English for Mathematics a short course for engineering students
STUDIUM JĘZYKÓW OBCYCH POLITECHNIKI ŁÓDZKIEJ 2011/2012
English fo M!"h#$!"i%s a short course for engineering students
NUMBE&S'NUMBE&S'NUMBE&S'NUMBE&S' I.
When do we use the word number and when do we use the word numeral?
Co$(l#"# "h# "#)" *i"h "h# !((o(i!"# *o+, A n---------- is an abstract entity that represents a count or measurement. In mathematics, the definition of a number has extended to include fractions, negatie, irrational, transcendental and complex n!!!!!!!!!!!!s. A n----------- is a symbol or group of symbols, or a "ord in a natural language that represents a n!!!!!!!!!!!!. #!!!!!!!!!!!!s differ from n!!!!!!!!!!s $ust li%e "ords differ from the things they refer to. &he symbols '11(, 'eleen( and ')I( are different n!!!!!!!!!!s, all representing the same n!!!!!!!!!!!. In common usage, n!!!!!!!!!!!s are often used as labels *e.g. road, telephone and house numbering+, as indicators of order *serial n!!!!!!!!!!s+, and as codes *I-#+ *Adapted from English for Mathematics+
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&#!+ "h# s#n"#n%#s %!#f.ll/, P!/ %los# !""#n"ion "o "h# n.$0#s in 0!%1#"s, Us# "h# (o(# fo$ of ! n.$#!l in #!%h s#n"#n%# !%%o+ing "o "h# %on"#)",
1+ adar "as first used in orld ar *2+. 2+ I hae a train to catch at *12+. 3+ Eli4abeth *2+ comes from the 5ouse of indsor. + I "as born on 6une *3+, *1789+ 2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
9+ -en(s telephone number is *20971+ :+ In the last match England beat ;oland *20+. 8+ 6ohn McEnroe "as leading *300+ in the *2+ game of the *1+ set "hen the match "as bro%en off due to a thunderstorm. + &he dictionary costs *<2.90+ 7+ =&he match is being "atched by *28,7+ spectators,> said the oice from the loudspea%ers. 10+ &he temperature in Italy rarely falls belo" *0+. 11+ ?hris saes *1/2+ of his poc%et money for summer holidays.
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12+ &he area of ?anada is *3,91,870+ s@uare miles. 13+ 5allo"een is obsered on ctober *31+ and &han%sgiing on the *+ &hursday of #oember. 1+ About *3/9+ of energy produced in the BA comes from coal and crude oil. 19+ If you "ant to pass this test, *91C+ of your ans"ers must be right. 1:+ ;elican Air"ays are sorry to announce that flight no. *003+ to uagadougou is cancelled today because of a dust storm. 18+ A meter is e@ual to *0.71+ yards. 1+ =pen your boo%s to page *38+,> as%ed the teacher. 17+ &he Earth(s olume is about *0.000003+ of the un(s olume. 20+ &his hotel "as built in the *1730+(s. 21+ ;oland(s foreign debts amount to *0,000,000,000+ dollars. 22+ Dou need a *12+ eggs to ma%e this layer ca%e. 23+ &he signature time of a "alt4 is *3/+. 2+ After the accident, -urt spent *102+ days in hospital. 29+ My school is about *2 + miles from my house. 2:+ 5enry *+ reigned in the *1+ *1/2+ of the *1:+ century. 28+ 32 F 7 2+ G7 F 3 27+ : H 3 F 7 30+ 7 3 F : 31+ 10 2 F 9 32+ 9 x 2 F 10 33+ log8 7 F 2 3+ J F 2 39+ E F mc2 3:+ #a2 H 52 K 2#a5 38+ 6anice is *9(>+ tall. 3+ &he score is *1919+ and Agassi is on his *2+ serice. 37+ &he BA "on the *x00+ relay race in eoul. 0+ About *2+ *20+ spea%ers too% part in the parliamentary debate on national defence. *by &omas4 Lasper+
