Transcript MATH ABC

Angles
 Type of angle:
 Acute: An Angle less than 90 degrees
 Right angle: An angle that is 90 degrees
 Obtuse angle: An angle more than 90 degrees
 Straight angle: an angle that is 180 degrees
 Reflex Angle: An angle that is greater than 180 degrees
Binomial
 A polynomial with two terms which are not like
terms. The following are all binomials: 2x – 3,
3x5 +8x4, and 2ab – 6a2b5.
Circle geometry
 Inscribed angle: an angle made from points
sitting on the circle's circumference.
 Angle in a Semicircle: An angle inscribed in
a semicircle is always a right angle
 Cyclic Quadrilateral: A "Cyclic" Quadrilateral has
every vertex on a circle's circumference.
 Tangent Angle: A tangent is a line that just
touches a circle at one point. It always forms a right
angle with the circle's radius.
Degree
 A unit of angle measure equal to of a complete
revolution. There are 360 degrees in a circle.
Degrees are indicated by the ° symbol, so 35° means
35 degrees.
Exponents
 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
Formula
 An expression used to calculate a desired result,
such as a formula to find volume or a formula
to count combinations. Formulas can also
be equation involving numbers and/or variables,
such as Euler's formula.
Geometrey
 The study of geometric figures in two
dimensions (plane geometry) and three
dimensions (solid geometry). It includes the
study of points, lines, triangles, quadrilaterals,
other polygons, circles, spheres, prisms, pyra
mids, cones, cylinders, and polyhedral.
Geometry typically includes the study
of axioms, theorems, and two-column proofs.
How to Add and Subtract
Positive numbers
 Adding Positive Numbers:
 Adding positive numbers is just simple addition.
 Example: 2 + 3 = 5 is really saying "Positive 2 plus Positive
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3 equals Positive 5"
You could write it as (+2) + (+3) = (+5)
Subtracting Positive Numbers:
Subtracting positive numbers is just simple subtraction.
Example: 6 − 3 = 3 is really saying "Positive 6 minus
Positive 3 equals Positive 3"
You could write it as (+6) − (+3) = (+3)
Inequalities
• The aim is to have x (or
whatever the variable is) on
its own on the left of the
inequality sign: x>8 or 16>5
• You have to pay attention to the
direction of an inequality
(which way the arrow points)
• If it doesn’t look right you have to
flip the sign. Multiply (or divide)
both sides by a negative number
or Swapping left and right hand
sides will flip the sign.
Symbol
Words
Example
>
greater
than
x+3>2
<
less than
7x < 28
≥
greater
than or
equal to
5≥x-1
≤
less than
or equal
to
2y + 1 ≤ 7
Jokes (math)
 Q: What happened to the plant in math class? A: It
grew square roots.
 Q: How do you make seven an even number? A: Take
the s out!
 Q: Why is a math book always unhappy? A: Because
it always has lots of problems
 Q: What do you call a number that can't keep still? A:
A roamin' numeral.
Kite
 A quadrilateral with two pairs
of adjacent sides that are congruent. Note that
the diagonals of a kite are perpendicular.
 Kite: d1 = long diagonal of kite, d2 = short diagonal of
kite, Area = (½) d1d2
Laws of Exponents
 Exponents are also called Powers or Indices
 The exponent of a number says how many times to use
the number in a multiplication.
 In this example: 82 = 8 × 8 = 64 in words: 82 could be
called "8 to the second power", "8 to the power 2" or simply
"8 squared"
M
 Definition: Multiplication (often denoted by the
cross symbol "×", or by the absence of symbol) is the
third basic mathematica operation of arithmetic, the
others being addition, subtraction and division (the
division is the fourth one, because it requires
multiplication to be defined).
 Example:
Number patterns
 A number pattern is made by adding some value
each time.
 Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ...
 This sequence has a difference of 3 between each
number.
The pattern is continued by adding 3 to the last
number each time, like this:
Order of operatoins

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Order of Operations
Do things in Brackets First. Example:

