English for Mathematics
a short course for engineering students
STUDIUM J
ZYKÓW OBCYCH
POLITECHNIKI A
ÓDZKIEJ
2011/2012
English for Mathematics
a short course for engineering students
NUMBERS!NUMBERS!NUMBERS!NUMBERS!
I. When do we use the word number and when do we use the word numeral?
Complete the text with the appropriate word.
A number is an abstract entity that represents a count or measurement. In
mathematics, the definition of a number has extended to include fractions, negative,
irrational, transcendental and complex num s.
A numeral is a symbol or group of symbols, or a word in a natural language that
represents a number. Numbers differ from numerls just like words
differ from the things they refer to. The symbols  11 ,  eleven and  XI are different
numerals, all representing the same numbers. In common usage, num s
are often used as labels (e.g. road, telephone and house numbering), as indicators of order
(serial num s), and as codes (ISBN)
(Adapted from English for Mathematics)
II. Read the sentences carefully. Pay close attention to the numbers in brackets.
Use the proper form of a numeral in each sentence according to the context.
1) Radar was first used in World War (2). Second
2) I have a train to catch at (12:48). twelve fourty-eight o'clock
3) Elizabeth (2) comes from the House of Windsor. the Second
4) I was born on June (3), (1975) the third of June nineteen seventy-five
5) Ben s telephone number is (205891) two oh five eight nine one
6) In the last match England beat Poland (2:0). two nil
7) John McEnroe was leading (30:0) in the (2) game of the (1) set when the match was
broken off due to a thunderstorm. thirty love, second ,first
8) The dictionary costs ($28.50) twenty-eight dollars fifty
9)  The match is being watched by (27,498) spectators, said the voice from the
loudspeakers.twenty-seven thousand four houndred ninety-eight
10) The temperature in Italy rarely falls below (0). zero degrees
1
11) Chris saves (1/2) of his pocket money for summer holidays. one over two
English for Mathematics | 2011/2012
12) The area of Canada is (3,851,790) square miles. 3million eight houndred and fifty-one thousand seven hundred ninety
13) Halloween is observed on October (31) and Thanksgiving on the (4) Thursday of
November. the thirty-first; fourth
14) About (3/5) of energy produced in the USA comes from coal and crude oil. three over five
15) If you want to pass this test, (51%) of your answers must be right. fifty-one per cent
16) Pelican Airways are sorry to announce that flight no. (003) to Ouagadougou is
cancelled today because of a dust storm. oh oh three
17) A meter is equal to (0.9144) yards. point nine one four four
18)  Open your books to page (374), asked the teacher. three hundred seventy four
19) The Earth s volume is about (0.000003) of the Sun s volume. point (x5) three
20) This hotel was built in the (1930) s. nineteen therties
21) Poland s foreign debts amount to (40,000,000,000) dollars. fourty miliard
22) You need a (12) eggs to make this layer cake. twelve
23) The signature time of a waltz is (3/4). three over four (three quaters)
24) After the accident, Burt spent (102) days in hospital. one hundred and two
25) My school is about (2 �) miles from my house. two and a half
26) Henry (8) reigned in the (1) (1/2) of the (16) century. the eighth; first half; sixteenth
27) 32 = 9 three squared equals nine
28) "9 = 3 square root of nine equals three
29) 6 + 3 = 9 six plus three equals nine
30) 9 - 3 = 6 The difference between nine and three is six
31) 10 : 2 = 5 ten divided by two equals five
32) 5 x 2 = 10 five multiplied by seven equals ten
the logarithm of 49 to the base 7 is 2
33) log7 49 = 2
34) 4! = 24 4 FACTORIAL 24
35) E = mc2
E equals mc squared
Sodium oxide plus water yields two sodium hydroxide
36) Na2O + H2O 2NaOH
Janice i 5st(feet)4Ibs(inches)
37) Janice is (5 4 ) tall.
38) The score is (15:15) and Agassi is on his (2) service. draw; second
39) The USA won the (4x400) relay race in Seoul.
40) About (2) (20) speakers took part in the parliamentary debate on national defence.
(by Tomasz Kasper)
two score
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III. Listen and write down the numbers that you hear in the following sentences.
Each sentence is repeated twice.