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2 1 0 2 / 1 1 0 2 | s c it a m e h t a M r fo h s li g n E
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Lis"#n !n+ *i"# +o*n "h# n.$0#s "h!" /o. h#! in "h# follo*ing s#n"#n%#s, E!%h s#n"#n%# is #(#!"#+ "*i%#,
1. ?urrent research sho"s that !!!!!!!!!!! Americans stop smo%ing each year. 2. ?ould you gie 6ac% a call at !!!!!!!!!!! 3. eNre thin%ing about getting a house. ?urrently, the aerage mortgage is about !!!!!!!!!!!!. . !!!!!!!!!!!! ne" $obs hae been created in the high tech sector oer the past !!!!!!!!!!!! years. 9. 6ane is celebrating her !!!!!!!!!! birthday next MondayJ :. !!!!!!!!!!! of all Americans eat a hamburger at least once a "ee%. 8. &he density of hydrogen is !!!!!!!!!!!! in that compound. . o, "hat time shall "e get together next "ee% hat do you say if "e meet for lunch at !!!!!!!!!!!!! . 7. tatistics sho" that flossing !!!!!!!!!! a day can greatly improe general dental hygiene. 10. all treet closed up !!!!!!!!!!!!! . *Orom http//esl.about.com/library/listening/blnumbers1.htm+
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2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
Lis"#n !n+ *i"# "h# "*i%#, n.$0#s "h!" /o. h#! in "h# follo*ing s#n"#n%#s, E!%h s#n"#n%# is +o*n #(#!"#+
1. ;arsifal "as first premiered at -ayreuth in !!!!!!!!!!!!!!. 2. OredNs ffice upplies turned an incredible profit of !!!!!!!!!!!! in this past @uarter. 3. INm sure you "ill find that the A&B !!!!!!!!!!!!!! is a remar%able machine. . Athletes from oer !!!!!!!!!!!! countries "ill be participating in the next meeting to be held on the !!!!!!!!!! of eptember. 9. ;eter "on the bean counting contest "ith a guess of !!!!!!!!!!!! beans. :. &iger oods shot an incredible !!!!!!!!!!!!! under par on the bac% !!!!!!!!! . 8. -y the time of his death in !!!!!!!!!!!!, oger Oran%line had accumulated oer !!!!!!!!!!!! patents. . It is estimated that the ne" tax reform "ill cost the goernment !!!!!!!!!!!!!!!. 7. 5is ne" computer coo%sJ 5eNs got !!!!!!!!!!! Mb am "ith a !!!!!!!!!!!!! Mh4 processor. 10. elaxJ &here are !!!!!!!!!!!!!miles left to go. *Orom http//esl.about.com/library/listening/blnumbers2.htm+
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B3SIC OPE&3TIONS 3DDITION 4 5 6 7 89
addend
addend sum
SYMBOLS
WO&DS
8 H : F 13
&he sum of 8 and : is 13
H 7 H : F 23
&he total of , 7 and : is 23
H8
&he number increased by 8
H xF 13
more than
x is 13
a+b=c
a plus b e@uals c
a+b=c
a add b e@uals c
A shortcut for adding is called %!/ing. It inoles three steps 1. rite the problem :#"i%!ll/ and lin# .( numbers "ith the same (l!%# :!l.#. 2. Add the numbers in each column separately moing from the right to the left. 3. If the sum of any column is greater than 7, (." +o*n the appropriate digit in the ones place and %!/ the other digit to the next column to the left.
E)!$(l#; 177 9 H 89
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7 H H 9 F 22 ;ut do"n 2. ?arry 2 to the tens place. 2 H 7 H 9 H 8 F 23 ;ut do"n 3. ?arry 2 to the hundreds place. &he sum is 332.
S"#( 8
8469
S"#( @
5=>? 95?7> &he !!!!!!!!!!!!! of and 9 e@uals 7.
S"#( A
6 5 > 7 8= &he number !!!!!!!!!!!!!! by 7 is 18. !!!!!!!!!!! do"n 8. !!!!!!!!!! 1 to the hundreds place.
