WORDING MATHEMATICAL SIGNS, SYMBOLS AND FORMULAE



Plus
- Minus
plus or minus
sign of multiplication; multiplication sign
sign of division; division sign
round brackets; parentheses
Curly brackets; braces
square brackets; brackets
Therefore
approaches; is approximately equal
~ equivalent, similar; of the order of
is congruent to; is isomorphic to
a equal b; a is equal to b
a is not equal to b; a is not b
approximately equals b
a plus or minus b
a is greater than b
a is substantially greater than b
a is less than b
a is substantially less than b
a second is greater than a d-th
x approaches infinity x tends to infinity
a is greater than or equals b
p is identically equal to q
n factorial
Laplacian
a prime
a double prime; a second prime
a triple prime
a vector; the mean value of a
the first derivative
a third; a sub three; a suffix three
a j th; a sub j product
f prime sub (suffix) c; f suffix (sub) c, prime
a second, double prime; a double prime, second
eighty seven degrees six minutes ten second
a plus b is c; a plus b equals c; a plus b is equal to c; a plus b makes c
a plus b all squared
c minus b is a; c minus b equals a; c minus b is equal to a; c minus b leaves a
bracket two x minus y close the bracket
a time b is c; a multiplied by b equals c; a by b is equal to c
a is equal to the ratio of e to l
ab squared (divided) by b equals ab
a divided by infinity is infinity small; a by infinity is equal to zero
x plus or minus square root of x square minus y square all over y
a divided by b is c; a by b equals c; a by b is equal to c; the ratio of a to b is c
a to b is as c to d
           a (one) half
  a (one) third
  a (one) quarter; a (one) fourth
   two thirds
twenty five fifty sevenths
2           two and a half
   one two hundred and seventy third
o [ou] point five; zero point five; nought point five; point five; one half
o [ou] point five noughts one
the cube root of twenty seven is three
the cube root of a
the fourth root of sixteen is two
the fifth root of a square
Alpha equals the square root of capital R square plus x square
the square root of b first plus capital A divided by two xa double prime
a) dz over dx b) the first derivative of z with respect to x
a) the second derivative of y with respect to x b) d two y over d x square
the nth derivative of y with respect to x
partial d two z over partial d square plus partial d two z over partial d  square equals zero
y is a function of x
d over dx of the integral from t nought to t of capital F dx
capital E is equal to the ratio of capital P divided by a to e divided by l is equal to the ratio of the product Pl to the product ae
capital L equals the square root out of capital R square plus minus  square
gamma is equal to the ratio of c prime c to ac prime
a to the m by nth power equals the nth root of (out of) a to the mth power
the integral of dy divided by the square root out of c square minus y square
capital F equals capital C sub (suffix) mu HIL sine theta
a plus b over a minus b is equal to c plus d over c minus d
capital V equals u square root of sine square i plus cosine square i equals u
tangent r equals tangent i divided by l
the decimal logarithm of ten equals one
a cubed is equal to the logarithm of d to the base c
four c plus W third plus two n first a prime plus capital R nth equals thirty three and one third
capital P sub (suffix) cr (critical) equals square capital El all over four l square
x + a is round brackets to the power p minus the r-th root of x all (in square brackets) to the minus q-th power minus s equals zero
Open round brackets capital D minus r first close the round brackets open square and round brackets capital D minus r second close round brackets by y close square brackets equals open round brackets capital D minus r second close the round brackets open square and round brackets capital D minus r first close round brackets by y close square brackets
u is equal to the integral of f sub one of x multiplied by dx plus the integral of f sub two of y multiplied by dy
capital M is equal to capital R sub one multiplied by x minus capital P sub one round brackets opened x minus a sub one brackets closed minus capital P sub two round brackets opened x minus a sub two brackets closed
a sub v is equal to m omega omega square alpha square divided by square brackets, r, p square m square plus capital R second round brackets opened capital R first plus omega square alpha square divided by rp round and square brackets closed
   a)  of z is equal to b, square brackets, parenthesis, z divided by c sub m plus 2, close parenthesis to the power m over m minus 1, minus 1, close square brackets; b) of z is equal to b multiplied by the whole quantity; the quantity 2 plus z over c sub m, to the power m over m minus 1, minus 1
the absolute value of the quantity  sub j of t one minus  sub j of t two is less than or equal to the absolute value of the quantity M of t one minus  over j, minus M of sub 2 minus  over j
  the limit as s becomes infinite of the integral of f of s and  of s plus delta n of s, with respect to s, from  to t, is equal to the integral of f of s and  of s, with respect to s, from  to t
   sub n minus r sub s plus l of t is equal to p sub n minus r sub s plus l, times e to the power of t times  sub q plus s
the partial derivative of F of lambda sub i of t and t, with respect to lambda, multiplied by lambda sub i prime of t, plus the partial derivative of F with arguments lambda sub i of t and t, with respect to t, is equal to zero
the second derivative of y with respect to s, plus y, times the quantity 1 plus b of s, is equal to zero
       f of z is equal to  sub mk hat, plus big 0 of one over the absolute value of z, as absolute z becomes infinite, with the argument of z equal to gamma
  D sub n minus 1 of is equal to the product from s equal to zero to n of, parenthesis, 1 minus x sub s squared, close parenthesis, to the power epsilon minus 1
the second partial (derivative) of u with respect to t plus a to the fourth power, times u, is equal to zero, where a is positive
set of functions holomorphic in D (function spaces)
Norm of f, the absolute value of f
distance between the sets  and  (curves, domains, regions)
b is the imaginary part of a + bi (complex variables)
a is the real part of a + bi (complex variables)
∂S the boundary of S
the complement of S
union of sets C and D
intersection of sets C and D
B is a subset of A; B is included in A
a is an element of the set A;                 a belongs to A