1. Current research shows that 3.5 Americans stop smoking each year.
2. Could you give Jack a call at 21208976543?
3. We're thinking about getting a house. Currently, the average mortgage is about 7.7%.
4. new jobs have been created in the high tech sector over (the past
______ ______ years. <----not in this listening)
5. Jane is celebrating her 30 birthday next Monday!
6. of all Americans eat a hamburger at least once a week.
7. The density of hydrogen is 0.004287 in that compound.
8. So, what time shall we get together next week? What do you say if we meet for lunch
at 1:15 p.m.
9. Statistics show that flossing twice a day can greatly improve general dental
hygiene.
10. Wall Street closed up 8 and 7/16 .
(From http://esl.about.com/library/listening/blnumbers1.htm)
IV. Listen and write down the numbers that you hear in the following sentences.
Each sentence is repeated twice.
1. Parsifal was first premiered at Bayreuth in 1882.
2. Fred's Office Supplies turned an incredible profit of 24,817,919 dollars in this past
quarter.
3. I'm sure you will find that the ATU 578.4 is a remarkable machine.
4. Athletes from over 70 countries will be participating in the next meeting
to be held on the 13th of September.
5. Peter won the bean counting contest with a guess of 14, 440 beans.
6. Tiger Woods shot an incredible 6 under par on the back 9 .
7. By the time of his death in 1962, Roger Frankline had accumulated over 174
patents.
8. It is estimated that the new tax reform will cost the government 367 bilion dollars.
9. His new computer cooks! He's got 256 Mb Ram with a 733 Mhz
processor.
10. Relax! There are 313 miles left to go.
(From http://esl.about.com/library/listening/blnumbers2.htm)
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BASIC OPERATIONS
ADDITION
6 + 8 = 14
addend addend sum
SYMBOLS WORDS
7 + 6 = 13 The sum of 7 and 6 is 13
8 + 9 + 6 = 23 The total of 8, 9 and 6 is 23
4 + 7 The number 4 increased by 7
x + 4 = 13 4 more than x is 13
a + b = c a plus b equals c
a + b = c a add b equals c
A shortcut for adding is called carrying. It involves three steps:
1. Write the problem vertically and line up numbers with the same place value.
2. Add the numbers in each column separately moving from the right to the left.
3. If the sum of any column is greater than 9, put down the appropriate digit in the
ones place and carry the other digit to the next column to the left.
Example: 199 9 + 8 + 5 = 22
58 Put down 2. Carry 2 to the tens place.
+ 75 2 + 9 + 5 + 7 = 23
Put down 3. Carry 2 to the hundreds place.
The sum is 332.
I. Fill in missing words in the example of long addition given below.
Step 1 1684
+795
Step 2 4 + 5 = 9
The sum of 4 and 5 equals 9.
Step 3 8 + 9 = 17
The number 8 increased by 9 is 17. Put down 7. Carry
1 to the hundreds place.
6 + 7 + 1 = 14
The total of 6, 7 and 1 is 14. Put down 4. Carry 1 to
the t ous nds place. The final is 2479.
(Adapted from English for Mathematics)
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BASIC OPERATIONS
SUBTRACTION
9  3 = 6
minuend subtrahend difference
SYMBOLS WORDS
9  3 = 6 The difference between 9 and 3 is 6
13  4 13 decreased by 4
17  9 = 8 9 from 17 is 8
x  5 = 9 5 less than x is 9
b  a Subtract a from b
A shortcut for subtracting is called borrowing. It involves three steps:
1. Write the problem vertically and line up numbers with the same place value.
2. Subtract the numbers in each column separately moving from the right to the left
3. If the digit in the minuend is less than the digit that has the same place value in
the subtrahend, rewrite the minuend by borrowing 1 from the digit immediately
to the left of the smaller digit and adding 10 to the smaller digit.
Example: 62 Since in the ones column 2 < 7, we must borrow.
- 37 Since 1 ten = 10 ones, borrow 1 from 6 in the tens
column to get 5 tens, and add 10 to the 2 in the ones
column to get 5 ones.
Subtract 12  7 = 5
Subtract 5  3 = 2
The result is 25.