4 5 = 5 8 7 89 &he !!!!!!!!!! of :, 8 and 1 is 1. !!!!!!!!!! do"n . !!!!!!!!!!! 1 to the !!!!!!!!!! place. &he final !!!!!!!!! is 287. *Adapted from English for Mathematics+
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2 1 0 2 / 1 1 0 2 | s c it a m e h t a M r fo h s li g n E
B3SIC OPE&3TIONS SUBT&3CTION > A 7 4
minuend subtrahend difference
SYMBOLS
WO&DS
7P3F:
&he difference bet"een 7 and 3 is :
13 P
13 decreased by
18 P 7 F
7 from 18 is
xP9F7
9 less than x is 7
b–a
ubtract a from b
A shortcut for subtracting is called 0oo*ing. It inoles three steps 1. rite the problem :#"i%!ll/ and lin# .( numbers "ith the same (l!%# :!l.#. 2. ubtract the numbers in each column separately moing from the right to the left 3. If the digit in the minuend is less than the digit that has the same place alue in the subtrahend, re"rite the minuend by borro"ing 1 from the digit immediately to the left of the smaller digit and adding 10 to the smaller digit. Example
2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
I, S"#( 8
:2 38
ince in the ones column 2 Q 8, "e must borro". ince 1 ten F 10 ones, borro" 1 from : in the tens column to get 9 tens, and add 10 to the 2 in the ones column to get 9 ones. ubtract 12 P 8 F 9 ubtract 9 P 3 F 2 &he result is 29.
=6
S"#( @ !n+ A
@
8
8 8
?
8 A4? > = 6 A 6 =
ince in the ones column 9 Q , !!!!!!!! 1 from the : in the !!!!!!!!!! column to get 9 tens. !!!!!!!!!! 10 to the 9 in the ones column. !!!!!!!!! from 19. 19 P F 8.
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e are no" left "ith 9 in the tens column. ince in the tens column 9 Q 8, !!!!!!!!!! 1 from the !!!!!!!! column to get 2 hundreds. !!!!!!!! 10 to the 9 in the tens column. !!!!!!!!! 8 from 19. ince in the hundreds column 2 Q7, !!!!!!!!! 1 from the !!!!!!!!! column. ince 1 thousand F 10 hundreds, !!!!!!!!! 10 to the 2 in the hundreds column. &he final result is 38.
E)#%is#s; rite the follo"ing problems ertically and gie stepbystep instructions for
! 73: H :9 0 3: H 8 H 12 and fill in the missing "ords in the instructions for subtraction
% 100 P 238 ince Q 8, !!!!!!!!!! 1 from the tens column. Det, the tens column is 4ero, so "e moe to the hundreds column and finally to the thousands column. e hae to borro" 1 !!!!!!!!!F 10 hundreds F 10 x 10 tens. #o", "e are able to borro" from the !!!!!!!!! column. 1 P 8 F 8 1 !!!!!!!!!! by 8 e@uals 8. In the tens column, "e are no" left "ith 7. 7P3F: 3 !!!!!!!!! than 7 is :. In the hundreds column, "e are no" left "ith 7 units, too. 7P2F8 2 !!!!!!!!! 7 is 8. In the thousands column, "e are no" left "ith 0. &he final !!!!!!!!!!! is 8:8. ?hec% the result by !!!!!!!!!!!! the !!!!!!!!!!!!! to the subtrahend. #o", follo" the example aboe and do the same for
+ 392 P 22 # 83 P 1
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*Adapted from English for Mathematics+
2 1 0 2 / 1 1 0 2 | s c it a m e h t a M r fo h s li g n E
B3SIC OPE&3TIONS MBR&I;RI?A&I# 8 x F 9:
multiplier multiplicand product factors If the multiplication problem is "ritten ertically, by conention, the larger number is considered the multiplicand and "ritten on top.
SYMBOLS
WO&DS multiplied by 8
x8
times 8 &he product of and 8
&o multiply "hole numbers 1. rite the problem ertically and place the number "ith the longer number digit on top and the smaller belo" it. 2. Multiply each digit of the top number *multiplicand+ by the ones digit in the bottom number *multiplier+, moing from right to left. 3. Oor a product that #)%##+s 7, carry the igh"$os" +igi" to the next column on the left and "rite it aboe the multiplicand. ?irculate the next product and be sure to add to that product the digit that "as carried. . Multiply each digit in the multiplicand by the next digit to the left in the multiplier. ;lace each product under the preiously calculated one, but +is(l!%#+ one column to the left. 9. epeat step for all remaining digits in the multiplier. :. Add the products to get the final result.
