Chapter 1 Linear relations 

1A Review of algebra CONSOLIDATING

1. Instruction and examples: Video – Algebraic Expressions (Basics of the language) – (10 mins) by Anwhere Math. This covers the language of algebra: expressions, equations, variables, operators, coefficients and terms.
2. Instruction and examples: Video – An Intro to Combining Like Terms | Simplifying Expressions by Combining Like Terms  – (approx 10 mins) by Math with Mr J.
3. Instruction and examples: Video – Algebra – Multiplying and Dividing Algebraic terms – (approx 6.5 mins) by Brett Leikas.
4. Instruction and examples: Video – Algebra Basics: The Distributive Property (Expanding Brackets) – (approx 12 mins) by Math Antics.
5. Instruction and examples: Video – FACTORISATION using the Highest Common Factor – (4 mins) by SHFT – Your Learning. This looks at the Highest Common Factor (HCF) in an expression when it is only a number.
6. Instruction and examples: Video – Factorising using the highest common factor – HCF –  (also known as greatest common factor – GCF) (2 mins) by eHowEducation.
7. Instruction and examples: Video – How to Evaluate Algebraic Expressions (5.5 mins) by Math with Mr J.
8. Worksheets with answers: PDF – Foundation algebra by Magnus Church of England Academy. Just look at pages 2 through 9 (half of which are the answers). MYJ
9. Worksheets with answers: PDF – Algebra workbook for year 9 by Magnus Church of England Academy. Work through the questions with answers up to quadratics (don’t do quadratics onwards).

1B Multiplying and dividing algebraic fractions

1. Instruction and examples: Video – Cancelling common factors in algebraic expressions (3 mins) – by Joel Speranza Math
2. Instruction and examples: Video – Simplifying Algebraic Expressions with Fractions & Outlining Common Errors with Simplification (11.5 mins) – by Eddie Woo. Even if you think you are good at simplifying algebraic expressions with fractions, watch this as he demonstrates some of the key errors students make.
3. Instruction: Video – Multiplying and dividing fractions (5 mins) by Ben Cosh Maths. Ben starts by linking back to how you would do this with numerical fractions.
4. Worksheet with answers: PDF – Simplifying algebraic fractions – by Corbett Maths.
5. Worksheets with answers: PDF – Algebraic Fractions – by Dr Austin Maths. MYJ
6. Worksheets with answers: PDF– Multiplying and dividing algebraic fractions – by MATHSprint.

1C Adding and subtracting algebraic fractions

1. Instruction: Video – Algebraic Fractions: Addition & Subtraction: Finding Lowest Common Denominator (LCD) (11.5 mins) – by Red River College – Tutoring. First revises finding LCD of numerical fractions.
2. Instruction: Video – The easy way to determine the LCD of two rational expressions and use it to find the sum (3 mins) – by Brian McLogan. Remember that LCD stands for Lowest Common Denominator.
3. Instruction: Video – Algebra: Expanding and Simplifying Brackets- harder questions with negatives! (6 mins) – by Kitty Love.
4. Worked Examples: Video – Adding algebraic fractions – several worked examples ( 7 mins) – by Corbett Maths.
5. Worked Examples: Video – Adding and subtracting algebraic fractions – exam-style examples (8 mins) – by Mark Lehain. The examples here are of the complex type and are good to watch.
6. Worksheet with answers: PDF – Adding or subtracting algebraic worksheet by Corbett Maths. The questions range from simple to more complex.
7. Worksheet with answers: PDF– Algebraic Fractions: Addition and Subtraction by RMIT Uni. The questions range from simple to medium difficulty.

1. Worksheet with answers: PDF – Practice exam on algebraic fractions (simplifying, adding/subtracting and multiplying/dividing) by Corbett Maths. Simple to complex. Note that this requires some knowledge of factorising quadratics for questions 16,17 and 18 so you can skip these if you are not yet familiar with quadratic factorisation. Answers to the practice exam are found here.

1D Solving linear equations

1. Instruction: Video – What is a linear equation? (Approx. 3.7 mins) by Study.com  NOTE: The slope/intercept form of a line is introduced in this video as y=mx+b. These days, in Australia, we usually refer to it as y=mx+c. They are interchangeable. Do not be tricked.
2. REMEMBER: When solving linear equations we are ultimately trying to get down to one lot of the variable that we are solving for.
3. Instruction: Video – How to Solve Linear Equations With Variables on Both Sides (2 mins) by eHow Education.
4. Instruction: Video – Solving Linear equations: review (11.5 mins) by Joel Speranza. This is a good revision overview of solving linear equations once you know what a linear equation actually is.
5. Instruction and worked examples: Video – An Intro to Solving Equations with Variables on Both Sides | Multi-Step Equations (9 mins) by Math with Mr J. This video contains a number of other worked examples.
6. Worksheet with answers: PDF – Solving linear equations – simple questions by Neshaminy School District.
7. Worksheet with answers: PDF – Little workbook with instruction on solving linear equations followed by some practice questions with answers. Easy to medium difficulty.
8. Worksheet generator: Web Page – Page with links to generate alot of different linear equation worksheets by HomeSchoolMath.net.

