From 96fde6b99a2b5a18d7cacb586a1704d183e488f9 Mon Sep 17 00:00:00 2001 From: James Su Date: Thu, 18 Apr 2019 01:49:01 +0000 Subject: [PATCH] added some inline math, yeet --- Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md | 31 +++++++++++-------- 1 file changed, 18 insertions(+), 13 deletions(-) diff --git a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md index 7df1de7..0e936a1 100644 --- a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md +++ b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md @@ -68,10 +68,10 @@ - The numbers in the interval represent the endpoint. E.g. **[x > 3, x ∈ R]** - ```|``` means ```such that``` - ```E``` or ∈ means ```element of``` -- ```N``` represents **Natural Numbers** (N = {x | x > 0, x ∈ Z}) -- ```W``` represents **Whole Numbers** (W = {x | x ≥ 0, x ∈ Z}) -- ```Z``` represents **Integers** (Z = {x | -∞ ≤ x ≤ ∞, x ∈ Z}) -- ```Q``` represents **Rational Numbers** (Q = {a⁄b |a, b ∈ Z, b ≠ 0}) +- ```N``` represents **Natural Numbers** $`N = \{x | x \gt 0, x \isin \mathbb{Z} \}`$ +- ```W``` represents **Whole Numbers** $`W = \{x | x \ge 0, x \isin \mathbb{Z}\}`$ +- ```Z``` represents **Integers** $`Z = \{x| -\infin \le x \le \infin, x \isin \mathbb{Z}\}`$ +- ```Q``` represents **Rational Numbers** $`Q = \{ \frac{a}{b} |a, b \isin \mathbb{Z}, b \neq 0 \}`$ | Symbol | Meaning | |:------:|:-------:| @@ -82,12 +82,12 @@ ## 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 -- a2 + b2 = c2 +- $`a^2+b^2=c^2`$ - ## Operations with Rationals -- Q = { | a, b ∈ Z, b ≠ 0 } +- $`Q = \{ \frac{a}{b} |a, b \isin \mathbb{Z}, b \neq 0 \}`$ - Any operations with rationals, there are 2 sets of rules 1. ```Rules for operations with integers``` @@ -98,20 +98,25 @@ - To Divide rationals, multiply them by the reciprocal ### Example Simplify Fully: -- [Reduce to lowest terms] -- [Multiply by reciprocal] +- $` \frac{3}{4} \div \frac{2}{14} `$ Reduce to lowest terms -- +- $` \frac{3}{4} \div \frac{1}{7} `$ Multiple by reciprocal + +- $` \frac{3}{4} \times 7 `$ + +- $` = \frac{21}{4}`$ Leave as improper fraction -- [Leave as an improper fraction] ### Shortcut for multiplying fractions - cross divide to keep your numbers small - Example: -- -- -- +- $` \frac{3}{4} \times \frac{2}{12} `$ + +- $` \frac{1}{2} \times \frac{1}{4} `$ + +- $` = \frac{1}{8} `$ + ## Exponent Laws