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8/13/2019 Chapter 1 Standard Form (1)
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Main Office: No. 25-01, 35-01 Jalan Austin Heights 3/1, Taan Mount Austin !Tel: 0"-3#1#53$%&'anch: No. 15A, 1"A, 21A ( )1A Jalan *n+ah 1#/12, Taan &uit *n+ah !Tel: 0"-23)1#$%
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"
/02+1/1,"doc
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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 +
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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/
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