English Grammar in Use (упражнения)

Exercise 1, Exercise 2, Exercise 3, Exercise 4, Exercise 5, Exercise 6, Exercise 7, Exercise 8, Exercise 9, Exercise 10, Exercise 11, Exercise 12, Exercise 13, Exercise 14, Exercise 15, Exercise 16, Exercise 17, Exercise 18, Exercise 19, Exercise 20, Exercise 21, Exercise 22, Exercise 23, Exercise 24, Exercise 25, Exercise 26, Exercise 27, Exercise 28, Exercise 29, Exercise 30, Exercise 31, Exercise 32, Exercise 33, Exercise 34, Exercise 35, Exercise 36, Exercise 37, Exercise 38, Exercise 39, Exercise 40, Exercise 41, Exercise 42, Exercise 43, Exercise 44, Exercise 45, Exercise 46, Exercise 47, Exercise 48, Exercise 49, Exercise 50, Exercise 51, Exercise 52, Exercise 53, Exercise 54, Exercise 55, Exercise 56, Exercise 57, Exercise 58, Exercise 59, Exercise 60, Exercise 61, Exercise 62, Exercise 63, Exercise 64, Exercise 65, Exercise 66, Exercise 67, Exercise 68, Exercise 69, Exercise 70, Exercise 71, Exercise 72, Exercise 73, Exercise 74, Exercise 75, Exercise 76, Exercise 77, Exercise 78, Exercise 79, Exercise 80, Exercise 81, Exercise 82, Exercise 83, Exercise 84, Exercise 85, Exercise 86, Exercise 87, Exercise 88, Exercise 89, Exercise 90, Exercise 91, Exercise 92, Exercise 93, Exercise 94, Exercise 95, Exercise 96, Exercise 97, Exercise 98, Exercise 11, Exercise 100, Exercise 101, Exercise 102, Exercise 103, Exercise 104, Exercise 105, Exercise 106, Exercise 107, Exercise 108, Exercise 109, Exercise 110, Exercise 111, Exercise 112, Exercise 113, Exercise 114, Exercise 115, Exercise 116, Exercise 117, Exercise 118, Exercise 119, Exercise 120, Exercise 121, Exercise 122, Exercise 123, Exercise 124

