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How to find the rate of change in math

Derive proofs involving properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems involving properties of angles and triangles

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Unit circle

Angles in a circle

Determining non-permissible values for trig expressions

Solve problems involving cosine law and sine law, including ambiguous case

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 to solve problems

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

Solve problems involving application of rates

Direct variation

Identifying direct variations

Rate of change

Applications of linear relations

Solve problems involving scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Understand relationships among scale factors, areas, surface areas, and volumes 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

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Inequalities of combined functions

Inequalities of Combined Functions

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of 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

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

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

Demonstrate understanding of normal distribution, including standard deviation and z-scores

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

Critically analyze society's use of inferential statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Mathematics 11

Logical Reasoning

Measurement

Relations and Functions

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: $y - y_1 = m (x - x_1)$