I. Fill in the missing words in the example of long subtraction given below.
Step 1 1365
- 978
0 2 5
Step 2 and 3 11 31615
- 9 7 8
3 8 7
Since in the ones column 5 < 8, borrow 1 from the 6 in the tens column to get
5 tens. Add 10 to the 5 in the ones column. Substract 8 from 15. 15  8 = 7.
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We are now left with 5 in the tens column. Since in the tens column 5 < 7, borrow 1
from the hundreds column to get 2 hundreds. Add 10 to the 5 in the tens column. Subtrsct
7 from 15.
Since in the hundreds column 2 <9, borrow 1 from the t ous nds column. Since 1
thousand = 10 hundreds, Add 10 to the 2 in the hundreds column. The final result
is 387.
Exercises:
Write the following problems vertically and give step-by-step instructions for:
a) 936 + 685
b) 36 + 87 + 12
and fill in the missing words in the instructions for subtraction:
c) 1004  237
Since 4 < 7, borrow 1 from the tens column. Yet, the tens column is zero, so we
move to the hundreds column and finally to the thousands column. We have to borrow 1 t ous nd
= 10 hundreds = 10 x 10 tens. Now, we are able to borrow from the tens
column.
14  7 = 7
14 decreased by 7 equals 7.
In the tens column, we are now left with 9.
9  3 = 6
3 less than 9 is 6.
In the hundreds column, we are now left with 9 units, too.
9  2 = 7
2 from 9 is 7.
In the thousands column, we are now left with 0.
The final result is 767.
Check the result by ____ _ the _____ _to the subtrahend.
Now, follow the example above and do the same for:
d) 352  228
e) 743  184 (Adapted from English for Mathematics)
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BASIC OPERATIONS
MULTIPLICATION
7 x 8 = 56
multiplier multiplicand product
factors
If the multiplication problem is written vertically, by convention, the larger number is
considered the multiplicand and written on top.
SYMBOLS WORDS
8 multiplied by 7
8 x 7 8 times 7
The product of 8 and 7
To multiply whole numbers:
1. Write the problem vertically and place the number with the longer number digit on
top and the smaller below it.
2. Multiply each digit of the top number (multiplicand) by the ones digit in the bottom
number (multiplier), moving from right to left.
3. For a product that exceeds 9, carry the rightmost digit to the next column on the left
and write it above the multiplicand. Circulate the next product and be sure to add to
that product the digit that was carried.
4. Multiply each digit in the multiplicand by the next digit to the left in the multiplier.
Place each product under the previously calculated one, but displaced one column to
the left.
5. Repeat step 4 for all remaining digits in the multiplier.
6. Add the products to get the final result.
I. Solve the multiplication problem and complete the missing words in the
instructions.
325 x 68 = ?
Multiply 325 by 8.
8 x 5 = 40 Put down 0, carry 4.
8 x 2 = 16 16 + 4 = 20 Put down 0, carry 2.
8 x 3 = 24 24 + 2 = 26 ___________ 26.
Put down
Multiply 325 by 6.
6 x 5 = 30 Put down 0, carry 3.
6 x 2 = 12 12 + 3 = 15 put down 5, carry 1.
6 x 3 = 18 18 + 1 = 19 ___________ 19.
Put down
Now, add the products.
The final result is 22100. (Adapted from English for Mathematics)
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BASIC OPERATIONS
DIVISION
a : b = c
dividend divisor quotient
SYMBOLS WORDS
a : b = c a divided by b equals c
a/b a over b
a/b The quotient of a and b
If you want to divide 31 by 4, write the problem as shown.
________ quotient
31 : 4
Think what biggest integer multiplied by 4 will give a product less than or equal to 31.
It is 7. Write 7 in the space for the quotient.
Multiply 7 x 4 = 28.
Subtract 28 from 31. 31  28 = 3, the remainder.
The quotient is 7, the remainder is 3.
I. Complete the instruction for solving ________ (quotient) using the words
369 : 7
from the box. There are more words than necessary.