English Grammar in Use 1998


absolute value The distance of a number   from zero; the positive value of a number. at the picture
acute   angle A positive angle measuring   less than 90 degrees.  
acute triangle A triangle each of whose   angles measures less than 90 degrees.  
additive identity The number zero is called   the additive identity because the sum of zero and any number is that number.  
additive inverse The additive inverse of any   number x is the number that gives zero when added to x. The additive inverse   of 5 is -5.  
adjacent angles Two angles that share both a   side and a vertex.  
angle The union of two rays with a   common endpoint, called the vertex.  
arc A portion of the   circumference of a circle.  
area The number of square units   that covers a shape or figure.  
associative property of addition (a + b) + c = a + (b + c)  
associative property of multiplication (a x b) x c = a x (b x c)  
average A number that represents the   characteristics of a data set.  
axis of symmetry A line that passes through a   figure in such a way that the part of the figure on one side of the line is a   mirror reflection of the part on the other side of the line.  
base The bottom of a plane figure   or three-dimensional figure.  
bisect To divide into two congruent   parts.  
box and whisker plot A type of data plot that   displays the quartiles and range of a data set.  
Cartesian coordinates A system in which points on   a plane are identified by an ordered pair of numbers, representing the   distances to two or three perpendicular axes.  
central angle An angle that has its vertex   at the center of a circle.  
chord A line segment that connects   two points on a curve.  
circle The set of points in a plane   that are a fixed distance from a given point, called the center.  
circumference The distance around a   circle.  
coefficient A constant that multiplies a   variable.  
collinear Points are collinear if they   lie on the same line.  
combination A selection in which order   is not important.  
common factor A factor of two or more   numbers.  
common multiple A multiple of two or more   numbers.  
commutative property of addition a + b = b + a.  
commutative property of multiplication a*b = b*a.  
complementary angles Two angles whose sum is 90   degrees.  
composite number A natural number that is not   prime.  
cone A three-dimensional figure   with one vertex and a circular base.  
congruent Figures or angles that have   the same size and shape.  
constant A value that does not   change.  
coordinate plane The plane determined by a   horizontal number line, called the x-axis, and a vertical number line, called   the y-axis, intersecting at a point called the origin. Each point in the   coordinate plane can be specified by an ordered pair of numbers.  
coplanar Points that lie within the   same plane.  
counting numbers The natural numbers, or the   numbers used to count.  
counting principle If a first event has n   outcomes and a second event has m outcomes, then the first event followed by   the second event has n times m outcomes.  
cross product A product found by   multiplying the numerator of one fraction by the denominator of another   fraction and the denominator of the first fraction by the numerator of the   second.  
cube A solid figure with six   square faces.  
cylinder   A three-dimensional figure   having two parallel bases that are congruent circles.  
data Information that is   gathered.  
decimal number The numbers in the base 10   number system, having one or more places to the right of a decimal point.  
degree A unit of measure of an   angle.  
denominator The bottom part of a   fraction.  
dependent events Two events in which the   outcome of the second is influenced by the outcome of the first.  
diagonal The line segment connecting   two nonadjacent vertices in a polygon.  
diameter The line segment joining two   points on a circle and passing through the center of the circle.  
difference The result of subtracting   two numbers.  
digit The ten symbols, 0, 1, 2, 3,   4, 5, 6, 7, 8, and 9. The number 215 has three digits: 2, 1, and 5.  
distributive property a(b + c) = ab + ac  
dividend In a / b = c, a is the   dividend.  
divisor In a / b = c, b is the   divisor.  
ellipse The set of all points in a   plane such that the sum of the distances to two fixed points is a constant.  
equation A mathematical statement   that says that two expressions have the same value; any number sentence with   an =.  
equilateral triangle A triangle that has three   equal sides.  
equivalent equations Two equations whose   solutions are the same.  
equivalent fractions Fractions that reduce to the   same number.  
error of measurement The difference between an   approximate measurement and the actual measure taken.  
evaluate To substitute number values   into an expression.  
even number A natural number that is   divisible by 2.  
event In probability, a set of   outcomes.  
exponent A number that indicates the   operation of repeated multiplication.  
equivalent fractions Fractions that reduce to the   same number.  
factor One of two or more   expressions that are multiplied together to get a product.  
factorial To break a number into its   factors.  
face A flat surface of a   three-dimensional figure.  
formula A equation that states a   rule or a fact.  
fraction A number used to name a part   of a group or a whole. The number below the bar is the denominator, and the   number above the bar is the numerator.  
frequency The number of times a   particular item appears in a data set.  
frequency table A data listing which also   lists the frequencies of the data.  
graph A type of drawing used to   represent data.  
greatest common factor (GCF) The largest number that   divides two or more numbers evenly.  
horizontal A line with zero slope.  
hypotenuse   The side opposite the right   angle in a right triangle.  
identity property of addition The sum of any number and 0   is that number.  
identity property of multiplication The product of 1 and any   number is that number.  
improper fraction A fraction with a numerator   that is greater than the denominator.  
independent events Two events in which the   outcome of the second is not affected by the outcome of the first.  
inequality A mathematical expression   which shows that two quantities are not equal.  read this
infinity A limitless quantity.  
inscribed angle An angle placed inside a   circle with its vertex on the circle and whose sides contain chords of the   circle.  
inscribed polygon A polygon placed inside a   circle so that each vertex of the polygon touches the circle.  
interval notation    read this
integers The set of numbers   containing zero, the natural numbers, and all the negatives of the natural   numbers.  
intercept The x-intercept of a line or   curve is the point where it crosses the x-axis, and the y- intercept of a   line or curve is the point where it crosses the y-axis.  
intercepted arc The arc of a circle within   an inscribed angle.  
interpolation A method for estimating   values that lie between two known values.  
intersecting lines Lines that have one and only   one point in common.  
inverse Opposite. -5 is the additive   inverse of 5, because their sum is zero. 1/3 is the multiplicative inverse of   3, because their product is 1.  
inverse operations Two operations that have the   opposite effect, such as addition and subtraction.  
irrational number A number that cannot be   expressed as the ratio of two integers.  
isosceles triangle A triangle with at least two   equal sides.  
least common denominator The smallest multiple of the   denominators of two or more fractions.  
least common multiple The smallest nonzero number   that is a multiple of two or more numbers.  
like fractions Fractions that have the same   denominator.  
line A straight set of points   that extends into infinity in both directions.  
line of symmetry Line that divides a   geometric figure into two congruent portions.  
line   segment Two points on a line, and   all the points between those two points.  