ANSWER KEYS

PART I

Unit 1

Reading and Vocabulary

1. 1c 2b 3a 4g 5f 6d 7e

 

2. 1b 2a 3g 4f 5c 6d 7e

 

3. 1 to apply, 2 to be admitted, 3 to take/to pass an exam, 4 to attend, 5 to miss, 6 to do research, 7 Bachelor’s degree

Grammar focus

A   1.How old is s/he? 2.Where does s/he come from? 3.Did he/she pass entrance exams? 4.What were his/her external scores? 5.What faculty does s/he study at? 6.What course does s/he take? 7.What subjects does s/he study? 8.Does s/he live in a dormitory? 9.What is s/he going to do after his/her Bachelor’s degree?  

LEARN MATHEMATICS IN ENGLISH

3. Beijing 14,123,274
  Mumbai (Bombay) 13,830,884
  Budapest 1,733,685
  Cairo 6,758,581
  London 7,825,200
  Madrid 3,213,271
  Moscow 11,551,930
  Munich 1,394,716
  New York 8,363,710
  Paris 2,144,700
  Rome 2,754,440
  Sao Paulo 13,651,085
  Sydney 4,399,722
  Tokyo 8,887,608

(Figures are based on the latest census findings available in 2011)

 

Unit 2

Reading and Vocabulary

 

1. 1g 2a 3e 4b 5d 6c 7f
2. 1g 2f 3c 4b 5a 6d 7e

 

3. 1 intelligent, 2 plump, 3 get on well with sb, 4 a spare time, 5 be good at, 6 cope with, 7 solve problems, 8 search for information

Grammar focus

A   1.Who is medium height? 2.Who gets on well with most people? 3.What is Max’s favourite sport? 4.What is Kate’s specialism? 5.Who has a good sense of humour? 6.What problems are easy for Max to solve? 7.Who plays piano in her free time?

LEARN MATHEMATICS IN ENGLISH

1. multiplication, 2 multiplication, 3 division, 4 subtraction, 5 division, 6 multiplication, 7 division, 8 addition, 9 addition, 10 subtraction.