I, 2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
Sol:# "h# $.l"i(li%!"ion (o0l#$ !n+ %o$(l#"# "h# $issing *o+s in "h# ins".%"ions,
329 x : F x 9 F 0 x 2 F 1: x 3 F 2
1: H F 20 2 H 2 F 2:
: x 9 F 30 : x 2 F 12 12 H 3 F 19 : x 3 F 1 1 H 1 F 17 #o", !!!!!!!!! the products. &he final result is !!!!!!!!!!!.
Multiply 329 by . ;ut !!!!!!!! 0, carry . !!!!!!!!!!! 0, carry 2. !!!!!!!!!!! 2:. !!!!!!!!!!! 329 !!!!!!!:. !!!!!!!!!!! 0, !!!!!!!! 3. !!!!!!!!!!! 9, !!!!!!!! 1. !!!!!!!!!!! 17. *Adapted from English for Mathematics+
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B3SIC OPE&3TIONS SITII# a : b = c
diidend diisor @uotient
SYMBOLS
WO&DS
a:b=c
a diided by b e@uals c
a/b
a oer b
a/b
&he @uotient of a and b
If you "ant to diide 31 by , "rite the problem as sho"n. !!!!!!!! 31
@uotient
&hin% "hat biggest integer multiplied by "ill gie a product less than or e@ual to 31. It is 8. rite 8 in the space for the @uotient. Multiply 8 x F 2. ubtract 2 from 31. 31 P 2 F 3, the #$!in+#. &he @uotient is 8, the remainder is 3.
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Co$(l#"# "h# ins".%"ion fo sol:ing -------FG.o"i#n" .sing "h# *o+s A4> ; = fo$ "h# 0o), Th## !# $o# *o+s "h!n n#%#ss!/, ;RA?ES U VB&IE#& U EMAI#SE U A-TE U SITI U VB&IE#& U #BM-E -BW5& U B-&A?&ES U IW5& U SITI U SITISE#S U EBR& U B-&A?&ES
Siision starts from the left of the !!!!!!!!!!!!!, and the !!!!!!!!!!!! is "ritten on the line aboe. tart from the left, the diisor is diided into the first digit or set of digits it diides into. In this case, 8 is diided into 3:, the !!!!!!!!!! is 9, "hich is placed aboe :. It is then multiplied by the !!!!!!!!!!! and the product is !!!!!!!!!!! from the set of digits in the diidend first selected. 9 x 8 e@uals 39, 39 subtracted from 3: e@uals 1. &he next digit to the !!!!!!!!!!! in the diidend is them brought do"n and the diisor is diided into this number. 5ere, 7 is brought do"n and the diisor is diided into 17, the result is 2, "hich is placed !!!!!!!!!! the 8. &he result is multiplied by the !!!!!!!!!!!! and the product is !!!!!!!!!!!! from the last number used in diision. 8 x 2 F 1X 1 subtracted from 17 e@uals 9. &his process is repeated until all digits in the diidend hae been !!!!!!!!!!! do"n. &he result of the last subtraction is the !!!!!!!!!!. &he number placed aboe the diidend is the !!!!!!!!!!!. *Adapted from English for Mathematics+
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HIE&3&CHY O< M3THEM3TIC3L OPE&3TIONS
Most mathematical operations addition, subtraction, multiplication and diision are normally (#fo$#+ in a particular order or s#G.#n%#. Multiplication and diision are done addition Bsually, mathematical are performed !(!" operations from (io left to"oright. &heand usesubtraction. of parentheses is common to s#"operations to be performed in a certain order.
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Co$(l#"# "h# ins".%"ions fo sol:ing #G.!"ions *i"h "h# *o+s fo$ "h# 0o), Th## !# $o# *o+s "h!n /o. n##+, * x 2+ H *3 H 2+ H
()
F
B&ISE U -EOE U ARR U I#ISE U ;I U ;EA&I# U MTE
1. !!!!!!!!!!! from left to right "ithin the e@uation and "ithin the set of parentheses 2. Oirst, perform all !!!!!!!!!!! "ithin the parentheses. x2F 3H2F9 ()
=
=4
Addition of 9 and 3 "as performed !!!!!!!!!! to diision.