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yes
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yes
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yes
2+5×3 =
2 + 15
no
2+5×3 =
7×3
Otherwise just go left to right. Example:
= 17
= 21
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yes
no
6×3
30 ÷ 15
6 × (5 + 3)
=
6×8
= 48
no
6 × (5 + 3)
=
30 + 3
= 33
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
5 × 22
=
5×4
= 20
no
5 × 22
=
102
= 100
Multiply or Divide before you Add or Subtract. Example:
30 ÷ 5 × 3
30 ÷ 5 × 3
=
=
= 18
=2
Polynomials
 A polynomial can have constants, variables and
exponents, but never division by a variable.
 Polynomials can have constants (like 3, -20 or ½)
variable's (like x and y) exponents (like 2 in
𝑦 2 ), but only 1,2,3 etc. are allowed.
Quotient

The answer after you divide one number by another
dividend ÷ divisor = quotient
 Example: in 12 ÷ 3 = 4, 4 is the quotient.
RATIONAL NUMBERS
 A Rational Number is a real number that can be
written as a simple fraction (i.e. as a ratio).
 Example: 1.5 is a rational number because 1.5=3/2
(it can be written as a fraction.
Symmetry
 The simplest symmetry is Reflection Symmetry (sometimes called Line
Symmetry or Mirror Symmetry). It is easy to see, because one half is
the reflection of the other half.
 With Rotational Symmetry, the image is rotated (around a central
point) so that it appears 2 or more times. How many times it appears is
called the Order.
 Point Symmetry is when every part has a matching part: the same
distance from the central point but in the opposite direction.
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Theorem (Pythagoras)
 a2 + b2 = c2
 c is the longest side of the triangle
 a and b are the other two sides
 In a right angled triangle:
the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
Units of measurement
 Definition: A unit of measurement is a
definite magnitude of a physical quantity, defined and
adopted by convention or by law, that is used as a standard
for measurement of the same physical quantity. Any other
value of the physical quantity can be expressed as a simple
multiple of the unit of measurement.
 For example, length is a physical quantity. The meter is a
unit of length that represents a definite predetermined
length. When we say 10 meters (or 10 m), we actually mean
10 times the definite predetermined length called "meter".
Variable
 A quantity that can change or that may take on
different values. Variable also refers to a letter or
symbol representing a number.
Whole Numbers and Integers
 Nonnegative Integers and the numbers 0, 1, 2, 3, 4,
5, etc are whole numbers.
 Integers are like whole numbers, but they also
include negative numbers, but still no fractions.
 So, integers can be negative {-1, -2,-3, -4, -5, … },
positive {1, 2, 3, 4, 5, … }, or zero
X and Y coordinates
 x, y coordinates are respectively the horizontal and
vertical addresses of any addressable point.
 The X coordinate is vertical and the y coordinate is
horizontal.
 Together, the x and y coordinates locate any specific
location.
Youtube
 I used YouTube when ever I was confused and did
not get how to solve a math problem. Whether
studying a few minutes before the test or using it to
help me understand the math more it helped a lot.
 Here are a few good channels and videos:
 https://www.youtube.com/watch?v=ZgFXL6SEUiI
 https://www.youtube.com/watch?v=jUAHw-JIo
Zero pairs

A zero pair is a pair of numbers whose sum is zero.
The thought behind zero pairs is to simplify addition and subtraction problems. Take the following
expression:
2+3-2+9-3
We can eliminate a few steps needed to simplify this expression (in fact, all of them) by using zero
pairs. To make the zero pairs easier to spot, let's rewrite the expression this way:
2 + 3 + (-2) + 9 + (-3)
The zero pairs are 2 and - 2, and 3 and -3. Let's rewrite the expression again, grouping the zero pairs
together
2 + (-2) + 9 + 3 + (-3)
and get
0+9+0
which is 9.
Sources
 http://www.mathisfun.com/
 http://en.wikipedia.org/wiki/Main_Page
 Math 9 text book