locus A path of points.  
logic The study of sound   reasoning.  
lowest   terms Simplest form; when the GCF   of the numerator and the denominator of a fraction is 1.  
mean In a data set, the sum of   all the data points, divided by the number of data points; average.  
median The middle number in a data   set when the data are put in order; a type of average.  
midpoint A point on a line segment   that divides the segment into two congruent segments.  
mixed   number A number written as a whole   number and a fraction.  
mode A type of average; the   number (or numbers) that occurs most frequently in a set of data.  
multiple A multiple of a number is   the product of that number and any other whole number. Zero is a multiple of   every number.  
multiplicative identity The number 1 is the   multiplicative identity because multiplying 1 times any number gives that   number.  
multiplicative inverse The reciprocal of a number.  
mutually exclusive events Two or more events that   cannot occur at the same time.  
natural numbers The counting numbers.  
negative number A real number that is less   than zero.  
normal Perpendicular.  
number   line A line on which every point   represents a real number.  
numerator The top part of a fraction.  
obtuse   angle An angle whose measure is   greater than 90 degrees.  
obtuse triangle A triangle with an obtuse   angle.  
octagon A polygon with 8 sides.  
odd   number A whole number that is not   divisible by 2.  
operation Addition, subtraction,   multiplication, and division are the basic arithmetic operations.  
opposites Two numbers that lie the   same distance from 0 on the number line but in opposite directions.  
ordered   pair Set of two numbers in which   the order has an agreed-upon meaning, such as the Cartesian coordinates (x,   y), where the first coordinate represents the horizontal position, and the   second coordinate represents the vertical position.  
origin The point (0, 0) on a   coordinate plane, where the x-axis and the y-axis intersect.  
outcome In probability, a possible   result of an experiment.  
parallel Two lines are parallel if   they are in the same plane and never intersect.  
parallelogram A quadrilateral with   opposite sides parallel.  
pentagon A five-sided polygon.  
percent A fraction, or ratio, in   which the denominator is assumed to be 100. The symbol % is used for percent.    read here
perimeter The sum of the lengths of   the sides of a polygon.  
permutation A way to arrange things in   which order is important.  
perpendicular Two lines are perpendicular   if the angle between them is 90 degrees.  
pi The ratio of the   circumference of a circle to its diameter.  
plane A flat surface that   stretches into infinity.  
point A location in a plane or in   space, having no dimensions.  
polygon A closed plane figure made   up of several line segments that are joined together.  
polyhedron A three-dimensional solid   that is bounded by plane polygons.  
positive number A real number greater than   zero.  
power A number that indicates the   operation of repeated multiplication.  
prime   number A number whose only factors   are itself and 1.  
probability For an experiment, the total   number of successful events divided by the total number of possible events.  
product The result of two numbers   being multiplied together.  
proper fraction A fraction whose numerator   is less than its denominator.  
proportion An equation of fractions in   the form: a/b = c/d  
protractor a/b = c/d  
pyramid A device for measuring   angles.  
Pythagorean Theorem The theorem that relates the   three sides of a right triangle: a2+b2=c2      
quadrant One of the quarters of the   plane of the Cartesian coordinate system  
quadrilateral A polygon with 4 sides.  
quotient   The answer to a division   problem.  
radius The distance from the center   to a point on a circle; the line segment from the center to a point on a   circle.  
range In statistics, the   difference between the largest and the smallest numbers in a data set.  
rate A ratio that compares   different kinds of units.  
ratio A pair of numbers that   compares different types of units.  
rational number A number that can be   expressed as the ratio of two integers.  
ray part of a line, with one   endpoint, and extending to infinity in one direction.  
real   numbers The combined set of rational   numbers and irrational numbers.  
reciprocal The number which, when   multiplied times a particular fraction, gives a result of 1.  
rectangle A quadrilateral with four   90-degree angles.  
reflection A transformation resulting   from a flip.  
regular polygon A polygon in which all the   angles are equal and all of the sides are equal.  
repeating decimal A decimal in which the   digits endlessly repeat a pattern.  
rhombus A parallelogram with four   equal sides.  
right   angle An angle whose measure is 90   degrees.  
right triangle A triangle that contains a   right angle.  
root The root of an equation is   the same as the solution to the equation.  
rotation A transformation in which a   figure is rotated through a given angle, about a point.  
sample   space For an experiment, the   sample space includes all the possible outcomes.  
scale drawing A drawing that is a   reduction or enlargement of the original.  
scalene triangle A triangle with three   unequal sides.  
scattergram A graph with points plotted   on a coordinate plane.  
scientific notation A method for writing   extremely large or small numbers compactly in which the number is shown as   the product of two factors.  
set A well-defined group of   objects.  
similar Two polygons are similar if   their corresponding sides are proportional.  
simplifying Reducing to lowest terms.  
skew   lines Lines that are not in the   same plane and that do not intersect.  
slope The steepness of a line   expressed as a ratio, using any two points on the line.  
solution The value of a variable that   makes an equation true.  
sphere A three-dimensional figure   with all points in space a fixed distance from a given point, called the   center.  
square A quadrilateral with four   equal sides and four 90 degree angles.  
square   root The square root of x is the   number that, when multiplied by itself, gives the number, x.  
statistics The science of collecting,   organizing, and analyzing data.  
stem and leaf plot A technique for organizing   data for comparison.  
straight angle An angle that measures 180   degrees.  
supplementary angles Two angles are supplementary   if their sum is 180 degrees.  
surface   area For a three-dimensional   figure, the sum of the areas of all the faces.  
terminating decimal A fraction whose decimal   representation contains a finite number of digits.  
translation A transformation, or change   in position, resulting from a slide with no turn.  
transformation A change in the position,   shape, or size of a geometric figure.  
transversal A line that intersects two   other lines.  
trapezoid A quadrilateral that has   exactly two sides parallel.  
tree   diagram A diagram that shows   outcomes of an experiment.  
triangle   A three-sided polygon.  
unit   price Price per unit of measure.  
variable A letter used to represent a   number value in an expression or an equation.  
vertex The point on an angle where   the two sides intersect.  
vertical angles A pair of opposite angles   that is formed by intersecting lines.  
volume   A measurement of space, or   capacity.  
whole numbers The set of numbers that   includes zero and all of the natural numbers.  
x-axis   The horizontal axis in a   Cartesian coordinate plane.  
x-intercept   The value of x at the point   where a line or curve crosses the x-axis.  
y-axis   The vertical axis in a   Cartesian coordinate system.  
y-intercept   The value of y at the point   where a curve crosses the y-axis.  
zero The additive identity; the   number that, when added to another number n, gives n.  
zero property of multiplication The product of zero and any   number is zero.  



