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How to find the rate of change in math

Grade 10 Math: Master Essential Skills & Concepts

Operations on powers with integral exponents

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Product rule of exponents

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Division rule: a^x / a^y = a^(x-y)

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Prime factorization

Evaluating and simplifying radicals

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Functions and relations: connecting data, graphs, and situations

Introduction to quadratic functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

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

Linear functions: slope and equations of lines

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

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)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Systems of linear equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Linear programming word problems

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Multiplication of polynomial expressions

What is a polynomial?

Classifying Polynomials

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Polynomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring difference of cubes

Factoring sum of cubes

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

Factoring perfect square trinomials

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

Find the difference of squares

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

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

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

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

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

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

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All our lessons are taught by experienced grade 10 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics and Pre-Calculus 10

math

<h2>What is in grade 10 math?</h2>
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https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade10math.png

Ex. 1

- 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 
$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? 
Thanks for watching.

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.

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