12B GAC004 Math Terminology Notebook by Matthew Bell

Roy

2017-09-14 10:18:57 UTC

words :binomi
A polynomial with two terms
e.g. 3x² + 2

Chris

2017-09-14 11:10:46 UTC

1.Subject: The solution to the optimization problem should satisfy the constraint.
Example: g(x, y)=c
2.Formula: A special type of equation that shows the relationship between different variables.
Example: V = l × w × h
3.Greater than: The symbol > means greater than (the symbol < means less than).
Example: 5 > 3 shows that 5 is greater than 3
4.Less than: The symbol < means less than (the symbol > means greater than).
Example: 4 < 9 shows that 4 is less than 9

Ricky

2017-09-14 11:12:07 UTC

lowest common multiple:
The smallest positive number that is a multiple of two or more numbers.
e.g:the Least Common Multiple of 3 and 5 is 15, because 15 is a multiple of 3 and also a multiple of 5. Other common multiples include 30 and 45, etc, but they are not the smallest

consecutive:Numbers which follow each other in order, without gaps, from smallest to largest.
e.g:12, 13, 14 and 15 are consecutive numbers.
22, 24, 26 and 28 are consecutive even numbers.

magnitude:
The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind.
e.g:

parabola:A parabola is a curve where any point is at an equal distance from a fixed point, and a fixed straight line.
e.g:If one introduces cartesian coordinates, such that

and the directrix has the equation

one gets for a point

from

the equation

null factor law:If the product of any two numbers is zero, then one or both of the numbers is zero.
e.g:ab = 0, then a = 0 or b = 0 (which includes the possibility that a = b = 0).

This is called the Null Factor Law

ruihaostevensun — 2017-09-14 11:14:33 UTC

John

2017-09-14 11:20:29 UTC

index laws
Indices are a useful way of more simply expressing large numbers.

Example:

power
The power of a number says how many times to use the number in a multiplication.

Example: 82 = 8 × 8 = 64

base
The number that is going to be raised to a power.

Example: in 82, 8 is the base

basic numeral
A basic numeral is an induce ily thx

Example:0 1 2 3 4 5 6 7 8 and 9

inverse
Inverse means the opposite in effect.

Example: 20 + 9 = 29 can be reversed by 29 − 9 = 20

Steven

ruihaostevensun — 2017-09-14 11:34:57 UTC

word： leading coefficient

definition： The coefficient of a polynomial's leading term.

e.g.5 is the leading coefficient of 5x4 – 6x3 + 4x – 12.

Justin

2017-09-14 11:40:24 UTC

Expand

Definition: become larger in size or volume or quantity

Example:5^2------>25^2

factorise

Definition:one of two or more integers that can be exactly divided into another integer

Example:2x 2=4, 2x3=6, 2x4=8

Substitute

Definition:instead of

Example:log

Variable

Definition:a symbol (like x or y) that is used in mathematical or logical expressions to represent a variable quantity

Example:2x=3y

Equation

Definition:a mathematical statement that two expressions are equal

Example: 1+1=2

Edward

2017-09-14 11:47:41 UTC

subject
Definition: It is a way to specify constraints.

Example: To put it very simply, the problem "do 'X' subject to 'Y'" means that, you have to do "X" (whatever X is), but you have to do it such that "Y" is also satisfied in the process.

formula
Definition: a group of mathematical symbols that express a relationship or that are used to solve a problem.

Example: y=kx+b

greater than
Definition: The symbol > means greater than

Example: 6>2

less than
Definition: the symbol < means less than.

