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How to find the rate of change in math

Grade 10 Math: Master Essential Skills & Concepts

FP10.1

Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

auto-gen

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

FP10.10

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

FP10.2

Evaluating and simplifying radicals

Product rule of exponents

Rational vs. Irrational numbers

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

Convert between radicals and rational exponents

Converting radicals to mixed radicals

Converting radicals to entire radicals

FP10.3

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

FP10.4

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

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

FP10.5

Solving polynomials with the unknown 

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

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

Factoring perfect square trinomials

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

Find the difference of squares

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

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

FP10.6

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

FP10.7

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

FP10.8

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

FP10.9

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Applications of linear equations

Get better math marks with our complete Grade 10 math help &ndash; be it <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grades.html">Ontario math curriculum</a>, math curricula of <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=foundations10">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces. We&apos;ve got you all covered!

Just like your class or textbook, our complete help for grade 10 math includes topics such as Trigonometry, Quadratic Equations, Radicals, Factoring polynomials, Linear equations, Linear systems, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 10 math problems. Then, strengthen your understanding with tons of grade 10 math practice. 

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

Number Sense

math

<h2>What is in grade 10 math?</h2>
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<h2>Is grade 10 math hard?</h2>
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<h2>How to pass grade 10 math?</h2>
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Stumped during practice? We&apos;re always here with 24/7 help so drop back into one our lessons and learn by example again!

<h2>How to prepare for 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.

Graphing a taxi fare with initial cost and per-kilometer rate

Ex. 2

Graphing rate of change for a car sales commission problem

Ex. 3

Finding a runner's speed using distance over time

Ex. 4

Calculating cost per person for a wedding with 150 guests

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