1E Linear inequalities

1. Instruction: Video – Firstly, let’s review what inequalities are. (5.5 mins) by Cognito.
2. Instruction: Video – Solving Algebraic Inequalities with 1 Inequality Sign (Inequalities Part 2)  ( 4.5 mins) by Cognito.
3. Instruction: Video – Year 10 – Linear Inequalities (6 mins) by Miss D Maths.
4. Worked Examples: Video – Year 10 Inequalities Example 1 (4 mins) by High School Maths With Mr George.
5. Worked Examples: Video – Grade 10 Solving linear inequalities – example (5 mins) by ThinkBrainwave.
6. Worksheet/s: PDF – Worksheet with answers by Pearson.

1F Graphing straight lines CONSOLIDATING (A quick recall from last year.)

1. Instruction: Video – Horizontal and vertical line graphs. (3 mins) by FuseSchool.
2. Instruction: Video – Parallel & Perpendicular Lines. (1.7 mins) by FuseSchool.
3. Instruction: Video – Let’s start by Plotting Straight Line Graphs. (4.25 mins) by FuseSchool.
4. Instruction: Video – Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts (7 mins) by Professor Dave Explains. REMEMBER: Slope is otherwise known as gradient and the slope/intercept form of a line (or gradient/intercept form of a line) can be written as either y=mx+b   OR y=mx+c.  In Australia and the UK, the second form is generally used; in the US, the first form is used but means the same thing.
5. Instruction: Video – Equation Of A Straight Line y=mx+c (3 mins) by FuseSchool.
6. Instruction: Video – All about gradient (Approx 7 mins) by Cognito.
7. Instruction: Video – Is a point on a line? (Approx 3.7 mins) by Brian McLogan.
8. Instruction: Video – Graphing using x and y-intercepts | Graphing lines and slope/gradient (4 mins) by Khan Academy.
9. Workbook: PDF – Graphing Straight Lines by the University of Wollongong.
10. Exam with answers: PDF – Drawing Linear Graphs by Corbett Maths. The answers for drawing linear graphs.

1G Finding an equation of a line

1. Instruction: Video – How to Find the Equation of a Straight Line (y = mx + c) (4.5 mins) by Cognito.
2. Instruction: Video – Yet another video on y=mx+c (9 mins) -> by Joel Speranza (Australian maths teacher). Watch this if you are still struggling with the basics of straight lines and finding the equations.
3. Instruction: Video – Finding the Equation of a Straight Line From 2 Sets of Coordinates  (so find the equation of a line given two points along it) (6 mins) by Cognito.
4. Instruction workbook: PDF– Equations of Straight Lines with instruction, questions and answers by Mathcentre.
5. Worksheets with answers: PDF –  A complete set of worksheets with answers by Corbett Maths.

1H Length and midpoint of a line segment

1. Instruction and examples: Video – Understanding how to find the length and midpoint of a line segment – (23.5 mins) by JensenMath.
2. Instruction: Video – A short video on the midpoint of a line segment – (3.5 mins) by MooMooMath and Science
3. Instruction: Video – Distance formula – what is the distance? – (5.5 mins) by Mashup Math. The length between two points is just the distance between them.
4. Worksheet and answers: PDF – Distance between two points by Corbett Maths
5. Worksheet and answers: PDF – The distance formula worksheet MYJ by Kuta Software
6. Worksheet and answers: PDF – An application of the distance and midpoint rules in the real world by Christina Nowlin.
7. Worksheet and answers: PDF– W1 – Midpoint and Length of a Line Segment by JensenMath  Worked solutions are here.

1I Perpendicular and parallel lines Applications and problem-solving

This builds on your knowledge of linear algebra and the gradient/intercept form of a line concept. Remember that gradient and slope are interchangeable so some people refer to that as the slope/intercept form of a line. Slope and gradient mean the same thing.

1. Instruction: Video – Parallel Lines (5 mins) by Cognito
2. Instruction: Video – Perpendicular Lines (5.5 mins) by Cognito
3. Instruction and examples: Video – Parallel and perpendicular lines: Linear Equations (10.66 mins) by Joel Speranza
4. Instruction and examples: Video – Determine if Lines are Parallel, Perpendicular, or Neither (4.5 mins) by Professor Kat.
5. Instruction: Video – How To Tell If Two Lines Are Parallel, Perpendicular, or Neither? (4 mins) by The Organic Chemistry Tutor.
6. Instruction: Video – Find the line perpendicular to a line through a given point (5.25 mons) by Brian McLogan.
7. Instruction: Video – Find the Equation of the Line Parallel to the Given Line through the Given Point (3.75 mins) by Mario’s Math Tutoring.
8. Worksheet and answers: PDF – Parallel and perpendicular lines extended worksheet by School District No. 43 (Coquitlam)
9. Worksheet and answers: PDF – Parallel and perpendicular lines worksheet by Corbett Maths.