Example: 2<6

binomial
Definition: A polynomial equation with two terms usually joined by a plus or minus sign

Example: 3x + 4

Grace

2017-09-15 08:47:09 UTC

inequation
Definition：unequal formula
x+5<7
unknown
defination：a variable whose values are solutions of an equation
X
linear
Definition：measured lengthwise

non-linear
Definition
：designating or involving an equation whose terms are not of the first degree

absolute value:
Defintion :numerical value regardless of its sign

Jack

2017-09-19 00:09:37 UTC

numerals: Numerals are written symbols used to represent numbers
For example：6

pronumerals: numbers in the formula is unknown.
For example: 6x=12

terms: It is easy to address, memorize, explain, use, and give the name of a part of the formula, the mathematical term general.
For example:

 1+x+xy+xyz

like terms:are algebraic terms having the same variables operating in the same way.
For example: 2xy

identical:exactly alike
For example：r4=3

Madison

2017-09-19 00:17:03 UTC

lowest terms

Definition:The lowest number that a numerator and denominator becomes when it is reduced by its greatest common factor.
Example:4/6->2/3

expression
Definition:Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.

Example: 2×3 is an expression

simplify
Definition:To reduce a fraction to its lowest terms by canceling to the lowest common factor for both numerator and denominator or to condense an algebraic expression by grouping and combining similar terms.

Example:
Start with: 5x + x − 3
Combine like terms: 6x − 3
It is now a little easier to use.

index
Definition:The index of a number says how many times to use the number in a multiplication.

It is written as a small number to the right and above the base number.

Example:
8² = 8 × 8 = 64

index form
Definition:Index form is where a number is expressed using exponents - one number to the power of another.

Example:2 x 2 x 2 x 2 x 2 is the same as 2 to the power of

John

2017-09-19 01:03:40 UTC

Hyperbola
The hyperbola is an open curve (has no ends).
ex:9x² - 4y² - 18x + 32 y - 91 = 0.

Origin
The starting point.

In the figure, x and y axis are intersecting at 'O'.
This O is called the origin of the graph. Its coordinates are (0, 0).

Discriminant
The Discriminant of an equation gives an idea of the number of roots and the nature of roots of the equation.

ex: If ax² + bx + c = 0 is a quadratic equation, then the Discriminant of the equation, i.e. D = b² - 4ac.

minimum
The smallest value.
ex.The minimum of {14, 4, 16, 12} is 4.

Modelling
Something that is made to be like another thing.
ex.A "Mathematical Model" tries to copy how a real world thing works using equations. It is not exactly the same, but can be useful: we can use the equations to try new things, such as predict what happens when sizes, temperatures, prices, etc change.

Edward

2017-09-19 07:15:55 UTC

Cartesian plane: a plane in which all points can be described in Cartesian coordinates.

general form: the form that use to solve the graph problem
Example: Ax + By + C = 0.

axes: A fixed reference line for the measurement of coordinates.

point: a primitive notion upon which the geometry is built.

Collinear points: When three or more points lie on a straight line.
(Two points are always in a line.)
These points are all collinear

Grace

2017-09-19 07:23:06 UTC

slope
Definition：the property possessed by a line or surface that departs from the horizontal
run
Definition：a regular trip
intersection
Definition：a point where lines intersect

functions
Definition：

even functions

Jack

2017-09-19 07:24:09 UTC

plot: A point that is drawn on to a Cartesian number plane is referred to as a plot
axis of symmetry: A line through a shape so that each side is a mirror image.
For example:When the shape is folded in half along the axis of symmetry, then the two halves match up.
maximum:The largest value
For example: The maximum of {14, 4, 16, 12} is 16
linear: A linear process or development is one in which something changes or progresses straight from one stage to another, and has a starting point and an ending point.
imaginary roots:When I tried to calculate the square root of

on my calculator, it gave me an error.

Madison

2017-09-19 07:26:33 UTC

Even functions
Definition:A function with a graph that is symmetric with respect to the y-axis. A function is even if and only if f(–x) = f(x).

Example: f(-x)=f(x)

Ordered pairs
Definition:A pair of numbers used to locate a point on a coordinate plane is called an ordered pair. An ordered pair is written in the form (x, y) where x is the x-coordinate and y is the y-coordinate.

Example:
the ordered pair (3, 4) is found in the coordinate system when you move 3 steps to the right on the x-axis and 4 steps upwards on the y-axis.