English Verb Tenses (from my teacher NB (NZ) My best wishes to her)

Present Forms
Present Simple Present Continuous Present Perfect Present Perfect Continuous
Time expressions, markers Usually, often,always, every day/week/month/year, in the morning/afternoon/evening, at night, at the weekend, on Mondays etc now, at the moment, at present, these days, still, nowadays, today, tonight etc For, since, already, yet, always, just, ever, never, so far, today, this week/month etc, how long, lately, recently, still, etc for, since, how long, lately, recently
When to use:

* for permanent states

He works in a bank                                                              

* repeated actions and daily routines 

They take the train to work every morning

* for actions taking place now, at the moment of speaking

He is giving the baby a bath at the moment

* for an action which started in the past and continues up to the present

Kate has had the dog for 3 years

* to put emphasis on the duration of an action which started in the past and continues up to present 

Sam has been talking on the phone for half an hour

* for general truths and law of nature 

 The sun sets on the west

* for temporary actions that are going on around now, but not at the actual moment of speaking 

I am looking for a new job these days

* for an action which has recently finished and whose result is visible in the present    

She has just washed her hair

* for an action which started in the past and lasted for some time. The action may have finished or may still be going on. The result of the action is visible in the present

Her feet hurt. She has been walking all morning.

* for timetables (planes,trains, etc) and programmes

The plane from Brussels arrives at 8:30

* for expressing annoyance, irritation or anger

You are constantly interrupting me when I am talking.

* for an action which happened at an unstated time in the past. The exact is not mentioned because it is either unknown or unimportant. The emphasis is placed on the action 

The Taylors have bought yacht

* for expressing annoyance, irritation or anger                                                      

Somebody has been sitting at my desk

* for sports commentaries

Peterson overtakes Williams and wins the race.                                                                  

* for actions that we have already arranged to do in the near future, especially when the time and place have been decided

They are moving into their new house next week

* for an action which has happened within a specific time period which is not over at the moment of speaking.

She has taken 15 pictures today (today is not over yet. She may take more pictures)

* narration                                    

Then the prince gets on his horse  and quickly rides away

* for changing or developing situations

More and more people are moving into the cities.

Past Forms
Past Simple Past Continuous Past Perfect Past Perfect Continuous
Time expressions, markers yesterday,then, when, how long ago..? last night/week/month/year/Tuesday, etc, 3 days/weeks,etc ago, in 1997, etc. while, when, as, all morning/evening/day/night, etc before, after, already, just, for, since, till/until, when, by, by  the time, never etc for, since, how long, before, until etc
When to use:

* for an action which happened at a definite time in the past. The time is stated, already known or implied                     

They went camping by the lake last month.

* for an action which was in progress at a stated time in the past. We do not mention when the action started or finished.

At 7 o'clock yestarday evening they were having dinner.

* for an action which happened before another past action or before a stated time in the past

She had finished work when she met her friends for coffee.

* to put emphasis on the duration of an action which started and finished in the past before another past action or a stated time in the past, usually with since or for 

They had been looking for a house for six months before they found one they liked

* for actions which happened immideately one after the other in the past

First she paid the driver, then she got out of the taxi.

* for an action which was in progress when another action interrupted it. We use past continuous for the action in progress(longer action) and the past simple for the action which interrupted it (shorter action)

He was walking down the street when he ran into and old friend.

* for an action which finished in the past and whose result was visible in the past 

He was happy. He had signed an important contract

* for anaction which lasted for some time in the past and whose result was visible in the past

Last Friday Ron had to fly to New York. Hisflight was delayed. He was annoyed. He had been waiting at the airport for three hours.

* for past habbits or states which are now finished. In such cases we can also use the expression USED TO

Kitchens were/used to be very different a hundred years ago.

* for two or more simultaneous past actions.

She was talking on her mobile phone whike she was driving to work.

* past perfect is the past equivalent of the present perfect

He had fixed the old armchair. It looked brand new

* past perfect continuous is the past equivalent of the present perfect continuous

I had been driving for ten hours, so I felt exhausted.

* to describe the atmosphere, setting, etc in the introduction to a story before we describe the main events.

One beautiful autumn afternoon Ben was walking downa quite country lane. The birds were singing and the sun was shining.

Future forms
Future Simple Future Continuous Future Perfect Future Perfect Continuous
Time expressions, markers tomorrow, the day after tomorrow, tonight, soon, next week/month/year, in a week/month/year, in two/three days/weeks etc before, by, then, by the time, until/till. by, for
When to use:

* in predictions about the future usually with the verbs think, believe, expect, etc. The expressions be sure, be afraid, etc and the adverbs probably, perhabs, certainly, etc

I am afraid we won't be on time for the meeting.

* for an action which will be in progress at a stated future time

This time next week we will be cruising round the islands

* for an action which will be finished before a stated future time.

She will have finished the report by tomorrowo'clock

* to emphasise the duration of an action up to a certain time in the future

By the end of next month she will have been teaching for twenty years.

* for immidiate decisions 

I will order this cheese cake

* for an action which will definitely happen in the future as the result of a routine or arrangement

Don't call Julia. I will be seeing her later, so I will pass the message on.

* for promises (usually with the verbs promise, swear, guarantee etc) threats, warnings, requests, hopes and offers 

I don't understand this exercise. Will you help me with it? (request)

* when we ask politely about someone's plans for the near future (we want to know if our wishes fit in with their plans) 

Will you be using the photocopier for long? No, why? I need to make some photocopies

* for actions/events/situations which will definetly happen in the future and which we cannot control

The temperature will reach 40C tomorrow.

