chapter 1 standard form (1)

8/13/2019 Chapter 1 Standard Form (1)

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Name : Class : F4 Maths

Subject : Mathematics Lesson No : 1Chapter

:

Standard Form (1) Date : 10114 (Fri)

!opic : 1.1 Significant Figure !ime : 11"1#am$1"1#pm

1.1 Significant Figure

Significant figuresare the rele%ant di&its in

an inte&er or a decimal number 'hich has

been rounded o to a certain de&ree o

accurac* e"&"+,+ - +.0 (/ si&niicant i&ures)"

Notes:$

n roundin& o positi%e numbers to a &i%en

number o si&niicant i&ures* the significance

of zero is as sho'n belo'"

(a) ll non-zero di&its are significant.

Example

i) 2+

ii) ./"/.

(b) ll 3eros bet'een non$3ero di&its are si&niicant"

Example

i)4"0,

ii) .002

(c) ll 3eros after an non$3ero di&it in a

decimal are significant.

Example

i)"20

ii) /2"00

(d) ll 3eros before an non$3ero di&it in a

decimal are not significant.

Example

i) 0".

ii) 0"0,020

(e) ll 3eros after an non$3ero di&it in a

'hole number are not significant unless

stated other'ise"

Example

i) /0 (1 si&" i&")

ii) /00 (1 si&" i&")


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56ercise

1 7ound o the ollo'in&* correct to

si&niicant i&ures"

(a) 2"//.

(b) .."4#

(c) +0."

(d) ,..2

(e) 0",4/.

() 0"020/#

(&) 0"0024.+

(h) 0"0/0.2

/ State the number o si&niicant i&ures in

each o the ollo'in& numbers"

(a) +0000,

(b) #"00

(c) 0"0/0,0

(d) 0"2+,

(e) 0"0.0

() ,000

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" Complete the ollo'in& table"

Numbers7ound o to

1"s" /"s" "s"

a) 2. 04

b) ,.+,c) 2+#"4

d) 10".#

e) 0",+.1

) 0"00121,

4" Find the %alue o each o the ollo'in&*

statin& our ans'er correct to / si&niicant

i&ures"

a) ."2#,6"/ 2"/4,+

b) 1"/#4 0"0 2"/#4.

c) /,#"/ 0"022 +2"2.x

d)1#"2/4

0"4

e),#0

/# /x

) 0"0012,

# !he len&th and breadth o a rectan&le are

11"# cm and ."# cm respecti%el" Calculate

the area o the rectan&le* statin& our ans'er

correct to si&niicant i&ures"

2 bo6 contains 2 cans" 5ach can has a mass

o #0# &" !he bo6 has a mass o 20 &" Find

the total mass* in &* o the 2 cans and thebo6*

statin& our ans'er correct to / si&niicant

i&ures"

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ns'er

1 (a) 2"/ (b) .."# (c) +0. (d) .000

(e) 0",4 () 0"020 (&) 0"002#0 (h) 0"0/10

/ (a) 2 (b)

(c) 4 (d) (e) # () 1

(a) +0000*2.000*2.00

(b) .000*.000*,.,0

(c) +00*2,0*2+# (d) 10* 11* 11"0

(e) 0".*0",,*0",+.

() 0"00/* 0"0012* 0"0012/

4 (a) + (b) 2 (c) 400 (d) .

(e) 1"1 () 0"041

# 10.cm

/

2 100 &

S8M 8ractice

1" 7ound o 0"0,22 correct to t'o

si&niicant i&ures"

0"0, C 0"0,2

9 0"0. D 0"0,+

/" +#,2 correct to three si&niicant i&ures"

+#, C +#,00

9 +#. D +#.00

" 7ound o 0"0.10. correct to three

si&niicant i&ures"

0"0. C 0"0.10

9 0"0.1 D 0"0.11

4" 7ound o ,2 00. correct to our

si&niicant i&ures"

,200 C ,2000

9 ,201 D ,2010

#" 7ound o 40"+,/ to three si&niicant

i&ures"

40"+ C 40",00

9 40", D 41"0

2" 7ound o 22"., correct to three

si&niicant i&ures"

22 C 22".

9 2+ D 2+"0

+" 7ound o 0"04+2 correct to t'o

si&niicant i&ures"

0"04 C 0"04+ 9 0"0# D 0"04,

," 7ound o 0"02/0. correct to three

si&niicant i&ures"

0"02 C 0"02/0

9 0"02/ D 0"02/1

." 5ach o the ollo'in& numbers

is e6pressed correct to t'o si&niicant

i&ures e6cept

2"0 C 0"0

9 0"+0 D 0"04#

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10 hich o the ollo'in& numbers

is e6pressed correct to three si&niicant

i&ures;

0"0,. C 4",20

9 0"0,0. D +2"#0

Notes:$

1" t is con%enient to 'rite %er lar&e numbers

or %er small numbers in standard form or

scientific notation.