3. ;erform !!!!!!!! operations !!!!!!!!! the parentheses. Moe from left to right. H 9 H F 18
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2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
Sol:# "h# #G.!"ion A ) F@ 5 9 ? 5 @ ) A, M!"%h "h# o(#!"ions *i"h "h#i +#s%i("ions,
1. 2 H F : 2. *3 x : P 9 H 2+ x 3 3. *1 P 9 H 2+ x 3 F *1 P 3+ x 3 F 19 x 3 . 19 x 3 F 9 a+ b+ c+ d+
;erform multiplication outside the brac%ets. !!!!! e"rite the e@uation. !!!!! ;erform operations in the innermost set of parentheses. !!!!! ;erform multiplication prior to addition and subtraction "ithin the brac%ets. !!!!!
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B&3CKETS YZ P braces, curly brac%ets [\ P s@uare brac%ets, brac%ets *+ P parentheses *sing parenthesis+, round brac%ets Q] angle brac%ets &he "ord brac%et is commonly used to mean any brac%et if there is only one set of brac%ets inoled.
III,
&#%ons".%" "h# .l#s, Th## is !l*!/s on# *o+ /o. +o no" n##+,
1. E)(!n+ing 0!%1#"s, or remoing brac%ets, is "riting an !!!!!!!!!!! such as 3*x H 2+ in an !!!!!!!!!!! form, in this case 3x H :, !!!!!!!!! any brac%ets. EVBITARE#&, I&5B&, IMIRA, E);EI# 2. To $.l"i(l/ o." a !!!!!!!!!!! of brac%ets, for example *x H 9+*x H 10+, each !!!!!!!!!! in the second brac%et is multiplied !!!!!!!!!! the first brac%et. &EM, ;AI, AWAI#&, TE 3. In the expression *2 H 3+, "e say that !!!!!!!!!!!! both the 0!%1#"#+ n.$0#s or !!!!!!!!!!!! itself !!!!!!!!!!! 2 and 3. MBR&I;RIE, TE, SI&I-B&E, MBR&I;RIES . e can !!!!!!!!!!! expressionsn#s"#+ in arious sets of brac%ets. In order to do that "e hae to !!!!!!!!!! from the !!!!!!!!! out. L, I#ISE, A?&, IM;RIOD 9. &o %eep our notation easy to understand, "e follo" the !!!!!!!!!! that "or%ing from the inside out, "e "rite the !!!!!!!!!!! in parentheses, then in brac%ets, and then in !!!!!!!!!!!. -A?E, B#S -A?LE&, E);EI#, ?#TE#&I# :. &o f!%"oi# 8*3 H x+, the common !!!!!!!!!!! must be "ritten !!!!!!!!!! the brac%eted !!!!!!!!, in other "ords, it has to be "!1#n o." of "h# 0!%1#"s. VB&IE#&, B&ISE, OA?&, &EM
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Sol:# "h# #G.!"ion !n+ #%ons".%" "h# .l#s, [*9 P 3+ H * x 3+ P * +\ 2 F
1. ;erform math operations !!!! each set of parentheses. 2. ;erform addition and subtraction !!!! left !!!! right. 3. ;erform diision !!!!! the brac%ets.
