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Master Scale Diagrams: Learn How to Create & Interpret

Solve problems that require the manipulation and application of formulas

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Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Rate of change

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

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

Operations with radicals

Operations with Radicals

Demonstrate an understanding of slope

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Characteristics of quadratic functions

Graphing reciprocals of linear functions

Solve problems by applying proportional reasoning and unit analysis

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

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

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Solve problems that involve two and three right triangles

Angle of elevation and depression

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Solve problems that involve scale

Applications of linear equations

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Applications of rational equations

Model and draw 3-D objects and their views

Surface area of 3-dimensional shapes

Graphing reciprocals of quadratic functions

Analyze puzzles and games that involve numerical reasoning, using problem-solving strategies

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Analyze costs and benefits of renting, leasing and buying

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Linear independence

Analyze an investment portfolio in terms of interest rate, rate of return, total return

Image and range of linear transformations

Geometric sequences

Geometric series

Geometric Series

Finance: Future value and present value

Solve problems that involve personal budgets

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Properties of linear transformation

Solve problems that involve creating and interpreting graphs

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

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

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

Reading and drawing bar graphs

read and draw bar graphs

Reading Bar Graphs

Reading and drawing histograms

Reading and drawing line graphs

Reading Line Graphs

Box-and-whisker plots and scatter plots

Financial and Workplace Mathematics 110

Number

math

Intro

- Hi and welcome to this question right here. We're trying to figure out the actual length of the objects now, okay? 
And there's a scale of the image of the leaf is 1.02 and here is the length of the image at 50 centimeters. Now there is something that we have to know, okay? The equation says the ratio is based on the image divided by actual part of the object. What happened is the image on top the actual object on bottom. Let's continue on with our work right here. We know the ratio is 1 and .2. The 1 is the image and the 
.2 is the actual. I'm going to continue my work right here. This is my 1. This is my 0.2 And I'm going to make it equal to another fraction here because I do know the length of my image. It's 50 centimeters. So again, the image goes on the top. Here's my 50 centimeter and the missing number is this part right here which is the actual, the length of the object, okay? It looks like you do know everything except this part right here. So the math here is quite simple. But think about this way. They're equal to each other. How do I go from 1 to 50? I multiply by 50, didn't I? You have to do the same to the bottom. You also have to times by 50 to the bottom part. So 50 times .2, if you use the calculator, you're going to get an answer of, just going to be, a ten for the final answer. The actual length of this leaf here is just going to be 10 centimeters, okay? 
Thanks for watching.

What is the actual length of a street on the map? All we need is a ruler and the map's scale factor! By using the scale factors, we can easily find the actual size of an object. See how to do that in this lesson.

Understanding scale drawings with examples