Domain:
Definition:All the values that go into a function
The output values are called the range.
Domain → Function → Range
Example:
when the function f(x) = x² is given the values x = {1,2,3,...} then {1,2,3,...} is the domain.

cubic
Definition:A solid with six congruent square faces. A regular hexahedron

asymptotes
Definition:A line that a curve approaches, as it heads towards infinity.

Justin

2017-09-19 07:36:21 UTC

interval
odd functions
real numbers
parabola
independent variable

2017-09-19 07:36:39 UTC

John

2017-09-19 07:48:10 UTC

adjacent side
The adjacent side is the non-hypotenuse side that is next to a given angle.
ex:Angle ABC is adjacent to angle CBD

opposite side
The opposite side is across from a given angle.
ex:

hypotenuse
The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.

cosecant
In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. In a formula, it is abbreviated to just 'csc'.

csc 30 = 2.000 | Means: The cosecant of 30 degrees is 2.000

horizontal
a horizontal line is one which runs from left to right across the page. It comes from the word 'horizon', in the sense that horizontal lines are parallel to the horizon.

John

2017-09-19 07:49:06 UTC

angle
an angle is the figure formed by two rays
The amount of turn between two straight lines that have a common end point

vertex
A point where two or more line segments meet. A corner.

ex: any corner of a pentagon (a plane shape)

acute angle
An Acute Angle is less than 90°

obtuse angle
An Obtuse Angle is more than 90° but less than 180°

reflex angle
A Reflex Angle is more than 180° but less than 360°

depth
the depth of a box is the horizontal distance from front to back

volume
The amount of 3-dimensional space an object occupies. Capacity.

ex: the volume is 4×5×10 = 200 units³

dimensional
A measurement of length in one direction

ex: width, depth and height are dimensions.

surface area

The total area of the surface of a three-dimensional object.

ex: the surface area of a cube is the area of all 6 faces added together.

John

2017-09-19 07:50:29 UTC

exponent
The exponent of a number says how many times to use the number in a multiplication.

In 82 the "2" says to use 8 twice in a multiplication,
so 82 = 8 × 8 = 64

roy

2017-09-19 07:52:42 UTC

word: gradient
How steep a straight line is.
e.g. the gradient is 3/5 = 0.6
word: sketch
a rough drawing representing the chief features of an object or scene
e.g. b:a
word:transposing form
e.g.

word: rise
gives us the slope of the line.
e.g.

word:midpoint
The middle of. The point halfway along.

Edward

2017-09-19 07:52:52 UTC

vertical: perpendicular to a horizontal line

reference angle: the smallest angle between the terminal side and the x-axis.

inclined: This angle is always between 0° and 180°, and is measured counterclockwise from the part of the x-axis to the right of the line.

Example:

line of sight: the straight path between a transmitting antenna and a receiving antenna when unobstructed by the horizon

Sector: The part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

Edward

2017-09-19 07:54:39 UTC

revolution: how many complete turns occur every minute.
Example:

Complementary: Two angles are said to be complementary if their sum is 90^o. This makes them add up to a right angle.

Example:

Supplementary: Two Angles are Supplementary when they add up to 180 degrees.
Example:

adjacent: Two angles that share a common side and a common vertex, but do not overlap

Vertically: one which runs from up and down the page.
Example:

Isosceles: a triangle that has two sides of equal length.
Equilateral: A triangle with all three sides of equal length.
Scalene: a triangle that has three unequal sides
Circle: the locus of all points equidistant from a central point.
Semicircle: a one-dimensional locus of points that forms half of a circle.
Quadrilateral: a polygon with four edges (or sides) and four vertices or corners.

Zoe

2017-09-19 07:55:40 UTC

dependent variable
definition: A variable that depends on one or more other variables
example:

element
Definition: In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
Example:

range
Definition：The difference between the lowest and highest values.
Example:

quartic
Definition: In mathematics, the term quartic describes something that pertains to the "fourth order"
Example:

region
definition:The set of all possible input values (commonly the "x" variable), which produce a valid output from a particular function.
Example:

Edward

2017-09-19 07:56:13 UTC

change of base law: A formula that allows you to rewrite a logarithm in terms of logs written with another base.
Example: Assume that x, a, and b are all positive. Also assume that a ≠ 1, b ≠ 1.