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2 1 0 2 / 1 1 0 2 | s c it a m e h t a M r fo h s li g n E
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Co$(l#"# "h# %oss*o+, 1 2 3 9 : 8
7 10 11 12 13 1 19 1: 18 1 17
2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
1. [^\ 2. a plus b 3. Q . ^ system 9. a x b :. a times b 7. a + b + d = c !. a decreased by b 7. *^+ 10. &he number that diides 11. &he result of 4 hat is the phrase in the ertical column
12. a P b 13. nought 1. the number remaining after the procedure of 8= is completed 19. the result of 8= 1:. the result of 6 18. a diided by b 1. the number diided into another number 17. the result of @ *Adapted from English for Mathematics+
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<&3CTIONS &OOTS 3ND POWE&S
A manufacturer is thin%ing about giing both $#"i% measurements *for example, millimetres+ and i$(#i!l measurements *for example, inches+ in its product specifications. ne of the company(s engineers is giing his opinion on the idea in a meeting. "#ne $roblem is% when &ou con'ert from metric to im$erial &ou no longer ha'e whole numbers – &ou get long decimal numbers. (or exam$le% one millimetre is nought point nought three nine three seveninches as a decimal. )o to be manageable% decimals ha'e to
be rounded up or down. *oud $robabl& round u$ that number to two decimal places% to gi'e &ou zero point zero four. ,ow% &ou might sa& the difference is negligible – its so small its not going to affect an&thing. -ut e'en if its ust a tin& fraction of a unit – one hundredth of an inch 0/0112% or one thousandth of an inch 0/01112 – and those numbers are then used in calculations% the rounding error can 'er& 3uic4l& add u$ to gi'e bigger inaccuracies.
0 mm = 1.15657 inches 1.18 inches
I, Wi"# "h# n.$0#s in *o+s,
1. 2. 3.092 3. . 9.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.
:. 0.29 8.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
. 0.16
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Co$(l#"# "h# +#s%i("ions of "h# n.$0#s .sing *o+s fo$ "h# "#)" !0o:#,
1. 0.29 F _
&he first number is a decimal, and the second is a ^^^^^^^. .
2. 0.:3: ` 0.:38 3. . 9. :.
&he second number is ^^^^^^^^ ^^^^^^^.. to three ^^^^^^^. ^^^^^^^. . 8.928 ` 8.9 &he second number is ^^^^^^^.. ^^^^^^^^ to one ^^^^^^^ ^^^^^^^. . , 2:, 19 &he numbers aren(t fractions or decimals. &hey(re ^^^^^^^^. numbers. Error 0.00001C &he error is so small that it(s ^^^^^^^^^... . 0.9: %g x 7,000 F 9,28 %g 0.97 %g x 7,000 F 9,310 %g &his difference is the result of a ^^^^^^ ^^^^^^.. . *Adapted from 9rofessional English in se+
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Ho* !# "h#s# :!l.#s s(o1#n
1. x 2. x 3. x . x
9. x
8. .
I2,
n
x
:.
n −1
−
3
x
n
x
P!%"is# #!+ing "h#s# #)(#ssions;
1. x
−
p
F
2. x p / q F
1
xp q
xp
3. x a F *x H a+ *x a+ . y F ae kx 9. x F
nx1
+
:. y y 1 F (
8.
x2 a
2
. d F
mx 2
m+n
+
y2 b
2
y2
−
y1
x2
−
x1
+
[( x
z2 c2
1 −
) * x x1 +
=
1
x2 ) 2
+
( y1
−
y2 )2
+
( z1
−
z2 )2 ]
7. b 2 F a 2 * 1 P e 2 + 10. x 2 H y 2 H 2gx H 2fy H c F 0 *Adapted from -asic English for )cience+
2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
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&E3DIN M3THEM3TIC3L EP&ESSIONS
I,
&#!+ o." "h#s# #G.!"ions; 1. x F
a+ b
c 2. x + y =
A a −b
3. I F a H *n 1+ d . TF I 9.
1 u
+
1
v
=
1
f
:. F u H at 8. Ot F m P mu 1
.
7.
R dQ dz
= −
M EI
= −
q
10. E F & H ; P c H e
II,
H## is "h# ##1 !l(h!0#", M!1# s.# /o. 1no* ho* "his is #!+,
q
|
}
ˆ
~
•
Š ‹
€
Œ
j k
v w
‚
ƒ
Ž
„
…
‘
z {
† ‡
’ “
Lis"#n !n+ #(#!",
14
‰
2 1 0 2 / 1 1 0 2 | s c it a m e h t a M r fo h s li g n E
III, P!%"is# #!+ing o." "h# #)(#ssions; 1
1. f F
2π LC 4 2. E F δT 2πf 3. S F P W0 . γ = F 4πR 9. z 0 F ‚ ” 10
:. ? F
7
−
5m
1
−
L R2
+
2
L2
I2, No* lis"#n !n+ *i"# +o*n "h# fo$.l!# /o. h#!,
&#f##n%#s; Sonoan ;., -asic English for )cience , xford, B; 1778. 2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
Ibbotson M., 9rofessional English in se , ?ambridge, ?ambridge Bniersity ;ress 2007. Lru%ie"ic4Wace% A., &r4as%a A., English for Mathematics, Lra%", AW5 Bniersity of cience and &echnology ;ress 2010.