PLACED �% QUOTIENT �% REMAINDER �% ABOVE �% DIVISOR �% QUOTIENT �% NUMBER
BROUGHT �% SUBTRACTED �% RIGHT �% DIVISOR �% DIVIDEND �% RESULT �% SUBTRACTED
quotient
Division starts from the left of the dividend, and the result is written on
the line above. Start from the left, the divisor is divided into the first digit or set of digits
it divides into. In this case, 7 is divided into 36, the is 5, which is placed
result
above 6. It is then multiplied by the divisor and the product is from
the set of digits in the dividend first selected. 5 x 7 equals 35, 35 subtracted from 36
equals 1. The next digit to the right in the dividend is them brought down and
the divisor is divided into this number. Here, 9 is brought down and the divisor is divided
above
into 19, the result is 2, which is placed
the 7. The result is multiplied by the
substracted
divisor
____________ and the product is ____________ from the last number used in division.
7 x 2 = 14; 14 subtracted from 19 equals 5. This process is repeated until all digits in the
dividend have been brought down. The result of the last subtraction is the
. The number placed above the dividend is the .
quotient.
(Adapted from English for Mathematics)
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HIERARCHY OF MATHEMATICAL OPERATIONS
Most mathematical operations: addition, subtraction, multiplication and division are
normally performed in a particular order or sequence. Multiplication and division are
done prior to addition and subtraction. Usually, mathematical operations are performed
from left to right. The use of parentheses is common to set apart operations to be
performed in a certain order.
I. Complete the instructions for solving equations with the words from the box.
There are more words than you need.
(4 x 2) + (3 + 2) + ( ) = ?
OUTSIDE �% BEFORE �% ALL �% INSIDE �% PRIOR �% OPERATIONS �% MOVE
1. Move from left to right within the equation and within the set of parentheses
2. First, perform all operations within the parentheses.
4 x 2 = 8
3 + 2 = 5
( )
= = 4 Addition of 5 and 3 was performed prior to division.
3. Perform all operations outside the parentheses. Move from left to right.
8 + 5 + 4 = 17
II. Solve the equation [3 x (2 + 4)  5 + 2] x 3.
Match the operations with their descriptions.
1. 2 + 4 = 6
2. (3 x 6  5 + 2) x 3
3. (18  5 + 2) x 3 = (18  3) x 3 = 15 x 3
4. 15 x 3 = 45
a) Perform multiplication outside the brackets. 4
b) Rewrite the equation.
c) Perform operations in the innermost set of parentheses. 1
d) Perform multiplication prior to addition and subtraction within the brackets.
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BRACKETS
{}  braces, curly brackets
[]  square brackets, brackets
()  parentheses (sing parenthesis), round brackets
<> - angle brackets
The word bracket is commonly used to mean any bracket if there is only
one set of brackets involved.
III. Reconstruct the rules. There is always one word you do not need.
1. Expanding brackets, or removing brackets, is writing an expression such as 3(x + 2)
in an equivalent form, in this case 3x + 6, without any brackets.
EQUIVALENT, WITHOUT, SIMILAR, EXPRESSION
2. To multiply out a pair of brackets, for example (x + 5)(x + 10), each term
in the second bracket is multiplied the first bracket.
TERM, PAIR, AGAINST, OVER
3. In the expression 4(2 + 3), we say that 4 multiplies both the bracketed numbers
or 4 distributes itself over 2 and 3.
MULTIPLIES, OVER, DISTRIBUTES, MULTIPLIED
4. We can simplify expressions nested in various sets of brackets. In order to do
that we have to from the inside out.
WORK, INSIDE, ACT, SIMPLIFY
5. To keep our notation easy to understand, we follow the CONVENTION that working
from the inside out, we write the EXPRESSIONS in parentheses, then in brackets, and
BRACES
then in ___________.
BRACES, ROUND BRACKETS, EXPRESSIONS, CONVENTION
6. To factorize 7(3 + x), the common FACTOR must be written OUTSIDE the
bracketed TERM, in other words, it has to be taken out of the brackets.
QUOTIENT, OUTSIDE, FACTOR, TERM
IV. Solve the equation and reconstruct the rules.
[(5  3) + (4 x 3)  (8 : 4)] : 2 = ?