Unit 3

Reading and Vocabulary

1. 1 f 2 g 3 e 4 a 5 c 6 d 7 b
2. 1 a 2 d 3 e 4 b 5 c 6 f 7 g

3. 1put on weight, 2 injection, 3 break a record, 4 moderation, 5 efficient,

6 absorb, 7 make sure

Grammar focus

A 1 e 2 f 3 a 4 g 5 b 6 d 7 c
B 1 2 3 4 5 6 7
  won’t it does she isn’t she were they does they does it could you

 

 

Unit 4

Reading and Vocabulary

1. 1 d 2 e 3 b 4 c 5 a
1.1. 1 d 2 a 3 e 4 b 5 c

1.2. 1 facilities, 2 accommodate, 3 excellence,4 fortnight, 5 alumni

2. 1d 2a 3b 4c 5e

2.1. 1merge, 2 be granted, 3 rapidly, 4 be engaged, 5 authority

4. 1 T 2 F 3 T 4 T 5 F 6 F 7 F

Grammar focus

A 1 am thinking, 2 think, 3 has, 4 is having, 5 is, 6 is being, 7 is, 8 is being, 9 cooks, 10 is meeting

B 1 is pouring, 2 haven’t got, 3 do you want, 4 are always asking, 5 feel tired, 6 start, 7 are visiting, 8 is baking, 9 am asking, 10 depends, 11 mean

LEARN MATHEMATICS IN ENGLISH

4.   a. One inch equals 2.54 centimeters. b. One foot equals 30.48 centimeters c. One yard equals .91 meters. d. One acre equals 4,446.86 square meters e. One mile equals 1.61 kilometers f. One pint equals .57 liters. g. One gallon equals 4.55 liters. h. One ounce equals 28.53 grams. i. One pound equals .454 kilos. j. One stone equals 6.35 kilos.

Unit 5

Reading and Vocabulary

1. 1 b 2 e 3 a 4 c 5 d
2. 1 e 2 b 3 a 4 c 5 d

3. 1 avenue, 2 boulevard, 3 carnival, 4 attractions, 5 famous

5.  4a  2b  5c  1d  3e 6 f 7 e

Grammar focus

A 1 a 2 b 3 b 4 b 5 b 6 a 7 b

B 1 the best, 2 bigger, 3 cleaner, 4 shorter, wider, more crowded, 7 friendlier, 8 more unemployed, 9 more regularly, 10more nervous, 11 more expensive, 12 the most expensive, 13 the most beautiful, the more, the happier

 

Unit 6

Reading and Vocabulary

1. / 2. 1 d 2 f 3 g 4 b 5 c 6 a 7 e

3. 1spirit, 2 require, 3 completeness, 4 rigour, 5 consistency, 6 take liking to, 7 encourage 

5. 1 c 2 e 3 a 4 d 5 b

Grammar focus

A 1was working/came, 2 was teaching/saw, 3 was proving/called, 4 was living/met, 5 was having/introduced, 6 was cooking/rang, 7 were driving/stopped, 8 was raining/left, 9 was studying/was thinking, 10 were solving/nocked

B 1 arrived, 2 looked, 3 didn’t see, 4 were holding, 5 weren’t waiting, 6 didn’t know, 7 was, 8 decided, 9 went, 10 looked, 11were waiting, 12 caught, 13 stopped, 14 got off, 15 walked, 16 gave, 17 was talking, 18 ran, 19 was carrying, 20 said, 21 was waiting, 22 thought, 23 were, 24 said

 

Unit 7

Reading and Vocabulary

1. / 2. 1 d 2 c 3 a 4 b 5 e

3. 1 roots, 2 be subjected, 3 deal with, 4 quantity, 5 contribution

Grammar focus

A 1 been, 2’ve been, 3 did you go, 4 finished, 5’ve already been, 6 did you go with, 7 went

B 2 taught, 3 have just come, 4 have you been, 5 was, 6 started, 7 have not finished, 8 have you been, 9 had, 10 did, 11 went, 12 have known, 13 got, 14 were, 15 have just met 

 

Unit 8

Reading and Vocabulary

1. / 2. 1 d 2 a 3 e 4 c 5 d

3. 1solids, 2 dimensions, 3 succeed, 4 masterpiece, 5 indispensable

Grammar focus

A 1 any, 2 some, 3 any, 4 some, 5 some, 6 anyone, 7 any

B 1 anything, 2 something, 3 something, 4 somebody, 5 anybody, 6 anywhere,

7 anything

Unit 9

Reading and Vocabulary

1. 1 f 2 d 3 c 4 e 5 a 6 b 7 g
2. 1 a 2 c 3 d 4 e 5 f 6 g 7 b

3. 1 reasoning, 2 precise, 3 encompass, 4 distinguish, 5 verbally, 6 abbreviations, 7 discouraging