1J Simultaneous equations using substitution

1. Instruction: Video – What Are Simultaneous Equations (5 mins) by Cognito
2. Instruction: Video – Looking at three cases of parallel lines – those with 1 solution, no solution, or infinite solutions. (1 min) by MianLearning.
3. Instruction: Video – How to Solve Simultaneous Equations Using Graphs (2.5 mins) by Cognito.
4. Instruction: Video – Simultaneous equations the substitution method (4.4 mins) by Joel Speranza Math.
5. Instruction: Video – The Maths Prof: Solve Simultaneous Equations (by substitution) (9 mins) by The Maths Prof.
6. Instruction and worksheet with answers: PDF – Solving linear simultaneous equations by substitution by Pearson.
7. Worksheet and answers: PDF – Solving linear simultaneous equations by substitution by exceleratemath.com.
8. Worksheets and answers: Web Page – A page with links to solving linear equation worksheets by Dr Austin Maths.
9. Worksheet and answers: PDF –  Solving systems of equations word problems worksheet by Hood River School. (Note: Question 2 should say “Ms. Kitts sold a total of 108 CDs over the 2 weeks.”)

1K Simultaneous equations using elimination

Assuming you have watched the first three videos from the previous section 1J which give you an overview of simultaneous equations you are ready to continue here.

1. Instruction: Video – How to Solve Simultaneous Equations – Using the Elimination Technique (8.5 mins) by Cognito.
2. Instruction and worked problems: Video – Simultaneous Equations using Elimination Method – three different examples (6.3 mins) by Smart Alex Mathematics.
3. Instruction: Video – Solving a System of Equations Using Elimination and Multipliers (3.75 mins) by Brian McLogan.
4. Instruction and worksheet with answers: PDF – Solving linear simultaneous equations by elimination by Pearson.
5. Instruction and worksheet with answers: PDF – Word problems of simultaneous equations that can be solved by elimination by the University of Newcastle.

1L Further applications of simultaneous equations

1. Instruction with worked example: Video – Further applications of simultaneous equations (3 mins) by Joshua Vigar.
2. Instruction with worked examples: Video – Further applications of simultaneous equations (11.75 mins) by Currerazy about maths.
3. Instruction with worked examples (more detail): Video – Further applications of simultaneous equations (11.5 mins) by Math,you?
4. Worked examples and more questions with solutions: Web Page – Word problems that lead to simultaneous equations by TheMathPage.com.
5. Worksheet with solutions: PDF – Word Problems (involving linear equations/simultaneous equations) by iesjovellanos. MYJ Solutions to this worksheet.

1M Half planes EXTENDING

Half planes show the side/s of linear inequalities that satisfy its solutions.

1. Instruction with worked examples: Video – Linear Half Planes (2.75 mins) by Maths Factory. This fellow differs from the textbook in that he prefers to shade the area that does NOT fall in the solution set because it is easier to show the solution set (intersection) when working with more than one linear inequality.  Regardless, you must read the question carefully and answer it in the way it specifically asks.
2. Instruction: Video – Check the half-plane for correct shading (5.5 mins) by LearnZillion.
3. Worksheet with solutions: – PDF – Graphing Linear Inequalities by Kuta Software.
4. Worked examples and more questions with solutions: PDF: Solving inequalities by Spring-Ford Area School District. This is a great workbook which covers: solving inequalities in one variable, graphing inequalities and then graphing systems of inequalities.

Chapter 2  Geometry

2A Review of geometry CONSOLIDATING

1. Instruction with examples: Video –  Review of geometry. (25.4 mins) by Monica Ren.
2. Practice: Textbook –  Go to page 106 and select various questions. The answers are on 826 (Remember, we discussed the textbook we are using right back at the start of this page.)

2B Congruent triangles

1. Instruction with examples: Video – Congruent triangles. (22.5 mins) by Corn Rad.
2. Worked examples: Video – Determining congruent triangles example (4.5 mins) by Khan Academy.
3. Worked examples: Video – Congruent Triangles Proof (10.5 mins) by Beast Mode Maths.
4. Worked examples: Video – Proving congruent triangles worked examples (9 mins) MYJ by Joel Speranza Math.
5. Practice: Worksheet with answers – Web Page – Links to proving congruence and answers by The Australian Association of Mathematics Teachers. And feel free to use their left menu to go back to some instruction on how to complete.
6. Practice: Worksheet with answers – PDF – Congruent triangles by Mr Barton Maths. And here are the answers.