English - Russion Math DICTIONARY 


abscissa - абсцисса

absolute - aбсолютный

absolute extremum - aбсолютныйэкстремум

absolute value - aбсолютная величина, модуль

accuracy - точность

acnode - изолированная точка

acute angle - острый угол

acute triangle- остроугольный треугольник

add- прибавлять, суммировать

addend - слагаемое

addition - суммирование

addition sign - знак сложения

adjacent angle - смежный угол

adjacent side - прилежащая сторона

adjacent supplementary angles - смежныеуглы

adjoint - сопряженный

admissible - допустимый

admissible solution - допустимоерешение

affine coordinates - аффинныекоординаты

algebra - aлгебра

algebraic equation - алгебраическоеуравнение

algebraic expression - алгебраическоевыражение

algorithm - aлгоритм

algorithm for division - алгоритмделения

alternance - чередование

alteration - изменение

alternate angles - накрестлежащиеуглы

alternate exterior angles - внешниепротиволежащиеуглы

alternate interior angles - внутренниепротиволежащиеуглы

altitude of a triangle - высотатреугольника

amplitude - aмплитуда

analogous - aналогичный

analogical - aналогичный

analogy - aналогия

analysis - aнализ

analyze - анализировать

angle - угол

anticosine - aрккосинус

antisine - aксинус

applicate - aппликата

approximate solution - приближенноерешение

arbitrary - произвольный

arc - дуга

arccosine - арккосинус

arc-length - длинадуги

arcsine - арксинус

arctangent - арктангенс

area - площадь

argument - aргумент

argument of a function - aргументфункции

arithmetic mean - среднееарифметическое

arithmetic progression - арифметическаяпрогрессия

associative law - сочетательный (ассоциативный) закон

associative property - сочетательное (ассоциативное) свойство

assumption - предположение

asymmetric(al) - асимметричный

asymmetry - aсимметрия

asymptote - асимптота

asymptotes of a hyperbola - асимптоты гиперболы

average - среднее значениe

average value - усреднение, среднее значение

axiom - aксиома

axis - ось


back-substitution - обратная подстановка

bar - дробная черта, черта

base - база, базис

base angle {of a triangle} - угол при основании треугольника

base vector - базисный вектор

basis - база, базис

billion - биллион

binary - бинарный

binomial - двучлен (бином)

