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How to find the rate of change in math

Solve problems that require manipulation and application of formulas related to perimeter, area, volume, capacity, Pythagorean theorem, trigonometric ratios, income, currency exchange, interest and finance charges

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Upper and lower bound

Upper and Lower Bound

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

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

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

Patterns

Patterns — Word Problem

Evaluating algebraic expressions

Evaluating Algebraic Expressions

Solving one - step equations:  x + a = b

1-step Equations

1-step Equations — Word Problem

Demonstrate an understanding of the Pythagorean theorem

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate an understanding of primary trigonometric ratios

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)

Solve problems that involve angle relationships between parallel, perpendicular and transversal lines

Parallel and perpendicular lines in linear functions

Applications of linear relations

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Solve problems that involve unit pricing and currency exchange, using proportional reasoning

Rate of change

Applications of rational equations

Converting repeating decimals to fractions

Demonstrate an understanding of simple and compound interest

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

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Applications of quadratic equations

Scientific notation

Demonstrate an understanding of credit options, including credit cards and loans

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

Geometry, Measurement and Finance 10

Measurement

Number

math

Ex. 1

<p>- Hi. Welcome to this question right here. So sometimes in this chapter we've got a little bit of a word problems we need to figure out. So, try to use your common sense and logic, okay? So, we're here to draw a graph. So we're gonna start off by saying that there's a graph over here. Roughly, okay? Let's make it a little longer if you need it. Describe a fare charged by a taxi with an initial cost of<br />
$10.5 plus 2.5 per kilometer traveled. So, by looking at the question right here, it sounds like that there's money over here, which is dollar sign on the y-axis, and there should be a kilometer down here, okay? Which is the distance of travel. So let's go ahead and actually figure this out. You see, there's an initial cost. For example, you go into the taxi. Even though the taxi hasn't driven yet it's gonna cost you $10.50 to start off. So, right here, at the zero kilometer, they haven't even started yet, you're already paying them $10.50. That's how much you're paying. Let's not worry about the scale for now. Let's just use the number right there. So that is your initial spot right there on the graph. But every kilometer you traveled...so let's go ahead and put down 1 kilometer, and let's do down 2 right there, and put a 3 there. You're gonna be adding another 2.50 on top of that, okay? So if that's 10... Let's just go ahead and put a couple of dots right here. So 10.50, if I add 2.50 to that it would be $13, okay? And then if I add another 2.50, it will be 15.50 right there, okay. And if I add another 2.50 it will be $18 over here, okay? So those are the money I assign over there, okay? So what happened is for every kilometer you travel, starting from here actually, every kilometer you travel you had to pay in another 2.50. Another kilometer over, you pay in another 2.50 Another kilometer over, you pay in another 2.50 right there. So, guess what will happen? You're actually have a straight line coming up this way. And then it goes on infinity depending on how far you've driven. So, this is a graph that describes the fare charge to you if you take the taxi with an initial cost of 10.50 right here if you start off at zero kilometer, and for every kilometer the graph will go up by $2.50, okay? $2.50 sorry. Okay?<br />
Thanks for watching.</p>


Ex. 2

Ex. 3

Ex. 4

Rate of change is all around us. For example, we express the speed of a car as Kilometer per hour (km/hr), the wage in a fast food restaurant as dollar per hour, and taxi fare as dollar per meter or kilometer. Let's solve some word problems on rate of change.

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

Slope intercept form: y = mx + b

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