ebsites """.math"ords.can """.about.com
15
English for Mathematics Glossary acute angle – kąt ostry add – dodawać addend – składnik sumy addition – dodawanie adjacent – przyległy angle – kąt base – podstawa base-ten system – system dziesiątkowy bisector – symetralna odcinka, dwusieczna k ąta bottom – dolny bracket – nawias broken line – linia przerywana circle – okrąg, koło circumcircle – okrąg opisany circumference – obwód koła circumscribe about – opisać na common fraction – ułamek zwykły common logarithm – logarytm zwykły, dziesiętny congruent – przystający curve – krzywa decimal fraction – ułamek dziesiętny denominator – mianownik derivative – pochodna diagonal – przekątna diameter – średnica difference – ró żnica digit – cyfra displace – przenosić, przesuwać divide – dzielić
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2 1 0 2 / 1 1 0 2 | s c it a m e h t a M r fo h s li g n E
dividend – dzielna division – dzielenie divisor – dzielnik dotted line – linia kropkowana equation – równanie equilateral triangle – trójk ąt równoboczny even numer – liczba parzysta expanded notation – zapis w formie rozszerzonej extract a root – wyciągać pierwiastek factor – czynnik factorial – silnia factorize – rozkładać na czynniki formula – wzór fraction – ułamek greatest common factor/divisor – największy wspólny dzielnik height – wysokość horizontal – poziomy hypotenuse – przeciwprostokątna inequality – nierówno ść inscribe in – wpisać w integer – liczba całkowita isosceles triangle – trójkąt równoramienny LCD (the least common denominator) – najmniejszy wspólny mianownik leg – przyprostokątna minuend – odjemna 2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
multiplicand – mnożna multiplication – mnożenie multiplier – mnożnik multiply – mnożyć natural number – liczba naturalna naught/nought – zero negative number – liczba ujemna number – liczba
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numeral – cyfra (np. arabska lub rzymska) numerator – licznik obtuse angle – kąt rozwarty octagon – ośmiokąt odd number – liczba nieparzysta operation – działanie ordinal number – liczba porz ądkowa parallel – równoległy parallelogram – równoległobok pentagon - pięciokąt perimeter – obwód perpendicular (to) – prostopadły, wysokość (np. trójkąta) positive number – liczba dodatnia power - potęga prime number – liczba pierwsza product – iloczyn proper fraction – ułamek wła ściwy quotient – iloraz raise a number to a power – podnosi ć liczbę do potęgi rational number – liczba wymierna real number – liczba rzeczywista reciprocal – wielkość odwrotna rectangle – prostokąt recurring decimal – ułamek dziesiętny okresowy reduce to lowest terms – skrócić/uprościć ułamek remainder – reszta repeating decimal – ułamek dziesi ętny okresowy rhomboid – równoległobok rhombus – romb right angle – kąt prosty root – pierwiastek round – zaokrąglić (np. liczbę) satisfy an equation – spełni ć równanie
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2 1 0 2 / 1 1 0 2 | s c it a m e h t a M r fo h s li g n E
semi-circle - półkole side – bok sketch a graph – narysować wykres solution – rozwiązanie solve an equation – rozwiązać równanie square – kwadrat square root – pierwiastek kwadratowy subscript – indeks dolny subtract – odejmować subtraction – odejmowanie subtrahend – odjemnik sum – suma superscript – indeks górny take a root – wyciągnąć pierwiastek tangent (to) – styczna (z) top - górny trapezium/trapezoid – trapez vertex - wierzchołek wavy line - linia falująca zigzag – linia łamana
2 1 0 2 / 1 1 0 2 | s itc a m e h t a M r fo h s li g n E
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