binomial coefficient - биноминальный коэффициент

binomial expansion - разложение

binomial formula - формула бинома

biquadratic equation - биквадратное уравнение

bisector - биссектриса

bisectrix - биссектриса

bounded interval - ограниченный интервал

braces - фигурные скобки

brackets - квадратные скобки

branch - ветвь

bridging - перенос

brocken line - ломаная линия


calculus - математический анализ, исчисление

cancel - сокращать

canonical - канонический

Cartesian coordinate system - декартова система координат

Cartesian coordinates - декартовыкоординаты

central angle - центральныйугол

central conic - центральное коническое сечение

central symmetry - центральная симметрия

centre - центр

centre of the escribed circle - центрвневписаннойокружности

center - центр

change of variable - заменапеременной

chord - хорда

circle - окружность, круг

circumcenter - центр описанной окружности

circumscribed figure - описанная фигура

closed - замкнутый

closed interval - замкнутый интервал

coefficient - коэффициент

coincident - совпадающий

collinearity - коллинеарность

combination - комбинация

combine similar terms - приведение подобных членов

common denominator - общий знаменатель

common difference - разность арифметической прогрессии

common divisor - общий делитель

common factor - общий делитель

common fraction - арифметическая (простая) дробь

common logs - десятичный логарифм

common multiple - общее кратное

common ratio - частное геометрической прогрессии

commutative law - переместительный (коммутативный) закон

comparation - сравнение

complementary angle - дополнительныйугол {до 90 o}

complete induction - полнаяиндукция

complete solution - полноерешение

complex number - комплексноечисло

computable - вычислимый

computation - вычисление

concave - вогнутый

concave curve - вогнутаякривая

concave function - вогнутаяфункция

concentric circles - концентрическиеокружности

condition - условие

cone - конус

congruence - конгруэнтность

congruent angles - равныеуглы

congruent figures - равныефигуры

congruent polygons - равныемногоугольники

congruent segments - равныеотрезки

conic - коническое сечение

conic section - коническое сечение

conjugate - сопряженный

conjugate angle - дополнительный угол до 360o

conjugate roots - сопряженные корни

consecutive integers - последовательные целые числа

constant - константа

continuity - непрерывность

continuous function - непрерывная функция

convex - выпуклый

convex curve - выпуклая кривая

convex polygon - выпуклый многоугольник

convexity - выпуклость

coordinate - координата

coordinate axis - координатнаяось

coordinate system - системакоординат

coplanar - компланарный

coplanar vector - компланарныйвектор

coprime numbers - взаимнопростыечисла

corollary - следствие

corresponding angles - соответственные углы

count - подсчитать, считать

criterion - критерий

criterion for divisibility - признакделимости

cross-product - векторное (внешнее) произведение

cube - куб

cubic - кубическая кривая

cubic curve - кубическая кривая

curve - кривая

cut - сечение

cylinder - цилиндр


data - данные

decimal - десятичный

decimal fraction - десятичная дробь

decimal number - десятичное число

decision - решение

decomposition - разложение

decomposition of a fraction - разложениедроби

decrease - убывать

decreasing function - убывающаяфункция

deduction - дедукция

define - определять

definition - определение

degenerate - вырожденный

degenerate conic - вырожденное коническое сечение

degree - степень

degree of a polinomial - степеньмногочлена

denominator - знаменатель

dependent - зависимый

derivative - производная

derivative at a point - производнаявточке

determinant - определитель

determine - определять

deviation - отклонение

diagonal - диагональ

diagonal element - диагональный элемент

diagonal matrix - диагональная матрица

diameter - диаметр

diametrically opposite point - диаметрально противоположная точка

difference - разность

differentiability - дифференцируемость

differentiable function - дифференцируемая функция

differential of area - элементплощади

digit - цифра

dihedral angle - двугранныйугол

dilatation - растяжение

dimension - размерность

direction - направление

direction cosine - направляющий косинус

directly proportional - прямопропорциональный

discontinuous - разрывный

discontinuous function - разрывнаяфункция

discriminant - дискриминант

disposition - расположение

distance - расстояние

distinct - различный

distributive law - распределительный (дистибутивный) закон

dividend - делимое

divisable {by} - делимый

division - деление

division algorithm - aлгоритм деления

divisor - делитель

domain - область; источник

domain of definition - область определения

dot - точка

dot product - скалярное произведение

dotted line - пунктирная линия

double root - двойной корень

dual - двойственный (дуальный)

duality principle - принцип двойственности


edge - ребро

element - элемент

element of area - элементплощади

elimination - исключение

elimination by substitution - исключение посредством подстановки

elimination method - методисключения

ellipse - эллипс

empty set - пустое множество

equation - уравнение

equation of a straight line - уравнениепрямой

equilateral - равносторонний

equilateral polygon - правильный многоугольник

equilateral triangle - равносторонний треугольник

equivalent - равносильный (эквивалентный)