2C Investigating parallelograms using congruence

1. Instruction with examples: Video – Investigating parallelograms using congruence (4.5 mins) by Cujo Maths.
2. Alternate Instruction with examples: Video – Investigating parallelograms using congruence (17 mins) by Math,you?
3. Worked examples: Video – Congruency in parallelogram (8 mins) by Maths.2Learn.
4. Worked examples: Video – Parallelograms (Part 2). (20 mins) by Mrs Neiman.
5. Practice: Worksheet with answers – PDF – Prove parallelogram properties by Edia.

2D Similar figures CONSOLIDATING

1. Instruction with examples: Video – Similarity and Similar figures (8 mins) by Dann Mallet mathematics.
2. Instruction with examples: Video – How to Find Scale Factor with Similar Figures? (Approx 2 mins) by Mario’s Math Tutoring.
3. Instruction with examples: Video – Scale Factors and similar triangles and use the scale factors to determine missing side lengths. (7.5 mins) by Doug Roberts.
4. Worked example: Video – Finding a missing length in similar triangles. (1.6 mins) by MathHelp.com.
5. 
6. Practice: Worksheet with answers – Web Page – This page has links to the worksheet and the answer sheet by Math-Drills.com.
7. Practice: Worksheet with answers – PDF – Similar shapes by Corbett Maths. And here are the answers.

2E Proving and applying similar triangles

1. Instruction with examples: Video – Proving and applying similar triangles (12 mins) by MathTutorMe.
2. Instruction with examples: Video – Proving and applying similar triangles (4.5 mins) by Adam Smith.
3. Instruction with examples: Video – Proving and applying similar triangles (5 mins) by Cate Hoskin.
4. Worked examples: Video – Similar & Congruent Triangles Applications (22.5 mins) by 1MJourney.
5. Practice: Worksheet with answers – PDF – Applications of Similar Triangles by MFM2P-Connell .
6. Practice: Textbook –  Go to page 133 and select various questions. The answers are on 830 (Remember, we discussed the textbook we are using right back at the start of this page.)

2F Circles and chord properties

1. Instruction: Video – Parts of a circle including circle, chord, sector, arc and segment. (Approx 5 mins) by Maths Digest.
2. Alternate Instruction: Video – Parts of a circle… circle, chord, sector, arc and segment. (3 mins) by Minity Maths.
3. Instruction: Video – What is a subtended angle (by an arc, chord, etc.) (6.5 mins) by Wrath of Math.
4. Instruction: Video – Cord Theorems (4.5 mins) by Ian Bailey-Mortimer
5. Instruction: Video – And an alternate video which formalises them with proofs (12.75 mins) by Lacey J STEM Education.
6. Developing understanding: Interactive – Chord Theorems by Neleigh Johnson on GeoGebra.
7. Practice: Textbook –  Go to page 141 and select various questions. The answers are on 832 (Remember, we discussed the textbook we are using right back at the start of this page.)

2G Angle properties of circles: Theorems 1 and 2

1. Instruction: Video – Circle theorems 1 and 2 (7 mins) by Peter Eley.
2. Worked examples: Video – Finding missing angles using circle theorem 1 (7.25 mins) by Maths Factory.
3. Worked examples: Video – Finding missing angles using circle theorem 2 (4.75mins) by Maths Factory.
4. Practice: Textbook –  Go to page 148 onwards and select various questions. The answers are on 833 (Remember, we discussed the textbook we are using right back at the start of this page.)

2H Angle properties of circles: Theorems 3 and 4

1. Instruction: Video – Circle theorems 3 and 4 (8 mins) by Peter Eley.
2. Alternate Instruction: Video – Circle theorems 3 and 4 (6.5 mins) by Maths Factory.
3. Practice: Textbook –  Go to page 158 onwards and select various questions. The answers are on 833 (Remember, we discussed the textbook we are using right back at the start of this page.)

2I Tangents to a circle EXTENDING

1. Instruction: Video – Tangents lines and circles explained (5.5 mins) by Mashup Math.
2. Instruction: Video – What is a secant line? (1 min) by Brian McLogan.
3. Instruction and example: Video – What is the alternate segment theorem (2.6 mins) by Beat the Calculator.
4. Instruction and examples: Video – Alternate segment theorem (5.5 mins) by Anil Kumar.
5. Interactive: Web Page – Alternate segment theorem by Interactive Maths.
6. Practice: Textbook –  Go to page 167 onwards and select various questions. The answers are on 834 (Remember, we discussed the textbook we are using right back at the start of this page.)