5. 1 F 2 T 3 T 4 F

Grammar focus

A 1 much, 2 a lot of, 3 none, 4 too, 5 a little, 6 too much, 7 too many, 8 a few, 9 a little, 10 enough experience

Unit 10

Reading and Vocabulary

1. / 2. 1 a 2 g 3 f 4 d 5 d 6 e 7 c

3. 1 survey, 2 current, 3 treatment, 4 fertilizer, 5 premium, 6 misconception, 7 average

Grammar focus

A 1 is used, 2 is being used, 3 are involved, 4 involve, 5were given, 6 gave, 7 had been proved, 8 requires, 9 was made, 10 made up

B   1. A lecture in Statistics is being written by Tom now. 2. Statistics is being used more and more in various applications. 3. Many people in government are involved in collecting data from surveys. 4. The mathematical basis for setting up models to describe random phenomena is provided by an inevitable link between Statistics and Probability. 5. A profound knowledge of the Theory of Probability and Calculus is required by this profession. 6. Specialized courses in Sampling theory, Statistical estimation, Statistical decision theory, Correlation theory are given by the faculty of Maths. 7. Data are collected in a manner that allows the statistician to answer the exact question posed. 8. Important preliminary procedures are needed before making a specific analysis. 9. Several tests have already been carried out to obtain definite data. 10.  Data will be displayed in a table. 

Unit 11

Reading and Vocabulary

1. 1 d 2 f 3 a 4 b 5 c 6 e
2. 1 d 2 f 3 b 4 a 5 c 6 e

3. 1 accept, 2 store, 3 touch, 4 fasten, 5 plug

Grammar focus

A 1are you going, 2 shall, 3 will wright, 4 are running, 5 will correct, 6 am going to study, 7 shall help, 8 won’t forget, 9 is going to rain, 10 are meeting

B 1 shall, 2 ‘m going to travel, 3 ‘m staying, 4 will make, 5 shall, 6 ‘m going to go, 7 will arrive/’re going to arrive, 8 will call, 9 shall, 10’re meeting

Unit 12

Reading and Vocabulary

1. / 2. 1 d 2 b 3 a 4 e 5 c

3. 1 moron, 2 supply, 3 arrowhead, 4 alter, 5 eliminate

Grammar focus

A 1must, 2 should, 3 have to create, 4 should, 5 have to debugged, 6 should, 7 must, 8 have to be involved, 9 mustn’t, 10 shouldn’t

B 1 mustn’t, 2 they have to, 3 don’t have, 4 shouldn’t, 5 mustn’t, 6 mustn’t, 7 shouldn’t

Unit 13

Reading and Vocabulary

1. 1 c 2 e 3 b 4 a 5 d 6 g 7 f
2. 1 a 2 c 3 b 4 e 5 d 6 f 7 g

3. 1carry out, 2 decipher, 3 colossus, 4 instance, 5 accuse, 6 quiet, 7comment suicide

5. / 6. 1 c 2 d 3 b 4 f 5 e 6 g 7 a

7. 1 access, 2 impact, 3 available, 4 software, 5 assist, 6 consortium, 7 chip

Grammar focus

A 1 to access, 2 revealing, 3 graduating, 4 smoking, 5 taking, 6 to prove, 7 learning, 8 to get, 9 not to make, 10 inviting

B 1 to ask, 2 to do, 3 getting, 4 losing, 5 to wait, 6 being, 7 thinking, 8 to ask, 9 to go, 10 to book.

Unit 14

Reading and Vocabulary

1. / 2. 1 c 2 a 3 d 4 b 5 g 6 f 7 e

3. 1blaze, 2 poverty, 3 spot, 4 confound, 5 no avail, 6 make amends, 7 commonplace

5. 1 F 2 NG 3 F 4 T 5 T 6 T 7 NG 8 F 9 T

Grammar focus

A 1 c 2 a 3 a 4 h 5 b 6 d 7 f 8 g 9 j 10 i

B 1 although, 2 but, 3 so, 4 because, 5 but, 6 but, 7 so, 8 but, 9 because, 10 although

Part II

Practical set 8

Crossword: 1 multiplier, 2 difference, 3 dividend, 4 quotient, 5 arithmetic, 6 multiplication, 7addend, 8 division, 9 decreased, 10 summand, 11 product, 12 minuend, 13 difference, 14 factors, 15 minus, 16 multiplicand, 17 subtraction

