables,x andy, are related by the equationx

xy2

3 += .Given thaty increases at a constant

rate of 4 units per second, find the rate of change ofx whenx = 2.

5 A curve with gradient function2

22

xx has a turning point at (k, 8).

(a) Find the value ofk.

(b) Determine whether the turning point is a maximum or a minimum point.


11/12

PROGRESSIONS

1. Given a geometric progression y , 2 ,y

4, p , ..express p in terms ofy . [2 marks]

2. Given an arithmetic progression - 7 , - 3 , 1 , ., state three consecutive terms in

this progression which sum up to 75 . [3 marks]

3. The volume of water in a tank is 450 liters on the first day. Subsequently, 10 liters

of water is added to the tank everyday.

Calculate the volume, in liters, of water in the tank at the end of the seventh day. [2 marks]

4. Express the recurring decimal 0.969696..as a fraction in its simplest

form. [4 marks]

5. The first three terms of an arithmetic progression are k 3, k + 3 , 2k + 2 . Find

(a) the value of k,

(b) the sum of the first 9 terms of the progression. [3 marks]

6. In a geometric progression, the first term is 64 and the fourth term is 27. Calculate

(a ) the common ratio,

(b) the sum to infinity of the geometric progression. [4 marks]


12/12

VECTORS

1. Diagram shows a parallelogram ABCD where BED is a straight line.

Given

AB = 6p,

AD = 4q and DE = 2EB, express, in terms ofp and q:

(a)

BD ,

(b)

EC . [4 marks]

2. Given

AB = ( )7

5,

OB = ( )3

2and

CD = ( )5

k, find

(a) the coordinates of A, [2 marks]

(b) the unit vector in the direction

OA , [2 marks]

(c) the value ofk, if

CD is parallel to

AB . [2 marks]

A

E

B

CD

Additional Mathematics Camp 2013

Documents

Transcript of Additional Mathematics Camp 2013