2J Intersecting chords, secants and tangents EXTENDING

1. Instruction: Video – Intersecting chords, secants and tangents (3.75 mins) by Ian Bailey-Mortimer.
2. Interactive: Web Page – Intersecting chords by Interactive Maths.
3. Worked examples: Video – Circles: Segment Lengths – Intersecting Chords, Secants, & Tangents (19.2 mins) by Anna Kauffmann.
4. Practice: Textbook –  Go to page 173 onwards and select various questions. The answers are on 834 (Remember, we discussed the textbook we are using right back at the start of this page.)

More resources

1. Worksheet with solutions: PDF – Contains a broad selection of geometry questions from the above topics. by Success Tutoring.

Chapter 3  Indices and surds

NOTE: With many maths terms, there are different names for the same things. Indices are known as powers and exponents whilst surds are also known as radicals.

3A Irrational numbers including surds

If a positive whole number is not a perfect square, then its square root is called a surd. A surd cannot be written as a fraction.

1. Instruction: Web Page – What are surds? by MathIsFun
2. Instruction: Web Unit of Learning – What are surds? by Third Space Resources
3. Instruction: Video – How to simplify surds (1 of 3) (5.5 mins) by Cognito Maths.
4. Instruction: Video – Surds – using a hybrid of prime factorisation to help you find perfect squares  (approx 3 mins) by Brian McLogan.
5. Instruction: Video – Another example of simplifying surds using using prime factorisation (1 minute) by RevisionBoost
6. Instruction:  Video  – How to Express Surds as a Single Surds (2.25 mins)
7. Practice: Web page – with links to worksheets by Mr Barton Maths.

3B Adding and subtracting surds

1. Instruction: Video – Adding and subtracting radicals – (8 mins) by Khan Academy. Remember that the terms surd and radical are interchangeable.
2. Instruction:  Video – Add and subtract radicals (3.7 mins) by Brian McLogan.
3. Worked Example: Video – Addition and Subtraction of Surds | Examples 1 (6 mins) by MathGuru.
4. Instruction, Examples, and Worksheet: Unit of work on adding and subtracting surds by MathSpace.
5. Practice: PDF – Surds – adding and subtracting worksheet with answers by Maths4Everyone.com

3C Multiplying and dividing surds

1. Instruction: Video – Multiplication & Division of Surds (4.25 mins) by TheMathsTutorAU.
2. Instruction: Video – Multiplying and Dividing Surds (Just over 2 mins) by Fuse School
3. Worked Examples: Video – Multiplying and Dividing Surds with Worked Examples (4.5 mins) by Maths Beacon
4. Instruction: Video – How to simplify surds (expressions) (2 of 3) (approx 8 mins) by Cognito Maths. This deals with both adding and subtracting as well as multiplying and dividing surds.
5. Instruction: Video – Surds and binomial products (approx 9 mins)
6. Practice: PDF – Surds – multiplying and dividing worksheet with answers by Maths4Everyone.com

3D Rationalising the denominator

1. Instruction: Video – How to Rationalise the Denominator of a Surd (3 of 3 in video series) (5.5 mins) by Cognito.
2. Instruction: Video – Rationalising the Denominator – (6.5 mins) by TheMathsTutorAU.
3. Instruction with worked examples: Video – Surds Rationalise the Denominator (7.75 mins) by Maths Genie.
4. Instruction, Examples and Practice with Solutions: PDF – Surds and rationalising the denominator by Shrewsbury Colleges Group.

3E Review of index laws CONSOLIDATING

Index laws are special rules for indices.  Now indices (the plural of index) in maths are also known as powers, exponents and it shows the number of times a given number has to be multiplied.

1. Instruction: Video – A review of the index laws (approx 14 mins) by Mathantics.
2. Worksheets: Web page – A page with links to various worksheets by Mr Barton Maths.
3. Worksheets: Web page – Worksheets with answers to all different indice areas by Dobmaths.

3F Negative indices

1. Instruction: Video – A complete explanation (7 mins) by Eddie Woo. This video starts by looking at index law 2 to show how you arrive at the negative index law.
2. Worksheets: PDF – Negative indices with answers by Corbett Maths.

3G Scientific notation CONSOLIDATING

1. Instruction: Video – All about scientific notation (14.5 mins) by Mathantics.
2. Worksheets: PDF – Worksheet with answers by Mayfield City Schools

3H Rational indices 10A

A rational index is an index that can be expressed as a fraction.

1. Instruction: Video – What happens when the power isn’t a whole number? (Fractional Indices) (10.7 mins) by Eddy Woo
2. Instruction: Video – Fractional indices (5 mins) by Corbett Maths.
3. Worksheets: PDF – Fractional indices worksheet with answers by Pearson.
4. Worksheets: PDF – Fractional indices worksheets with answers by Corbett Maths.