Change of base formula:

roy

2017-09-19 08:04:18 UTC

sine: the trigonometric function that is equal to the ratio of the side opposite a given angle
e.g.

cosine: e.g.

adjacent over to the hypotenuse
tangent:
opposite over to adjacent

Roy

2017-09-19 08:18:39 UTC

word:circumference
a circle is the distance around the circle

word: square metre
It is the area of a square whose sides measure exactly one metre.

e.g.Reynaldo's painting was huge: more than 10 square meters.

word: segment

e.g. it got two points not like the bear
word:rhombus
A 4-sided flat shape with straight sides where all sides have equal length.
word: sector
the area between two radiuses and the connecting arc of a circle.

word: rectangle
a quadrilateral with four right angles

word: square
is a regular quadrilateral, which means that it has four equal sides and four equal angles

word: units
Used to show the "ones" place value
327 has three hundreds, two tens and 7 units
word: ellipse
s a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve
e.g. a generalization of a circle, which is a special type of an ellipse having both focal points at the same location

Chris

2017-09-19 08:38:03 UTC

1. Modeling: a description of a system using mathematical concepts and language.
Example: Volume = l × w × h, so there has a (very simple) mathematical model of the space in that box.
2.Vertex: A point where two or more line segments meet.
Example: • any corner of a pentagon (a plane shape)
• any corner of a tetrahedron (a solid)
3.Angle of inclination: The angle subtended by the altitude of the triangle.
Example: The shadow of a 100m long pole is of 10m. Then what will be the angle of inclination? To solve such a problem we must first draw a rough sketch. Let AB = height of the pole = 100, BC = length of shadow = 10. Now, angle of inclination is C. Hence,

tanC tanC = ABBCABBC

tanC tanC = 1001010010

C = tan−110

4.Intercept: The point at which a curve intersects an axis
Example: In the figure, the line cuts the x-axis at (- 2, 0) and y-axis at (0, - 3). So, x-intercept is - 2 and y-intercept is - 3.
5.Coordinates: A set of values that show an exact position.
Example: The point (12,5) is 12 units along, and 5 units up.

Zoe

2017-09-19 11:03:06 UTC

Completing the Square
Definition: In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form.
Example:

Zoe

2017-09-19 11:13:56 UTC

angle of depression
Definition: Angle of depression can be explained as the angle between the horizontal line and the line joining the viewer
Example:

angle of elevation
Definition: The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye
Example:

tangent
Definition: tangent is a ratio between opposite and adjacent.
Example:

Jack

2017-09-19 11:15:58 UTC

Quadrant:Any of the 4 areas made when we divide up a plane by an x and y axis (as shown)
For example They are usually numbered I, II, III and IV
compass bearings:a bearing relative to north as indicated by a magnetic compass
included angle:The angle between two sides.
For example:

Ricky

2017-09-19 11:16:34 UTC

radian:
The radian is the standard unit of angular measure, used in many areas of mathematics.
e.g: 1 Radian is about 57.2958
Unit circle:
he "Unit Circle" is a circle with a radius of 1.
e.g: picture
Minor segment:

ROY

2017-09-19 11:16:43 UTC

word:inverse function
is a function that "reverses" another function
e.g.

word:natural logarithm
a number is its logarithm to the base of the mathematical constant e , where e is an irrational and transcendental number
e.g 2.718281828459

Justin

2017-09-19 11:17:17 UTC

1.The upper right is called the first quadrant, the left is called the second quadrant, the lower left is called the third quadrant, the lower right is called the fourth quadrant. The points on the axes are not in any quadrant.

2.compass bearings

3.included angle
An included angle is the angle between two sides of a triangle
.

Madison

2017-09-19 11:18:47 UTC

Heading
Definition:
The position of a digit in a number is very important. A digit's value depends on its position in the number.
Use place value headings to work out the value of each digit in a number.

Example:
The number 351489.3 is three hundred and fifty-one thousand, four hundred and eighty nine, and three tenths.

