Boxes in Additional Mathematics

8/9/2019 Boxes in Additional Mathematics

1/9

S2FO2R: Search, Strategy, Formula, Operation, Output, Re-check

BOXES IN ADDITIONAL MATHEMATICSBY: CG. SHAIFUR AZURA BIN SUHAIMI

Box #1: Inverse Function

2

5-x=f-1(x)

5+2x=f(x)

Box # 2 : Inverse Function

2-

5x 5+

3x

terms in thebox remainunchanged

5-3x

=f-1(x)

5+2x=f(x)

Box # 3 : Form the quadratic equation given the roots

(a) 3 and -4 are the roots

Roots

= 0Eqn: +x -12x2

= 04 )+( xx=- 4

= 0)3-x(x=3

(b) 2 and3

1are the roots

Roots

= 0Eqn: -7x +23x2

= 01 )-(3xx=13

= 0)2-x(x=2

AFS Technic: Answering For Success Technic


2/9


Box # 4 : Form the quadratic equation using given roots

Example: Given that and are the roots of quadratic equation 2x2 + 7x -15 = 0.Form an equation with the roots of 2 and 2.

Form

1

xx

eqn:

1

cbxax 2

x2 -30+7x-304()-72(+)

()(+)

-15

2-7

2

2x2+7x-15=0: a=2, b=7, c=-15

+c

a-b

a+

a

a

Box # 5: Index Numbers

Alternative Method: Using Index Box

r o w fo r p ri c e in

i n d e x n u m b

r o w f o r Q u a n

P r i c e e ta d a p e r k a ta a n '

y e a r ', in d e x n u

o r p r ic e i n d e x m

1 0 0

I1 0 0

Q1Q0

S p e c i f iY e a r

B a s eY e a r

orI

QQ10

100= 10 100QxIQ =

Example:



3/9


Q1: The mean electric bill of Ali increases from RM420 a month in 2006 to RM630 a

month in 2009. Calculate the index number of the electric bill of Ali in 2009 based

on 2006.

I

630420

100

20092006

630100420 xI =

420

63000=I

150=I

Box # 6 : RELATED RATES OF CHANGES



4/9


dd

THE RATES BOX

column

for time

column for he ight,

radius & x

column for Area,

Volume & y

t

h, r, x

h, r, x

A, v, y

Briefing about Rates Box:

s y m b o l X = t i

r e s p e c t tod iv id e o r

d i f f e re n t i a

dd

T H E R A T E S B

t

h , r , x

h , r , x

A , v , y

d dA

r

r

t

column for Are a

column for radius column

for time

THE RATES BOX

1)dt

drX

dr

dA

dt

dA=


Refer to general


5/9


dd

THE RATES BOX

column

for timecolumn for radius

column for

volume

t

r

r

v

2)dt

drX

dr

dv

dt

dv=

d dhv

h t

column forvolume

column for height columnfor time

THE RATES BOX

3)dt

dhX

dh

dv

dt

dv=

d dcolumnfor time

THE RATES BOX

column for height

column forvolume

tx

v x

4)dt

dxX

dx

dv

dt

dv=


Refer to s here

Refer to cylinder

Refer to cube


6/9


dd

h,r,x

h,r,x t

S,A, V, Y

2: Find the value

[ ] [ ]xrhXyvAsdt

yvAsd,,,,,

),,,(=

ddh,r,x

h,r,x t

S,A, V, Y

3: Find the value

[ ][ ]xrh

yvAs

dt

xrhd

,,

,,,),,(=

Example: SPM 2005, Q20

hhv 83

1 3+= 8)3(

3

1 2+= h

dh

dv

10=dt

dv= h2 + 8

= (2)2 + 8

?=dt

dh, when h = 2

dh

dv= 12



7/9


12

10dd

h

h t

V

3: Find the value

12

10=

dt

dh

= 0.833cms-1

Example 2: Sasbadi Nexus, pg 152

12 = cms

dt

dr, spherical balloon

r = 7 cm. Find ?=dt

dv

Solution:

V sphere =3

3

4r

2)3(3

4r

dr

dv=

= 24 r

= 4 (7)2

= 196

2196dd

r

r t

V

2196 Xdt

dv=

= 392

SMALL CHANGES IN QUANTITIES

Using Small Changes Box



8/9



x

yit

dx

dy

x

0lim.1

= , when x is very small

dx

dy

x

y

xdx

dyy =

2. Using Small Changes Box

divide or by

y = dydx

x

dx is a reference,

dx = 1

= times

dx

dy

x

y

3. Small changes in X

x increase from, 2 to 2.01

To find x:

x = xend - xstart = 2.01 - 2

= 0.01

endstart

x:22.01

4. ynew = yinitial +y

A. Example 1:

y = x3 +2 , find the approximate increase

in y or y when x increases from 2 to

2.01

solution:

x: 2 2.01201.2 =dx

= 0.01

23x

dx

dy=

= 3(2)

2

= 12Using the small changes box:

Depend on question:May be y, A, etc

Depend on question:

May be dy, dA, etc


9/9


C. Example 3:

Given y = 416

x, find the value of

dx

dy

when x = 2. Hence, find the

approximate value of 4)04.2(16 .

Solution:

y =4

16

x=16x -4 = 4)2(

16,

yinitial = 1)2(16

4=

5)4(16

= xdx

dy

= 16(-4) (2)-5

= -2

x : 2 04.2

x = 2.04 -2

= 0.04

ynew = ?

y -2

0.04 1

y = 0.04 x -2= -0.08

ynew = yinitial + y= 1 + (-0.08)

= 0.92

Check: using calculator

press < >

< = >

Answer shown on a screen as0.9233845426


Boxes in Additional Mathematics

Documents

Transcript of Boxes in Additional Mathematics