equivalent figure - конгруэнтнаяфигура

error - ошибка

escribed - описанный, вневписанный

essential - существенный

estimation - оценка

Euclidean algorithm - алгоритм Eвклида

Euclidean geometry - евклидова геометрия

Euclidean space - евклидово пространство

evaluation - вычисление

evaluation of determinant - вычисление определителя

even - четный

even function - четнаяфункция

even number - четноечисло

everywhere defined - всюду определенный

exact - точный

exact division - деление без остатка

exact solution - точное решение

example - пример

excentre - центр вневписанной окружности

exclusion - исключение

existential quantifier - квантор существования

expansion - разложение

expansion of a determinant - разложение определителя

explementary angle - дополнительный угол до 360o

exponent - показатель, экспонент

exponential - показательный, экспоненциальныйы

exponential equation - показательное уравнение

expression - выражение

exterior angle {of a triangle} - внешний угол {треугольника}

extremal - экстремальный

extremum point - экстремальная точка


factor - множитель

factor theorem - теоремаБезу

factoring - разложение

factorization - разложение на множители

family - семейство

field - поле

first derivative - первая производная

first-order equation - уравнение первого порядка

flow chart - блок-схема

flux - поток

focal point - фокальная точка

focus - фокус

foot {of a perpendicular} - основание {перпендикуляра}

formula - формула

fraction - дробь

function - функция

function of a complex variable - функциякомплексной переменной

function of a single variable - функцияодной переменной

function of several variables - функция несколько независимых переменных

fundamental - основной

fundamental theorem of arithmetic - основнаятеорема арифметики


general - общий

general form - общийвид

general solution - общеерешение

general term - общийчлен

geometric average - среднеегеометрическое

geometric locus - геометрическоеместоточки

geometric mean - среднеегеометрическое

geometric progression - геометрическая прогрессия

geometry - геометрия

grade - степень

greatest common divisor - наибольший общий делитель

greatest common factor - наименьшее общее кратное


half-angle formulas - формулы половинного угла

halve - делить пополам

height - высота

hemisphere - полусефра, полушар

hexagon - шестиугольник

hexaeder - гексаэдр, шестигранник

hexahedron - гексаэдр, шестигранник

hill climbing - поиск экстремума

homogeneous - однородный

homogeneous equation - однородное уравнение

homogeneous system - однородная система

horizontal - горизонтальный

horizontal axis - горизонтальная ось

Horner's scheme - схема Горнера

hyperbola - гипербола

hyperbolic - гиперболический

hypotenuse - гипотенуза

hypothesis - гипотеза


identity - тождество

if and only if - тогдаитолько тогда

image - образ

implication - импликация

improperfraction - неправильная дробь

incenter - центр вписанной окружности

incircle - вписанная окружность

include - включать

inclusion - включение, вложение

inconsistent - несовместимый, противоречивый

incorrect - ошибочный, неточный

increase - расти

increment - приращение

indefinite - неопределенный

independent - независимый

independent variable - независимая переменная

indeterminancy - неопределенность

induction - индукция

inequality - неравенство

infinite - бесконечный

infinite decimal fraction - бесконечная десятичная дробь

inflexion - перегиб

inhomogeneous - неоднородный

initial - начальный

initial condition - начальное условие

initial value - начальное значение

inscribe - вписать

inscribed angle - вписанный угол

inscribed circle - вписанная окружность

inscribed polygon - вписанный многоугольник

integernumber - целое число

integral - интеграл

integral curve - интегральная кривая

integrand - подинтегральное выражение

integration by parts - интегрирование по частям

integration constant - постоянная интегрирования

inter-stage function - ступенчатая функция

intercept - отрезок; отрезок отсекаемый от оси

intercept theorem - теорема Фалеса

interdependency - взаимозависимость

interior angle - внутренний угол

intersection - пересечение

interval - интервал

inverse - обратно

inversely proportional - обратно пропорциональный

irrational number - иррациональное число

irreductibility - неприводимость

isosceles triangle - равнобедренный треугольник


jump - скачок

jump function - ступенчатая функция


kilogram(me) - килограмм

kilometre - километр

known - известный


law - закон

law of composition - закон композиции

law of sines - теоремасинусов

law of the excluded middle - законисключенного третьего

least common denominator - наименьший общийд елитель

least common multiple - наименьшее общее кратноe

leg - боковаясторона

Leibniz rule - формула Лейбница

lemma - лемма

length - длина

like denominators - одинаковые знаменатели

like signs - одинаковые знаки

limit - предел

limit value - предельное значение

limits of integration - пределы интегрирования

line - прямая

line segment - отрезок

linear - линейный

linear equation - линейное уравнение

linear function - линейная функция

linear independency - линейная независимость

linearity - линейность

local - локальный

logarithm - логарифм

lower limit - нижний предел

lowest common denominator - наименьший общий знаменатель

lowest common multiple - наименьшее общее кратное

lozenge - ромб


magnitude - величина

main diagonal - главная диагональ

major axis - главная ось

many-variable system - система с несколькими переменными

map - отображение

mapping - отображение

meter - метр

mathematical induction - математическая (полная) индукция

mathematics - математика

matrix - матрица

matrix of the transformation - матрица преобразования

maximum - максимум

mean - среднееарифметическое

mean proportional - среднее геометрическое

measurable - измеримый

measure - мера

median {of a triangle} - медиана

member {of a set} - элемент {множества}

minimum - минимум

minuend - уменьшаемое

minus {sign} - знакминус

module - модуль

monom - одночлен (моном)