3I Exponential equations 10A

1. An aside – Instruction with examples: Video – Helpful video that describes three different forms of equations: linear, quadratic and exponential. (9.25 mins) by Tyler L. Wallace.  Just remember that for functions, y = something can be replaced with f(x) = something. The notations essentially mean the same thing, but “f(x)” (a function of x) gives more flexibility and more information. Watch this video by Eddie Woo for more specific detail on what a function is and when an equation is a function.  And don’t forget that in Australia we tend to refer to the gradient/intercept form of a line as y = mx + c (as opposed to y = mx + b)
2. Instruction with worked problems: Video – Solving Exponential Equations with the Same Base on Each Side (4.25 mins) by John’s Solution Set. Exponential equations with the same base are the easiest type to solve but are not very common.
3. Instruction: Video –  Introduction to Exponential Functions (3.4 mins) by NerdSt
4. Worksheet with answers: PDF –  Solving exponentials with the same base by Hazleton Area School District.
5. Worksheet with answers: PDF – Exponential Equations Worksheet #1 by Wappingers Central School District. And the answers are here.
6. Worksheet with answers: Web Page – Solve exponential equations with the same base – simple to difficult questions. By Science Exercises.EU.

3J Graphs of exponentials

1. Instruction: Quick Video – Animation of what happens when you drag different elements of an exponential graph. (30 secs) by Time Brzezinski.
2. Instruction: Video – Identify Key Features of Exponential Functions (11.33 mins) by AlgebraConceptVideos
3. Alternative – Instruction with examples: Video – Characteristics of Exponential Functions (6 mins) Erin’s Essential Equations.
4. Alternative – Instruction with examples: Video – Key Features of Exponential Functions (18.75 mins) by Tanya Pena.
5. Instruction with example: Video – Solving the intersection of a line and an exponential function (2.5 mins) by Ian Bailey-Mortimer.
6. Worksheet with answers: PDF – Linear vs. Exponential Word Problems by Mayfield Schools.

3K Exponential growth and decay

1. Instruction: Video – Introduction to exponential functions (3.4 mins) by Nerdstudy
2. Instruction with examples: Video – Exponential Growth and Decay | Year 10 (39 mins) by LMKMaths
3. Worksheet with answers: PDF – Exponential Growth / Decay Problem Set by tsfx.edu.au
4. Worksheet with answers: PDF – Exponential Growth and Decay Worksheet by Coppin Academy High School.

3L Compound interest and comparing simple and compound interest

1. Instruction: Video – Compound Interest Explained (1.5 mins) by One Minute Economics.
2. Instruction: Video – Simple v compound interest explained for beginners including the rule of 72. (10.66 mins) by Money with Pennies. Just note that the interest rates currently are different from what she says in the video because the video is from some years ago, and interest rates differ depending on the economy of your country.
3. An alternative to the above… Instruction: Video – Cash Course: Simple vs. Compound Interest (5.5 mins) by PragerU. Explains the difference between simple and compound interest in simple terms.
4. Instruction with examples: Video – The compound Interest Formula Explained and Examples (8.5 mins) by Joel Speranza Math
5. Instruction: Video – Calculating interest for different compounding periods (17.25 mins) by Eddie Woo. This is where the interest periods might not be annual… they may be daily, monthly or quarterly so you need to consider that when you work out the interest rate to be used in the formula.
6. Instruction with examples: Video – Determining Money Earned (Interest) (7 mins) by TheMathClips. The actual interest amount earned is the difference between your investment’s final amount and the principal (starting amount).
7. Worksheet with answers: PDF – Compound Interest by TQN. Simple questions.
8. Lesson with worked solutions then questions with answers: Web Page – 4.01 Compound interest by Mathspace.

Chapter 4 Trigonometry

4A Trigonometric ratios

Source: aplustopper.com

1. Instruction: Video – Orienting – Where do Sin, Cos and Tan Actually Come From – Origins of Trigonometry? (9.25 mins) by Syed Institute. You don’t need to know this but it does give some interesting background to the ratios.
2. Instruction: Video – Trigonometry For Beginners! (22 mins) by The Organic Chemistry Tutor
3. Instruction: Video – Learn a trick if you are interested. Trick for doing trigonometry mentally with the basic angles. (5 mins) by Tecmath.
4. Worksheets with answers: Pdf –  Various trigonometry worksheets are linked from this page by Mr Barton Maths.