/" number e6pressed in standard orm is

'ritten as 10nAx * 'here 1 10A < and

n is a positiveor a negativeinte&er"

1"/a 56pressin& 8ositi%e Numbers in

Standard Form

56ercise

1" rite the ollo'in& numbers in standard

orm"

(a) 4,

(b) .1#,4

(c) 2,0000

/" rite the ollo'in& numbers in standard

orm"

(a) 0"./

(b) 0"042

(c) 0"000#4#/

1"/b Con%ert Numbers in Standard Form

!o Sin&le Numbers

56ercise

1" 56press the ollo'in& in sin&le numbers"

(a) "02 6 l0

(b) 2"//, 6 l0$4

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1"/c Computation o Numbers in Standard

Form

56ercise

1" Find the %alues o the ollo'in&* e6pressin&

our ans'ers in standard orm"

(a) 4" 6 l0#


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(b) its area* in cm/"

56press our ans'ers in standard

orm"

/" 56press +0 ,22 >m/in standard

orm* correct to three si&niicant

i&ures*

(a) in >m/*

(b) in m/"

3 Calculate the %alue o+

12. 10

24 10

x

x&i%in&

our ans'er in standard orm"

4 5%aluate( )

/2

10

+"/ 10

10

x

x

" &i%in& our

ans'er in standard orm"

5 Calculate the %alue o 0"00#/142*

.00

&i%in& our ans'er in standard orm"

1 ?uadratic 56pressions

Notes:$

1" ?uadratic e6pressions are e6pressions

'hich

ulill the ollo'in& characteristics:

(a) ha%e onl one %ariable (b) ha%e / as the hi&hest po'er o the

%ariable

/ ?uadratic 'ith three terms are

o the orm ax2< bx < c* 'here

a @ 0* b 0 and c 0* e"&" /x/< x< #"

!he ollo'in& are also Auadratic

e6pressions:

(a) 'ith t'o terms* e"&" /x/< 4x* c - 0

(b) 'ith one term* e"&" #p/* b - c - 0

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/"1a denti Auadratic e6pressions

56ercise /"1a

1"State 'hether each o the ollo'in& is a

Auadratic e6pression in one %ariable"

(a) /m

(b) 2 x

(c) / /1#m n

(d) / k

(e) / 11 /h h +

() // ,d

(&)

1 1

// m m+

(h)/0"# , 0"1f f+

(i)/1 1

4 +y y

/" Find the product o the ollo'in& pairs o

Linear e6pressions"

(a) (i) ( )m m

(ii) ( )1p p +

(iii) ( )/q q

(i%) ( ) #x x

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(%) ( )1

/ ,/

d d+

(%i) ( )

/2 .m

(%ii)

1 1

1/ 4 /h h

+

(i6) ( )4n n

(6) ( )/ /x x

(b) (i) ( ) ( )+ x x+

(ii) ( ) ( )1 /x x +

(iii) ( ) ( )# 4x x +

/02+1/1,"doc .


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(i%) ( ) ( )4 1p p

(%) ( ) ( )/ m m + +

(%i) ( ) ( )/ 1 #m m+ +

(%ii) ( ) ( ) / 4 1p p +

(%iii) ( )4 / 2/

pp

+ +

(i6) ( ) ( ) # x x

(6) ( ) ( )/ # # 1x x +

/02+1/1,"doc 10


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ns'er

1 (a) Bes (b) No (c) No (d) Bes

(e) Bes () Bes (&) No (h) Bes

(i) Bes (i) Bes

/ (a) (i) m/

(ii)p/ + p

(iii) =q/ < /q (i%) x/ < 1#x (%) d/ < 4d

(%i) 2m/ $ #4 (%ii) h/


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) ( )/

/ 1p

&) ( )/

/ #h +

h) ( )/

/m

i)

/1

/n

+

4" rite a Auadratic e6pression to represent

the area* in cm/* o each o the ollo'in&

i&ures"

/02+1/1,"doc 1/

chapter 1 standard form (1)

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