1. Perform math operations in each set of parentheses.
2. Perform addition and subtraction from left to right.
3. Perform division outside the brackets.
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English for Mathematics | 2011/2012
V. Complete the crossword.
1
s
r c k e
a t
b
2
i i
a d t o n
d
3
s
s
l
e
i a
4 e c
m l
d
o
a t s
r
5 f c
m l
i i
i p
t l t
n
u a
o
c
6
e
qu
i
o
a
t
7 n
b
u
r
i
s t n
t a
c
o
8
n
t
h
s
p r
e
9 a e
e
s
i
v
o
d
i r
s
10
r
t
p
11 o d u c
i
u
m
e
d
n
12 n
o
r
z e
13
a
14 r m i d e r
e
n
t
t i e n
u
o
15 q
f
e
f
d e r
n e
16 i c
d
i
o
i
17 v i
s n
n
18 d
d d
v
i
i e
s
19 u m
1. [& ] BRACKETS 12. a  b MINUEND
2. a plus b ADDITION 13. nought ZERO
3. < LESS 14. the number remaining after the
DECIMAL
4. & system ?
procedure of 17 is completed REMAINDER
5. a x b FACTORS
15. the result of 17 QUOTIENT
6. a times b MULTIPLICATION
16. the result of 8 DIFFERENCE
7. a + b + 2d = c EQUATION
17. a divided by b DIVISION
8. a decreased by b SUBSTRACTION
18. the number divided into another
9. (& ) parentheses
number ?
DIVIDEND
10. The number that divides DIVISOR
19. the result of 2 SUM
11. The result of 6 PRODUCT
What is the phrase in the vertical column? (Adapted from English for Mathematics)
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FRACTIONS, ROOTS AND POWERS
A manufacturer is thinking about giving both metric measurements (for example,
millimetres) and imperial measurements (for example, inches) in its product
specifications. One of the company s engineers is giving his opinion on the idea in a
meeting.
 One problem is, when you convert from metric to imperial you no longer have whole
numbers  you get long decimal numbers. For example, one millimetre is nought point
nought three nine three seven inches as a decimal. So to be manageable, decimals have to
be rounded up or down. You d probably round up that number to two decimal places, to give
you zero point zero four. Now, you might say the difference is negligible  it s so small it s
not going to affect anything. But even if it s just a tiny fraction of a unit  one hundredth of
an inch (1/100), or one thousandth of an inch (1/1000)  and those numbers are then used in
calculations, the rounding error can very quickly add up to give bigger inaccuracies.
1 mm = 0.03937 inches H" 0.04 inches
I. Write the numbers in words.
1.
& a half& & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & ..
2. 3.0452 & three point four five two& & & & & & & & & & & & & & & & & & & & & & & & & & & & & &
3.
& & & & & & & & quarter& & & & & & & & & & & & & & & & & & & & & & & & & & & & & .
4.
& one over seven & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & &
5.
& sixteen over twelve & & & & & & & & & & & & & & & & & & & & & & & & & &
6. 0.25 & a quarter& & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & &
7.
& & two over three & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & &
8. 0.16 point one six& & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & &
II. Complete the descriptions of the numbers using words from the text above.
1. 0.25 = ź The first number is a decimal, and the second is a fraction .
2. 0.6368 H" 0.637 The second number is & & ROUNDED& & & & & & & UP.... to three
DECIMAL PLACES .
3. 7.5278 H" 7.5 The second number is ROUNDED DOWN to one
& & & DECIMAL PLACE& & & .
4. 8, 26, 154 The numbers aren t fractions or decimals.
They re WHOLE numbers.
5. Error: 0.00001% The error is so small that it s negligible.
6. 0.586 kg x 9,000 = 5,274 kg
0.59 kg x 9,000 = 5,310 kg This difference is the result of a & & & ROUNDING ERROR .
12
(Adapted from Professional English in Use)
English for Mathematics | 2011/2012
III. How are these values spoken?
-n
x squared
1. x�
5. x x to the power of MINUS n
2. xł
x cubed
square root of x
x
6.
3. x
x to the power of n
3
x cube root of x
n-1
7.
4. x
x to the power of n MINUS 1
n
x
nTH root of x
8.