4B Finding unknown angles

1. Instruction: Video – How to use the inverse sine function to find the angle of a triangle (4.5 mins) by Brian McLogan
2. Instruction with problems: Video – Finding Angles Using Trig Sin, Cos, Tan (4.75 mins) by Math with Sohn
3. Worked Problems: Video – Trigonometry Basics : how to find missing sides and angles easily (6 Golden Rules of SOHCAHTOA) (Approx. 7.5 mins) by Maths Videos by Jayates.
4. Worksheet with answers: PDF – Using Trigonometry to Find Angle Measures by Kuta Software.
5. Worksheet with answers: PDF – Solving right triangles and word problems (also contains questions to find the sides) by Mr Yang.

4C Applications using angles of elevation and depression (applications in two dimensions)

1. Instruction: Web Page: What is an angle of elevation, angle of depression and how to use these with trigonometric ratios such as sin, cos and tan. by nagwa.com
2. Instruction: Video – Angles Of Elevation & Depression | Trigonometry (2.5 mins) by FuseSchool.
3. Worked Problem: Video – Distance Between 2 Ships (Angle of Depression) (4 mins) by Mario’s Math Tutoring.
4. Worked Problems: Video – Trigonometry Pt 3 – Angles of Elevation and Depression – various worked problems (14 mins) by MikeDobbs76
5. Worksheet with solutions: PDF – Angle of Elevation & Depression Trig Worksheet by ebnet.org.
6. Worksheet with solutions: PDF – Angles of Elevation and Depression by mathsonline.com.au.
7. Worksheet with solutions: PDF – Worksheet (only have answers for the first 12 questions) – Angles of Depression and Elevation by Koltymath. Answers to the first 12 questions were located here (see last few pages).
8. Worksheet with solutions: PDF – Trig word problems by TD Christian High School.
9. Worksheet with answers: PDF – This is a great workbook as it contains lots of worked solutions to more difficult worded problems then it provides more questions for you to do with the answers by Chino Valley Unified School District.

4D Bearings

1. Instruction: Video – What are Bearings? (5.5 mins) by Cognito.
2. Worked Problems: Video – How To: Bearings Problem (approx 8 mins) by VividMaths.com
3. Worked Problems: PDF– Milford Haven School Worksheet with Answers.
4. Worksheets: Web Page – A page of links to bearing worksheets by Mr Barton Maths.
5. Practice Exam: PDF – Practice exam on bearings. And here are the answers. By CorbettMaths.com.

4E Applications in three dimensions

1. Instruction with examples: Video – Applications in 3 dimensions (Approx 5 mins) by Maths IGS.
2. Instruction with example: Video – Trigonometry – Applications in three dimensions – part 2 (1.3 mins) by Adam Smith.
3. Instruction with examples: Video – Trigonometry – Applications in three dimensions – part 3 (3.7 mins) by Adam Smith.
4. Worked examples: Web Page – 10.11 Trigonometry in 3D by MathSpace.
5. Worked examples with extra questions and solutions: Web Page – 3D trigonometry by Third Space Learning.
6. Worksheet with solutions: PDF – 3D Trigonometry assessment by Mathster.

4F The sine rule

This can be used when your triangle is not right-sided but you have at least one pair of opposite dimensions (angle and side) along with another angle or side length.

1. Instruction with examples: Video – The sine rule – Finding an unknown side | Trigonometry (2.5 mins) by teachingwithmissdunford
2. Instruction with examples: Video – Year 10 5.3 Trigonometry 5 – The Sine Rule (12.5 mins) by MathTutorMe. This also discusses the ambiguous case – when it leads to two possible triangles involving either an acute or obtuse angle.
3. Instruction with examples: Video – The Sine Rule (2 of 2: Ambiguous case) (11.6 mins) by Eddie Woo. Introduces the ambiguous case.
4. Instruction with examples: Video – Applying the Sine Rule (1 of 2: Finding an acute angle) (6 mins) by Eddie Woo.
5. Instruction with examples: Video – Applying the Sine Rule (2 of 2: Finding an obtuse angle) (4 mins) by Eddie Woo.
6. Instruction with examples: Web Page – Sine Rule – GCSE Maths – Steps, Examples & Worksheet by Third Space Learning.
7. Instruction with examples with worksheets and solutions: Web Page – The Sine Rule by MME.

4G The cosine rule/law

This can be used when your triangle is not right-sided and the information given is all three sides or two sides and the included angle.

1. Instruction: Video – The Cosine Rule/Law (5.75 mins) by Nerdstudy.  A simple and easy-to-understand summary.
2. Instruction with examples: Video – The Cosine Rule (1 of 2: Introduction & relation to Pythagoras’ Theorem) (Approx 11 mins) by Eddie Woo. Extends your understanding.
3. Instruction with examples: Video – The Cosine Rule (2 of 2: Examples of finding sides & angles) (Approx 11 mins) by Eddie Woo. Extends your understanding.
4. Instruction with examples with worksheets and solutions: Web Page – The Cosine Rule by MME.
5. Worksheet with solutions: PDF – Law of cosines worksheet by Mr Cas’s Website.
6. Worksheet with solutions: PDF – Sample cosine law exam by Maths Genie. And here are the solutions.

