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Master Simplifying Rational Expressions: Step-by-Step Guide

Derive proofs involving properties of angles and triangles

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Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems involving properties of angles and triangles

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Classifying triangles

Isosceles and equilateral triangles

Solve problems using cosine law and sine law

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Analyze and prove conjectures using inductive and deductive reasoning

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Test statistics

Analyze puzzles and games involving spatial reasoning using problem-solving strategies

Line symmetry

Rotational symmetry and transformations

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Solving absolute value equations

Solve problems involving application of rates

Rate of change

Applications of linear relations

Solving rational equations

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Simplifying rational expressions and restrictions

Applications of rational equations

Simplifying complex fractions

Solve problems involving scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Understand relationships between scale factors and areas of similar 2-D shapes and 3-D objects

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Model and solve problems involving systems of linear inequalities in two variables

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Understand characteristics of quadratic functions including vertex intercepts domain and range

Introduction to quadratic functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

Understand normal distribution including standard deviation and z-scores

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Interpret statistical data using confidence intervals confidence levels and margin of error

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Confidence intervals to estimate population mean

Student's t-distribution

Student"s t-distribution

Determining a Confidence Interval for a Population Mean using t-distributions

Foundations of Mathematics 11 (MAT521A)

Logical Reasoning

Measurement

Relations and Functions

math

Intro

A rational expression is a fraction that its numerator and/or <a href='[[glossary.html|{"keyword":"Denominator","term":"Denominator"}]]'>denominator</a> are polynomials. In this lesson, we will first learn how to find the non-permissible values of the variable in a rational expression. Then, we will how to simplify rational expressions.

Simplifying algebraic fractions and restrictions

Rules to simplifying rational expressions

Common factors of polynomials

Factoring polynomials: \(ax^2 + bx + c\)

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Solving polynomial equations