5.5 KiB
Unit 1: Essential Skills
Simple Arithmetics
Addition / Subtraction
Expression | Equivalent |
---|---|
Multiplication / Division
Signs | Outcome |
---|---|
Positive | |
Negative | |
Negative | |
Positive |
BEDMAS / PEMDAS
- Follow
BEDMAS
for order of operations if there are more than one operation
Letter | Meaning |
---|---|
B / P | Bracket / Parentheses |
E | Exponent |
D | Divison |
M | Multiplication |
A | Addition |
S | Subtraction |
Interval Notation
A notation that represents an interval as a pair of numbers.
The numbers in the interval represent the endpoint. E.g.
|
meanssuch that
E
or ∈ meanselement of
N
represents Natural Numbers
W
represents Whole NumbersZ
represents IntegersQ
represents Rational NumbersSymbol Meaning Between but not including or , you also use this for Inclusive \(`a ∪ b`\) Union (or) Intersection (and)
Pythgorean Theorem
a and b are the two legs of the triangle or two sides that form a 90 degree angle of the triangle, c is the hypotenuse
Operations with Rationals
Any operations with rationals, there are 2 sets of rules
Rules for operations with integers
Rules for operations with fractions
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:
Reduce to lowest terms
Multiple by reciprocal
Leave as improper fraction
Shortcut for multiplying fractions
cross divide to keep your numbers small
Example:
Exponent Laws
Rule | Description | Example |
---|---|---|
Product | ||
Quotient | ||
Power of a Power | ||
Power of a Quotient | ||
Zero as Exponents | ||
Negative Exponents | ||
Rational Exponents |
Note:
- Exponential Form –> Expanded Form
- 64 = 6 × 6 × 6 × 6
Scientific Notation
They convey accuracy and precision. It can either be written as its original number or in scientific notation:
555 (Exact) or (3 significant figures).
In scientific notation, values are written in the form , where is a number within 1 and 10 and is any integer.
Some examples include the following: , and .
When the number is smaller than 1, a negative exponent is used, when the number is bigger than 10, a positve exponent is used
Remember: For scientific notation, round to
3 significant
digits
Rates, Ratio and Percent
Ratio
: A comparison of quantities with the same unit. These are to be reduced to lowest terms.
Examples:
a:b, a:b:c, a/b, a to b
Rates
: A comparison of quantities expressed in different units.
Example:
10km/hour
Percent
: A fraction or ratio in which the denominator is 100
Examples:
50%, 240/100
Number Lines
- a line that goes from a point to another point, a way to visualize
set notations and the like
- A solid filled dot is used for
[]
and a empty dot is used for()
Tips
- Watch out for the
+/-
signs
- Make sure to review your knowledge of the exponent laws
- For scientific notation, watch out for the decimal point
- Use shortcut when multiplying fractions