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Master Solving Systems of Linear Equations by Graphing

Grade 10 Math: Master Essential Skills & Concepts

1.1 Investigating the Basic Properties of Quadratic Relations

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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

2.1 Relating the Graph of y = x^2 and Its Transformations

Combining transformations of functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

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

3.1 Solving Quadratic Equations

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

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Completing the square

Completing the Square

1.1 Using Linear Systems to Solve Problems

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

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

2.1 Solving Problems Involving Properties of Line Segments

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)

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

3.1 Using Analytic Geometry to Verify Geometric Properties

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

1.1 Investigating Similarity and Solving Problems Involving Similar Triangles

Similar triangles

Similar polygons

Isosceles and equilateral triangles

2.1 Solving Problems Involving the Trigonometry of Right Triangles

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)

3.1 Solving Problems Involving the Trigonometry of Acute Triangles

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

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.

Principles of Mathematics, Grade 10, Academic (MPM2D)

1. Quadratic Relations of the Form y = ax^2 + bx + c

2. Analytic Geometry

3. Trigonometry

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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To give you a taste of what to expect in your grade 10 math test, we dedicate a good portion of our lessons taking you through step-by-step examples. We do this so that you are familiar with questions that you will see in your test or exam. Learn techniques to tackle similar kinds of questions and find out how to avoid making silly mistakes.
Finally, practice with our repository of 936 practice questions! This is a very important part of grade 10 math exam prep, so don&apos;t miss out on this! Test your knowledge and understanding of the topics and see how well you do in this mock test/exam. The more questions you do, the more prepared you&apos;ll be to pass grade 10 math with flying colours!
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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Intro

Ex. 1

- Hello, welcome to this question right here. We're trying to graph these two equations here, and figure out a way they intersect each other, or not, right? 
So, let's go ahead and actually solve in terms of y equals mx plus b, because that's the easiest way to graph this. So, I'm gonna move the y over here and move the negative nine on this side to solve the y. So, I've got myself a 2x plus nine. And this one over here is just going to be, let me do a little bit work here, I'm gonna move the negative x over and I get this, divide everything by three, okay? 
So, now my second equation says negative one over three x plus two, okay? Now, if you have a grid paper, or just a piece of paper is fine, because we're just gonna do a rough sketch to figure out where they intersect each other. So, I've got a positive nine on top, one, two, three, four, five, six, seven, eight, nine. There's a point right there for the first equation, and it's going in this direction, up to over one. That's the slope right there. So, in another way, you can actually do the other direction. So, instead of going up two over one because I ran out of space, I can go down two left one, which is here. And down two left one, which is here. So, I've got myself a nice single straight graph coming down this way, okay? 
Now, if you do the second equation quickly it's actually, your y intercepts at the point y equals two, and the slope is this direction, because it's negative. So, you go down one and over three. So, you go down one and over three, so one, two, three, you're somewhere over here. Two points usually gives you a good point so we're gonna draw a line over here, draw a line over here. Sorry it's not right going straight.okay? 
We've got a little approximate point right here, which is right over here, okay? 
That's a point of intersection. Now, if you're wondering what that point is, it happens at negative three, and a positive three, okay? So, if you have a grid paper, grid paper you can actually plot them really good. And you will see that the both lines right here intersect each other at negative three, and three. Thanks for watching.

In order to determine the number of solutions to a system of linear equations, other than by finding the slope of the lines, we can also graph the equations out and look for the intersection of the lines.