monotone decreasing function - монотонно убывающая функция

monotone increasing function - монотонно возрастающая функция

monotonic function - монотонная функция

monotonous - монотонный

multiple - многократный; кратное

multiplex - многократный

multiplicand - множимое

multiplication - умножение

multiplier - множитель

multiply - множить

mutually - взаимно

mutually disjoint - взаимно (попарно) непересекающиеся


natural logarithm - натуральный логарифм

natural number - натуральное число

necessary and sufficient condition - необходимое и достаточное условие

negative - отрицательный

negligible - пренебрегаемый

node - узел

non-decreasing - неуменьшающийся

non-degnerate - невырожденный

non-degenerate conic - невырожденное коническое сечение

non-degenerate conic section - невырожденное коническое сечение

non-linear - нелинейный

non-linear equation - нелинейное уравнение

non-orthogonal coordinate system - неортогональная координатная система

non-periodic - непериодический

non-symmetric - несимметричный

non-terminating decimal - бесконечная десятичная дробь

non-trivial solution - нетривиальное (ненулевое) решение

non-zero solution - нетривиальное (ненулевое) решение

normal - нормаль

normal to the surface - нормаль к поверхности

normal vector - вектор нормали

null-vector - нулевой вектор

null-matrix - нулевая матрица

null-set - нуль-множество, пустое множество

number - число

number line - числовая прямая

numerator - числитель


oblique - oblic

obtuse angle - тупойугол

obtuse triangle - тупоугольный треугольник

octagon - восьмиугольник

odd - нечетный

odd-function - нечетая функция

one-to-one - взаимно-однозначный

open interval - открытый интервал

opposite interior angles - внутренние накрест лежащие углы

order - порядок

order of derivative - порядок производной

order of equation - порядок уравнения

ordered pair - упорядоченная пара

ordinal number - порядковый номер

ordinate - ордината

origin {of coordinates} - начало {координат}

orthogonal base - ортогональный базис

orthogonal coordnate system - ортогональная система координат

orthonormal basis - ортонормированный базис

oval - oвал


pair - пара

parabola - парабола

parabolic - параболический

parallel - параллельный

parallelepiped - параллелепипед

parallelogram - параллелограмм

parallelogram law - закон параллелограмма

parallelogramrule - закон параллелограмма

parameter - параметр

parametricform - параметрическая форма

parentheses - круглые скобки

partialfraction - элементарная дробь

partial-fractionexpansion - разложение правильной дроби на простейшие

pencil - пучок

pencil of lines - пучокпрямых

pentagon - пятиугольник

per cent - процент

perimeter - периметр

period - период

periodic decimal fraction - периодическая десятичная дробь

periodic function - периодическая функция

periodic solution - периодическое решение

permissible solution - допустимоерешение

perpendicular - перпендикуляр

pivot - ось вращения, центр вращения

plane - плоскость

plane geometry - планиметрия

planimetry - планиметрия

plus sign - знак плюс

point - точка

point of discontinuity - точкаразрыва

point of inflexion - точкаперегиба

polygon - многоугольник

polyhedron - многогранник

polynomial - многочлен

positive - положительный

possibility - возможность

power - показатель степени

pre-image - прообраз

preceding - предыдущий

prime factorization - разложение на простые множители

prime number - простое число

pimitive - первообразная функция

principal - главный

principal axis - главнаяось

principal diagonal - главная диагональ

principle of complete induction - метод полной индукции

prism - призма

product - произведение

progression - прогрессия

projection - проекция

proof - доказательство

proper factor - собственный делитель

proper fraction - дробь

property - свойство

proportion - пропорция

proposition - предложение

prove - доказывать

pyramid - пирамида

Pythagorean theorem - теорема Пифагора


quadrate - квадрат

quadratic - квадратный

quadratic equation - квадратное уравнение

quadratic formula - формула корней квадратного уравнения

quantifier - квантор

quotient - частное


radian - радиан

radical - радикал, знак корня

radical sign - радикал, знак корня

radius - радиус

radius vector - радиус-вектор

raise to a power - возводить в степень

range - область, множество значений

rank of a matrix - рангматрицы

ratio - частное, отношение

rational - рациональный

rational function - рациональная функция

rational number - рациональное число

ray - полуось

real - действительный, вещественный

real number - действительное (вещественное) число

reciprocal matrix - обратная матрица

rectangle - прямоугольник

rectangular coordonate system - прямоугольная система координат

reduce - приводить, сокращать

reducible - приводимый

regular polygon - правильный многоугольник

relation - отношение

relative - относительный

relatively prime numbers - взаимно простые числа

remainder - остаток

repeated root - кратный корень

replace - подставлять, заменять

represent - представлять

rest - остаток

restriction - ограничение, рестрикция

rhomb - ромб

rhombus - ромб

right angle - прямой угол

right triangle - прямоугольный треугольник

root - корень

rotation - вращение

round - округлять

rounding error - ошибка округления

rule - правило


same denominators - одинаковые знаменатели

satisfy - удовлетворять

scalar - скаляр

scalene triangle - разносторонний треугольник

secant - секущая

sector of a circle - секторкруга

segment - отрезок, сегмент

semi-circle - полукруг

semiclosed interval - полузамкнутый интервал

set - множество

set theory - теориямножеств

side {of an angle} - сторона {угла}

sign - знак

signum function - сигнум-функция

similar fractions - дроби с равными знаменателями

similar polygons - подобные многоугольники

similar terms - подобные члены

similar triangle - подобный треугольник

similarity - подобие

similitude - подобие

simple - простой

simple root - простой (однократный) корень

simplification - упрощение

sine curve - синусоида

sine rule - теоремасинусов

single - один, отдельный, единственный

single root - простой (однократный) корень

skew lines - скрещивающиеся прямые

slope - наклон; угловой коэффициент

slope angle - угол наклона

slope formula - формула углового коэффициента

solution {of a problem} - решение {задачи}

solution set - множество решений

solve - решать

space - пространство

speed - скорость

sphere - сфера, шар

square - квадрат; возводить в квадрат

square brackets - квадратные скобки

square root - квадратный корень

standard form - общий вид, стандартная форма

statement - утверждение, высказывание

step function - ступенчатая функция

straight - прямой, правый

straight angle - развернутый угол

straight-line - прямая линия

straight-line segment - отрезок прямой, отрезок

stretching - растяжение

strict - строгий

strongly monotonic - строго монотонный

subset - подмножество

substitution - подстановка

subtraction - вычитание

subtrahend - вычитаемое

sum - сумма

summand - слагаемое

supplementary angles - дополнительные углы

surface - поверхность

surface area - площадь поверхности

surface element - элемент площади {поверхности}

surface of revolution - поверхностьвращения

symbol - символ

symmetric - симметричный

symmetric function - симметричная (четная) функция

synthetic division - схема Горнера

system - система

system of linear equations - системалинейных уравнений


tangent - касательная; тангенс, функция тангенс

tangent line - касательная

tangent plane - касательная плоскость

term - член

term of a fraction - числитель дроби

terminating decimal fraction - конечная десятичная дробь

tetragon - четырехугольник

tetrahedron - четырехгранник, тетраэдр

theorem - теорема

theory - теория

transcendental number - трансцендентное число

transform - преобразовать

transform of coordinates - преобразование координат

transitivity - транзитивность

translation - трансляция

trapezium - трапеция

trapezoid - трапеция

triangle - треугольник

triangular - треугольный

trigonometric - тригонометрический

trigonometric function - тригонометрическая функция

trigonometry - тригонометрия

trisection of the angle - трисекция угла

truth - истинность


unambiguous - недвусмысленный, однозначный

unbounded - неограниченный

uncertainty - недостоверность, неопределенность

undefined - неопределенный (недефинированный)

undetermined - неопределенный

unequal - неравный

union - объединение

unique solution - единственное решение

uniqueness - единственность

unit - единица

unit circle - единичная окружность

unit tangent vector - касательный единичный вектор

unit vector - единичный вектор

universal quantifier - квантор общности

universal set - универсальное множество

unknown - неизвестное

unlike denominators - неодинаковые знаменатели

unsymmetric - несимметричный


valid - справедливый

value - величина, стоимость

vanish - исчезать, обратиться в нуль

variable - переменная

vector - вектор

vector product - векторное (внешнее) произведение

velocity - скорость

verify - проверять

vertex - вершина

vertex angles - вертикальные углы

vertical - вертикаль; вертикальный

vertical axis - вертикальная ось

vice versa - наоборот, обратно

vinculum - дробная черта

volume - объем


way - путь

well-defined - вполне определенный

whole - целый


x-axis - ось x

x-intercept - отрезок на оси x

xy-plane - плоскость xOy


y-axis - ось y


z-axis - ось z

zero - нуль

zero solution - нулевое решение