Practice set 9

II (1b, 2c, 3a, 4e, 5d)

Practice set 10

II (axis, angle, arc, circle, circumference, corner, cube, chord, diameter, parallelogram, plane, polygon, radius, rhomb, square, vertex, point…)

P O C A X I S L U S W D N
B A I D G Y P C I O X I V
C I R C L E W U Z N B A K
A B C A W O G B J R E M O
R K U P L A N E C O N E R
S T M P O L Y G O N U T A
C A F W U F E J B C N E S
R U E O A N G L E I A R C
A C R H O M B Y O V M S Y
D H E V C I D P U G W A N
I O N V E R T E X P R T D
U R C A M Y B V H C G A O
S D E G S Q U A R E J K M

 

IV (A parachute)

Practice set 13

II The following description will help you to do this task.

Computer system consists of two main components: hardware and software. Each component is subdivided into different parts. The CPU and the peripheral devices constitute the hardware component. Systems software and applications software comprise the software component. Secondary storage devices along with Input and Output devices are referred to as peripheral devices.

PART III

Text 1

SOME FACTS FROM THE HISTORY OF MATHS EDUCATION

I 1 d 2 a 3 g 4 b 5 c 6 e 7 f

II 1 F 2 T 3 F 4 T 5 T 6 F 7 NG 8 F 9 F 10 T

Text 2

ANCIENT SOURCES OF INFORMATION

I 1 c 2 d 3 a 4 b 5 e 6 g 7 f

II 1 E 2 A 3 J 4 G 5 F 6 C 7 B D- I-

Text 3

THE HISTORY OF THE SYMBOLS FOR PLUS AND MINUS

I 1 b 2 a 3 e 4 g 5 c 6 d 7 f
III 1 √ 2 3 √ 4 √ 5

Text 4

STATISTICS

I 1 d 2 c 3 b 4 a 5 e
II 1 T 2 F 3 T 4 F 5 F

Text 5

DEGREES AND DIPLOMAS IN STATISTICS

I 1 c 2 d 3 a 4 e 5 b
II 1 F 2 T 3 F 4 F 5 T

Text 6

WHY IS THERE NO NOBEL PRIZE IN MATHEMATICS?

I 1 b 2 d 3 e 4 c 5 a 6 g 7 f
II 1 d 2 a 3 f 4 b 5 h 6 e 7 g
III 1 T 2 F 3 T

Text 7

MAJOR AWARDS IN MATHEMATICS

I

1 d

2 c

3 e

4 g

5 a

6 b

7 f
V

1 like

2 unlike

3 like

4 unlike

5 like

                         

Text 8

FIELDS MEDALIST

I 1 e 2 q 3 d 4 b 5 f 6 c 7 g

II 1 F 2 T 3 T 4 F 5 T 6 NG 7 F 8 F 9 T 10 T
III 1 b 2 g 3 i 4 j 5 c 6 h 7 e 8 a 9 d 10 f

Text 9

CULTURAL ASSOCIATIONS OF SOME NUMBERS

II 1 e 2 q 3 b 4 d 5 c 6 g 7 f
III 1 d 2 f 3 g 4 c 5 a 6 b 7 e

Text 10

NUMBER AND REALITY

I 1 d 2 e 3 i 4 b 5 a 6 c 7 h 8 g 9 j 10 k 11 f
II 1 F 2 T 3 F 4 T 5 F 6 F 7 T        

 

Text 11

A STRONG MATHEMATICAL COMPONENT

I 1 C 2 a 3 b 4 d    
II 1 c 2 d 3 e 4 b 5 f 6 a

Text 12

FRACTAL

I 1 e 2 c 3 a 4 b 5 f 6 d
II 1 e 2 b 3 a 4 f 5 d

Text 13

HEALTHY COMPUTER WORK

I 1 e 2 a 3 g 4 f 5 b 6 c 7 i 8 h 9 j 10 d  
II 1 T 2 F 3 F 4 T 5 F 6 F 7 T 8 F 9 F 10 T 11NG

Text 14

COMPUTERS CAN DO WONDERS

I 1 d 2 a 3 b 4 c 5 e
II 1 T 2 F 3 T 4 F 5 T

 


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