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@ -23,7 +23,7 @@
> |Part|Question|
> |:---|:-------|
> |A|9 multiple choice|
> |B|10 Short Answer --> <br>- 7 Knowledge questions<br>- 30 Application Questions|
> |B|10 Short Answer --> <br>- 7 Knowledge questions<br>- 3 Application Questions|
> |C|10 Open Response --> <br>- 10 Knowledge Questions<br>- 5 Application Questions<br>- 3 Thinking Questions<br>- 1 Communication Question|
# Essential Skills (1)
@ -65,9 +65,9 @@
>> A notation that represents an interval as a pair of numbers.
>> The numbers in the interval represent the endpoint. E.g. **[x > 3, x &isin; R]**
>> ```|``` means ```such that```
>> ```E``` or &isin; means ```element of```
>> ```W``` represents **Whole Numbers** (W = {x | x > 0, x &isin; Z})
>> ```N``` represents **Natural Numbers** (N = {x | x &ge; 0, x &isin; Z})
>> ```E``` or &isin; means ```element of```
>> ```N``` represents **Natural Numbers** (N = {x | x > 0, x &isin; Z})
>> ```W``` represents **Whole Numbers** (W = {x | x &ge; 0, x &isin; Z})
>> ```Z``` represents **Integers** (Z = {x | -&infin; &le; x &le; &infin;, x &isin; Z})
>> ```Q``` represents **Rational Numbers** (Q = {<sup>a</sup>&frasl;<sub>b</sub> |a, b &isin; Z, b &ne; 0})
@ -94,10 +94,11 @@
>> To Add / subtract rationals, find common denominator and then add / subtract numerator
>> To Multiply rationals, first reduce the fraction to their lowest terms, then multiply numerators and denominators
>> To Divide rationals, multiply them by the reciprocal
>> ### Example Simplify Fully:
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{2}{14}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{2}{14}" title="= \frac{3}{4} \times \frac{2}{14}" /></a> [Reduce to lowest terms]
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{1}{7}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{1}{7}" title="= \frac{3}{4} \times \frac{1}{7}" /></a> [Multiply by reciprocal]
>> ### Example Simplify Fully:
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\div&space;\frac{2}{14}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\div&space;\frac{2}{14}" title="= \frac{3}{4} \div \frac{2}{14}" /></a> [Reduce to lowest terms]
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\div&space;\frac{1}{7}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\div&space;\frac{1}{7}" title="= \frac{3}{4} \div \frac{1}{7}" /></a> [Multiply by reciprocal]
>>><a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;7" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;7" title="= \frac{3}{4} \times 7" /></a>
@ -106,9 +107,9 @@
>> ### Shortcut for multiplying fractions
>>> cross divide to keep your numbers small
>>> Example:
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{2}{14}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{2}{14}" title="= \frac{3}{4} \times \frac{2}{14}" /></a>
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{1}{1}&space;\times&space;\frac{1}{3}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{1}{1}&space;\times&space;\frac{1}{3}" title="= \frac{1}{1} \times \frac{1}{3}" /></a>
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{1}{3}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{1}{3}" title="= \frac{1}{3}" /></a>
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{2}{12}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{3}{4}&space;\times&space;\frac{2}{12}" title="= \frac{3}{4} \times \frac{2}{12}" /></a>
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{1}{2}&space;\times&space;\frac{1}{4}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{1}{2}&space;\times&space;\frac{1}{4}" title="= \frac{1}{2} \times \frac{1}{4}" /></a>
>>> <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\fn_phv&space;=&space;\frac{1}{8}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\fn_phv&space;=&space;\frac{1}{8}" title="= \frac{1}{8}" /></a>
>> ## Exponent Laws
@ -163,7 +164,7 @@
# Polyomials (2)
> ## Introduction to Polynomials
>> A ```variable``` is a letter that represents one or more numbers
>> An ```algebraic expression``` is a combination of variables and constants ```(e.g. x+y+6 = 5)```
>> An ```algebraic expression``` is a combination of variables and constants ```(e.g. x+y+6. y + 8)```
>> When a specific value is assigned to a variable in a algebraic expression, this is known as substitution.
> ## Methods to solve a polynomial
>> 1. ```Combine like terms```
@ -408,7 +409,7 @@
>> ```Y-intercept Form```: **y = mx + b**
>> ```Point-slope Form```: **y<sub>2</sub>-y<sub>1</sub> = m(x<sub>2</sub>-x<sub>1</sub>)**
>> The slope of a vertical lines is undefined
>> The sloope of a horizontal line is 0
>> The slope of a horizontal line is 0
>> Parallel lines have the ```same slope```
>> Perpendicular slopes are negative reciprocals