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Mastering Pythagorean Theorem Applications in Real Life

Grade 10 Math: Master Essential Skills & Concepts

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

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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

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

Solve problems that involve parallel, perpendicular and transversal lines, and pairs of angles formed between them

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex, by drawing, replicating and constructing, bisecting, solving problems

Direct variation

Identifying direct variations

Inverse variation

Money related questions in linear equations

Rate of change

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Demonstrate an understanding of income, including wages, salary, contracts, commissions, piecework

Word problems of polynomials

Rectangular shape related questions in linear equations

Applications of linear relations

Applications of quadratic functions

Applications of polynomials: x^2 + bx + c

Research and give a presentation on a current event or an area of interest that involves mathematics

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Bivariate, scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Demonstrate an understanding of the International System of Units (SI) by describing the relationships of the units for length, area, volume, capacity, mass and temperature; applying strategies to convert SI units to imperial units

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

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

Demonstrate an understanding of the imperial system by describing the relationships of the units for length, area, volume, capacity, mass and temperature; comparing the American and British imperial units for capacity; applying strategies to convert imperial units to SI units

Angle of elevation and depression

Upper and lower bound

Upper and Lower Bound

Imperial systems

Imperial Length Conversion

Solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements

Applications of polynomials

Solve problems that involve SI and imperial area measurements of regular, composite and irregular 2-D shapes and 3-D objects, including decimal and fractional measurements, and verify the solutions

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

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Demonstrate an understanding of the Pythagorean theorem by identifying situations that involve right triangles, verifying the formula, applying the formula, solving problems

Bearings and direction word problems

Bearings and Direction Word Problems

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Isosceles and equilateral triangles

Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons

Similar triangles

Similar polygons

Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by applying similarity to right triangles, generalizing patterns from similar right triangles, applying the primary trigonometric ratios, solving problems

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

Parallel and perpendicular lines in linear functions

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

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

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.

Mathematics 10-3

math

<h2>What is in grade 10 math?</h2>
Coming out of a terrible <a href="[[region_textbook.html|{"textbook_key":"grade9"}]]">grade 9 math</a> experience? Unsettled and unprepared for what&apos;s next? Let us help you break down what to expect next &ndash; StudyPug offers a <a href="[[region_textbook.html|{"textbook_key":"grade10"}]]">comprehensive math 10 provincial tutoring program</a> that will meet your every need. So whether you are coming from grade 10 math Alberta, the Ontario math curriculum, or preparing for B.C. math 10, we&apos;ve got you covered. Learn grade 10 math and breeze through topics like factoring polynomials, linear equations, and quadratic functions. Master radicals, overcome exponents, and conquer your fear of trigonometry as we explore Math 10 in depth.
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That&apos;s Math 10 in a nutshell for you! Access our entire grade 10 math library of lessons, questions and always be prepared for that homework assignment, test, or exam!

<h2>Is grade 10 math hard?</h2>
Not if you study hard! Like any other subject or grade level, grade 10 math questions and content come in various levels of difficulty. What some of you might find super easy the next person might find incredibly hard. To level the playing field, we offer you the greatest grade 10 math online course on the Internet! Let us do the heavy lifting and take that burden of anxiety off your back.
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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.
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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>
Getting ahead of the game is always recommended for aspiring students and math keeners! Partnering with StudyPug as your tutor is the best way to do so as we offer a plethora of math courses to prepare you well in advance for the future! Whether you feel like the grade 9 math curriculum is too easy, or find yourself in search of a challenge, or perhaps have had enough of grade 9 math worksheets, StudyPug is here to save you from boredom and grow your potential. Master grade 10 math ahead of time or swing back to refresh your memory on <a href="[[region_textbook.html|{"textbook_key":"grade9"}]]">grade 9 math</a> anytime and everywhere. Many topics learnt in grade 9 math will be expanded on in grade 10 math, so take your time, and have no shame in skipping back.
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Throughout each lesson, don&apos;t forget to visit our bank of questions to help you sharpen your grade 10 math skills &ndash; challenge yourself each lesson to completing all the questions related to that chapter before moving on as this is the true test to seeing how prepared you are for grade 10 math!

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade10math.png

Intro

Hi, welcome to this question right here. So we&apos;ve got a plane, kinda flew from a point A starting from here, it went to the point B for 300 meters, then for some reason a 90&deg; turn and went to a point C for another 400 meters, okay. And we're trying to figure out how far is a plane from point A which means you're now here, we're looking for how far are you, from where you start, okay? 
So that's the side right there, and as you can see, that's a right triangle, okay? 
So it looks like you're missing the X over here which is the hypotenuse. So Pythagorean theorem, here it comes one more time. So C&sup2; = a&sup2; + b&sup2;, 
and once again the hypotenuse is always the longest side of the right triangle. So you have to put your X&sup2; here, but for A and B it's your choice, you can put your a for this one or this one, b for this one or that, it doesn't matter so let's just plug it in 300 and square that plus the 400 and square that. Now I'm just gonna find out the answer on the right hand side. Squaring the both sides and adding them together we get ourselves the 250,000, and my X square is still missing. So to figure out the X, I will square root both sides. Why do I do that? 
Because it allows me to cancel the square sign right there. So I end up with just the X and I just have to square root my 250,000 then I get myself the 500 and it looks like it's meter, and that's the answer for this question. Thanks for watching.

We will need to apply Pythagorean Theorem often in our daily life. In this lesson, we will focus on tackling some Pythagorean Theorem word problems. 

Word problems of pythagorean relationship

Applying the Pythagorean Theorem

Estimating square roots