Chord
Definition:
A line that links two points on a circle or curve.

Example:
Below is a formula for the length of a chord if you know the radius and central angle.

Chord length=2r sin(c/2)

Reciprocal
Defintion:
To find the reciprocal of a fraction, simply exchange the top and bottom of the fraction (numerator and denominator)

Example:
he reciprocal of 4 is one quarter:
The reciprocal of 4 is 1/4 which is equal to 0.25

Grace

2017-09-19 11:21:14 UTC

secant
defintion ： a straight line that intersects a curve at two or more points

function sol=secant(fn,a,b,tol)
x0 = a; x1 = b; fa = feval(fn, x0); fb = feval(fn, x1);
while abs(x1-old)> tol
new = x1 − fb ∗ (x1 − x0)/(fb − fa);
x0 = x1; fa = fb; x1 == new; fb = feval(fn, new);
end; sol=new

cotangent
defintion ：ratio of the adjacent to the opposite side of a right-angled triangle
beta=(1.05:.1:20); M=(1.05:.1:20); [B,M]=meshgrid(beta,M); theta=atand((2.*cot(beta)).*(((M.^2).*(sind(beta-1).^2))./((M.^2).*(1.4+cosd(2.*beta))+2))); contour(theta,B,M)

clockwise ：in the same direction as the rotating hands of a clock

angles = atand2d((y-yCenter) ./ (x-xCenter));

Zoe

2017-09-19 11:22:42 UTC

boundary
Definition: A line or border around the outside of a shape. It defines the space or area.
Example:

perimeter
Definition:Perimeter is the distance around a two-dimensional shape
Example:

area
Definition: Area is the size of a surface
Example:

region
Definition: The term Regions is a space in the shape that either is separated by lines or is surrounded by lines it also includes the outside of the shape.
Example:

triangle
Definition: A triangle is a polygon with three edges and three vertices.
Example:

edge
Definition:An edge is a line segment that joins two vertices (on the boundary or where faces meet)
Example:

face
Definition: Any of the individual surfaces of a solid object
Example:

prism
Definiton: In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy of the first, and n other faces
Example:

Jack

2017-09-19 11:23:00 UTC

hectare: A hectare is a unit of area equal to 10,000 square meters. Usually used to measure land.
For example:1 ha = 2.47 Acres approximately.
cubic: having the shape of a cube.
centimetre: A centimeter is a measure of length.
For example: 1 inch = 2.54 cm
subtended: The angle made by a line, arc or object.
For example: Here the Subtended Angle of the tree (from the person's point of view) is 22°

Justin

2017-09-19 11:35:35 UTC

1.parallel
extending in the same direction, equidistant at all points, and never converging or diverging

2.exterior angle
an angle formed outside parallel lines by a third line that intersects them.

3.right angle

the angle formed by two radii of a circle that are drawn to the extremities of an arc equal to one quarter of the circle; the angle formed by two perpendicular lines that intersect; an angle of 90°

4.perpendicular
d down; upright

5.edge

a line or border at which a surface terminates

6.face
in any direction

7.prism
a transparent block of glass that breaks up white light into ifferent colours

8.cylinder
a shape,object or container with circular ends and long stright sides.

steven-sun

2017-09-19 11:37:11 UTC

1)regions: A region is an area. A region can be geographic.

Example: at Uploaded with Pad let

2)convention: A statistic. Used to count official data

Example: at Uploaded with Pad let

3)concave up/down :Concave up/down: the data is going up or down

Example: at Uploaded with Pad let

4)turning point: point at which the derivative changes sign – see stationary point in mathematics

Example: For the graph of a function of one variable, this corresponds to a point on the graph where the tangent is parallel to the x-axis. For function of two variables, this corresponds to a point on the graph where the tangent plane is parallel to the xy plane.

5)function notation: is the way a function is written. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation.

Example:
The most popular function notation is f (x) which is read "f of x".

