1. What You Know About Math
From the song, we know that the singer said that he represented math league when he add shorty subtract. He know all about math that an answer’s 44 it’s really easy because it’s sig figs. We got 45 our answer high we rounded too big. TI-80 silver edition know he was shining dog. An extra memory on the back to do his natural log. We know we multiply while memorizing pi and we take limits to the sky be sure to simplify graphing utility, it’s trigonometry 100 our math distance was rate times time. The sign graph ain’t no line, and exponential decline, but our score can’t beat him. We are memorizing rate for our math league states against the math league greats, and not getting many dates.
2. Equality
- ax = b
For example:
a. 4x = 12
Solution: 4x/4 = 12/4 (divide 4)
They are canceled out and left x = 3.
b. 7x = 63
Solution: 7x/7 = 63/7 (divide 7)
They are canceled out and left x = 9.
Get the variable by dividing itself.
- ax + b = c
For example:
5x + 3 = 18
Solution:
5x + 3 = 18 (in this case we subtract both sides by 3)
5x = 15 (both sides divided by 5)
x = 3
3. Function in Mathematics
Definition function : an algebraic statement that has a special relationship between values: Each of its input values gives back exactly one output value.
Function can also be interpreted as relation in which each element of one set is paired with one.
Two kind of function, they are:
a. Quality, just one value for y after be subtituted. Example: 1 +3 = 4, y = 3x + 4.
b. Inequality, not only one value for after y after be substituted. Example: 8 > 5.
Function of x often written as f(x) = y.
e.g. : y = 3x + 4 (function of x)
y = f(x) = 3x + 4 (standard form)
If we find the function not yet in standard form we have to change first into a standard form.
We can replace f(x) with h(x), g(x), d(x), etc.
f(x) = 3x + 41
g(x) = x^2 – 3x + 2
h(x) = 2^x
We can easily find out the results of the equation when it is to know the value of x.
Given an equation g(x) = 5x^2 – 3x + 2, x = 5
Solution : g(5) = 5(5)^2 – 3(5) + 2
= 112
4. Degrees
One full counterclockwise rotation of terminal side of angle back to its starting point measures 3600 (make a circle).
Degree measurements :
90° (right angle) = ¼ revolution
180° (straight angle)
Degrees and radian have a measurements are related. So important for us to understand the conversion from radians to degrees and vice versa. Relationship of radians and degrees :
360° a single counterclockwise revolution
1 full revolution = 2Ï€ radians
Then ,
Example:
1. 120°= . . . rad
Solution:
1° = Ï€/180 radians
120° = 120 . Ï€/180 radians
= 2Ï€/3 radians
2. 11Ï€/12 radians = . . . °
Solution:
(180°)/Ï€ = 1 radian
(180°)/Ï€ . 11Ï€/12 = 11Ï€/12 radians
= 15° . 11 = 165°
5. Integer
Integer :
- Whole numbers are not fractions and decimal.
- Can positive, negative, or zero.
For example: -1, -2, -3, 0, 1, 2, 3, . . .
Number line :
- Horizontal or vertical line
- Marked at interval units.
- The number line goes on forever in both directions. This is indicated by the arrows.
- Whole numbers greater than zero are called positive integers. These numbers are to the right of zero on the number line.
- Whole numbers less than zero are called negative integers. These numbers are to the left of zero on the number line.
- The integer zero is neutral. It is neither positive nor negative.
For example: 1492
- 2 as unit - 9 as ten
- 4 as hundred - 1 as thousand
6. Trigonometry Functions
Trigonometry functions only need to know values of decimal.
There are 6 basic trigonometry functions:
1. Sine 4. Cosine
2. Cosine 5. Secant
3. Tangent 6. Cotangent
sin θ = opposite/hypotenuse csc θ = hypotenuse/opposite
cos θ = adjacent/hypotenuse sec θ = hypotenuse/adjacent
tan θ = opposite/adjacent cot θ = adjacent/opposite
7. Quadrilateral (4 sided polygon)
a. Rectangle
- Rectangle is a quadrilateral with four right angles.
- Its adjacent sides are perpendicular
- 2 opposite sides equal in length
b. Parallelogram
- Parallelogram is a quadrilateral that has opposite sides parallel
- 2 congruent pairs of supplementary angles
c. Square
- All four sides are congruent
- Right angles – parallel sides – congruent sides
d. Rhombus
- Quadrilateral with four congruent and parallel sides
- Two rhombus called rhomb
e. Trapezoid
- Trapezoid is a quadrilateral with only one pair of parallel sides
- Sides AB and CD parallel but unequal length
Parallelogram have opposite sides parallel, and also true with rectangle, square, rhombus. So alright rectangle, square, rhombus all also parallelogram. But not all parallelogram belong to rectangle, square, rhombus.
Key theorem: Parallelogram
Parallel line and triangle theorems used with other shapes
Theorem : opposite sides of a paralellogram are congruent
Given : ABCD is a parallel
Prove : Sides AB and CD are congruent, sides AD and BC are congruent
Statement
1. ABCD is parallelogram
2. Draw diagonal BC
3. Side AB is parallel to side CD, side AD is parallel to side BC
4. ∠ABD is congruent to ∠BDC, ∠DBC is congruent to ∠ADB
5. Side BD is congruent to side BC
6. ∆ABC is congruent to ∆CDB
7. Side AB is congruent ti side CD, side DA are congruent to side BC
Reason
1. Given
2. Points/one true
3. Definition
4. Alt. Interior angle theorem
5. Reflexive prop.
6. Angle – side – angle postulate
7. CPCTC
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