IV. Practise reading these expressions:
1
- p
1. x =
x to the power of MINUS p equals ONE OVER x to the power of p
p
x
q
p / q p
2. x = x x to the power of p over q equals qth root of x to the power of p
x squared minus a squared equals x plus a in brackets times x minus a in brackets
3. x� - a� = (x + a) (x - a)
kx
4. y = ae y equals a multipled by e to the power of kx
nx1 + mx2
x equals the n times x1 increased by m times x2 over the sum of m and n
5. x =
m + n
y2 - y1
6. y - y1= ( ) ( x - x1) y minus y1 equals y2 minus y1 all over x2 minus
x2 - x1
x1 all in brackets times x minus by x1 all in brackets
2
x2 y2 z
x squared over a squared plus y squared over b squared plus z squared over c squared equals 1
7. + + = 1
a2 b2 c2
d equals square root of, open square brackets, open brackets x1 decreased by x2 close
8. d = [(x1 - x2 )2 + (y1 - y2 )2 + (z1 - z2 )2] brackets ,squared,plus open brackets y1 decreased by y2 close brackets squared plus open brackets
z1 decreased by z2 close brackets squared close square brackets.
2 2 2
9. b = a ( 1  e )
b squared equals a squared open brackets time one decreased by e squared close brackets
2 2
10. x + y + 2gx + 2fy + c = 0 The total of x squared, y squared, g multiplied by 2x, 2f multiplied by y and c equals nought
(Adapted from Basic English for Science)
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READING MATHEMATICAL EXPRESSIONS
I. Read out these equations:
a + b
1. x = x equals a increased by b all over c
c
A
2. x + y =
the sum of x and y is capital A over a decreased by b
a - b
l equals a increased by open brackets n minus 1 close brackets times d
3. I = a + (n - 1) d
4. V= IR
V equals I times R
1 1 1
one over u plus one one over v equals one over f
5. + =
u v f
6. v = u + at
plus a multiplied by t
v equals u
7. Ft = mv  mu F times t equals m times v decreased by m times u
1 M
8. = - one over R equals minus M over E times I
R EI
dQ
9. = -q d multiplied by Q over d multiplied by z equals minus q
dz
E squals T plus P minus by c plus e
10. E = T + P  c + e
II. Here is the Greek alphabet. Make sure you know how this is read.
ą ę alpha �  eta � � � ń tau
nu (ni)
upsilon
xi
� ł beta � Ś � ś � Ą
theta
omicron
ł � ą � ż ź Ć Ś
gamma iota
pchi
pi
� " � � Ą  � ż
delta kappa
chi
psi
� � epsilon  � � Ą rho � �
lambda
ś
 ź ś � Ł � � omega
zeta mu (mi) sigma
Listen and repeat.
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English for Mathematics | 2011/2012
III. Practise reading out the expressions:
1
f equals one over 2pi multiplied by the square root of L times C
1. f =
2Ą LC
4
E equals delta multiplied by T to the power of 4
2. E = �T
2Ąf
Ws equals 2pi multiplied by f over P
3. W =
S
P
W0
4. ł = F
gamma equals Wo over 4pi times R all times F
4ĄR
-7 -1
mi equals 4 pi multiplied by 10 to the power of minus 7 capital H small m to
5. ź = 4 Ą � 10 Hm
0
the power of minus one
L
6. C =
2
R2 + � L2 C equals L over R squared plus omega squared multiplied by L squared
IV. Now listen and write down the formulae you hear.
References:
Donovan P., Basic English for Science, Oxford, OUP 1997.
Ibbotson M., Professional English in Use, Cambridge, Cambridge University Press 2009.
Krukiewicz-Gacek A., Trzaska A., English for Mathematics, Kraków, AGH University of
Science and Technology Press 2010.
Websites:
www.mathwords.can
www.about.com
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English for Mathematics | 2011/2012
English for Mathematics
English for Mathematics
English for Mathematics
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 kąta
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  różnica
digit  cyfra
displace  przenosić, przesuwać
divide  dzielić
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dividend  dzielna
division  dzielenie
divisor  dzielnik
dotted line  linia kropkowana
equation  równanie
equilateral triangle  trójkąt 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  nierówność
inscribe in  wpisać w
integer  liczba całkowita
isosceles triangle  trójkąt równoramienny
LCD (the least common denominator)  najmniejszy wspólny mianownik
leg  przyprostokątna
minuend  odjemna
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 porządkowa
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 właściwy
quotient  iloraz
raise a number to a power  podnosić 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 dziesiętny okresowy
rhomboid  równoległobok
rhombus  romb
right angle  kąt prosty
root  pierwiastek
round  zaokrąglić (np. liczbę)
satisfy an equation  spełnić równanie
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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
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