6)distinct: In tables, duplicates may be included
Example:Editing an Excel document often encounters the need to find duplicate values and delete them

Steven-sun

2017-09-19 11:39:24 UTC

1)Three figure bearings :You radio for help and are told to turn 125° clockwise. But 125° from where? Which direction should you be facing in the first place? One sensible idea is to start by facing north. This is the way that 3-figure bearings work.

2)true bearings :The clockwise angle between a direction line and a meridian line

Example： that is referenced to the geographic North Pole.

3)arc: Any portion of a circle or the angle that it makes.

Example：The electrical discharge between two electrodes. When the electrodes are surrounded by gas in a lamp, they become a bright, economical light source.

Steven-sun

2017-09-19 11:40:20 UTC

1)opposite The opposite; Relative; The opposite; [mathematics] (top, edge, etc.);

2)corresponding: In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two other lines in the Euclidean plane are parallel.

Example:The intersections of a transversal with two lines create various types of pairs of angles: consecutive interior angles, corresponding angles, and alternate angles.

3)straight angle : In planar geometry, an angle is the figure formed by two rays.

Example:the sides of the angle, sharing a common endpoint, called the vertex of the angle

4)coinheritor: It is a subject of the concept of quantity, structure, change, space and information, which is a kind of form science in some way.

5)alternate: The definition of A function: given A number set A, apply the corresponding rule f to A, call it f (A), and get another set of B, which is B=f (A).

Example: into alternate(int x, int y) { static int sign = -1; sign = -sign; return x + (y * sign); }

Zoe

2017-09-19 11:41:54 UTC

common logarithm
Definition: In mathematics, the common logarithm is the logarithm with base 10.
Example:

exponential
definition: In mathematics, an exponential function is a function of a format that b as the base and x as the index
Example:

general term
definition: a mathematical expression composed of variables and constants that yields the successive terms of a sequence or series when integers are substituted for one of the variables often denoted by k
Example:

unit4 Three figure bearings example:

2017-09-19 13:49:42 UTC

Unit 5 Exampel

2017-09-19 14:20:58 UTC

Steven sun

Chris

2017-09-20 04:56:48 UTC

1.Radius: The distance from the center to the circumference of a circle
It is half of the circle's diameter.
2.Diameter: A straight line going through the center of a circle connecting two points on the circumference.
3.Oval: An oval or ovoid is any curve that looks like an egg or an ellipse.
It is not a precise term and there are many curves that get called "oval".
4.Solid: A three dimensional (3D) object.
The 3 dimensions are called width, depth and height.
Examples include, spheres, cubes, pyramids and cylinders.
5.Three-dimensional: An object with three dimensions (such as height, width and depth) like any object in the real world.
Example: your body is three-dimensional.

Also known as "3D".

Chris

2017-09-20 05:08:07 UTC

1.Reflected: An image or shape as it would be seen in a mirror.
2.Logarithm: A logarithm answers the question "How many of one number do we multiply to get another number?"

Example How many 2s must we multiply to get 8?
Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2s to get 8

We say the logarithm of 8 with base 2 is 3

Grace

2017-09-20 05:33:39 UTC

radius
the length of a line segment between the center and circumference of a circle or sphere
r=3
diameter
the length of a straight line passing through the center of a circle and connecting two points on the
Φ=9
circumference
the size of something as given by the distance around it

oval
a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it

solid
a substance that is solid at room temperature and pressure
A=7

three-dimensional
involving or relating to three dimensions or aspects; giving the illusion of depth
S=ah

Madison

2017-09-24 16:40:00 UTC

Base
Defintion:
A base is one side of a polygon, usually used as a reference side for other measurements. Most often used with triangles.
Example:
Choose any convenient side to be the base. In an isosceles triangle, the base is usually taken to be the unequal side.

Height
Defintion:
Vertical distance from the top of an object or figure to its base is called Height

Example:
The height of a toy is about 3 clips as shown in the figure below.

plane
Defintion:
A flat surface that is infinitely large and with zero thickness
Example:
The figure shown is a flat surface extended in all the directions. So, it is a plane.

Two-Dimensional
Defintion:
A shape with no thickness, can be measured in only two faces (such as width and height).