4H Area of a triangle

1. Instruction with examples: Video – Yr 10 Trigonometry 9 – Area of a triangle (Approx. 6.5 mins) by MathTutorMe.
2. Alternative Instruction with examples: Video – Area of a Triangle using trigonometry (2.25 mins) by teachingwithmissdunford.
3. Proof – Instruction: Video – Proof of formula for the area of a triangle using sine (3.75 mins) by Whiteboard Maths.
4. Worksheet with solutions: PDF – Find the area of various triangles by Kuta Software.
5. Worksheet with solutions: PDF – Area of a triangle using the sine of an angle by Maths4Everyone.

4I The unit circle 10A

1. Instruction: Video –  Trig Visualized: One Diagram to Rule them All (six trig functions in one diagram) (4.25 mins) by Mathematical Visual Proofs. Orientation.
2. Instruction: Video – The Unit Circle Part 1 (8 mins) by Joel Speranza Math.  And if you like Joel’s explanations, feel free to continue on with his video playlist.
3. Instruction: Video – The unit circle part 3 What about tan? (2.5 mins) by Joel Speranza Math.
4. Instruction: Video – The Trigonometric Functions and the Unit Circle (13.25 mins) by Maths Explained.
5. Instruction with example: Video – How to find a reference angle (44 secs) by Andy Math.
6. Instruction with examples: Video – Unit circle values for multiples of 90 degrees (5.5 mins) by Brian Thornley.
7. Instruction with examples: Video – The four quadrants (17.5 mins) by MathTutorMe.
8. Worksheet with solutions: Refer to textbook 4I Page 331 and select questions from there. Answers are located on pages 849 and 850.

4J Graphs of trigonometric functions

1. Instruction: Video – Properties of trig graphs (5.5 mins) by Ian Bailey-Mortimer.
2. Instruction: Video – Graphing Trig Functions – in particular the sine and cosine functions. (Approx 11 mins) by Peter Eley.
3. Instruction with example: Video – Graphing Trigonometric Functions (18 mins) by Eddie Woo.
4. Instruction with example: Video – Graphing Trigonometric Functions (Example: y = 3cos(x) – 2) (10.5 mins) by Eddie Woo.
5. Instruction and worked examples: Web Page – 6.02 Graphs of trigonometric functions by MathSpace.
6. Worksheet with solutions: Refer to textbook 4J Page 340 and select questions from there. Answers are located on pages 849 and 851.

Chapter 5  Quadratic expressions and equations

5A Expanding expressions CONSOLIDATING

1. Instruction: Video – Recap: The distributive law used to expand single brackets. ie. a(b+c) (4 mins) by Olico TV.
2. Instruction: Video – Recap: The distributive law used to expand the product of two binomials. ie. (a+b)(c+d) (Approx 4 mins) by Olico TV.
3. Instruction: Video – Recap: Expanding Perfect Squares (Approx 5 mins) by Joel Speranza Math.
4. Instruction: Video – Recap: Expanding Difference of Two Squares (Approx 4 mins) by Joel Speranza Math.
5. Instruction: Video – Recap: Expand and Simplify Algebraic Expressions | Binomial Expansions (Approx 3 mins) by iiTutor.com.
6. Instruction, Questions, and Answers: Pdf –  Expanding brackets and simplifying expressions by Edexel. MYJ.
7. Instruction, Questions, and Answers: Pdf – Further Algebra – Distributive Laws and their application by Macquarie University.

5B Factorising expressions

1. Instruction: Video – Recap: Factoring Expressions Algebra (2.5 mins) by MooMooMath and Science.
2. Instruction: Video – A more detailed look at factorising expressions with different types of problems (8.5 mins) by Anywhere Math.
3. Instruction: Video – RECAP: Lets step aside for a moment and revisit perfect squares and differences of squares. (18.5 mins) by Treena. This video shows how these can be used in mental arithmetic on numerical problems too.
4. Instruction and worked problems: Video – How To Factor Difference of Squares (difference of perfect squares (DOPS)) (19.5 mins) by The Organic Chemistry Tutor.
5. Instruction and worked problems: Video – Factorising difference of perfect squares and DOPS using surds (14.5 mins) by Kym Markwick.
6. Worksheet with answers: Pdf – Factorising expressions by Corbett Maths.  Relatively easy problems.
7. Worksheet with answers: Pdf – Factoring the Difference of Squares by School District 43.
8. Worksheet with answers: Pdf – Difference Between Two Squares by Corbett Maths.
9. Practice exam with answers: Pdf – Algebra – Expand and Factorise by ExExcel GCSE and answers can be found here.
10. Worksheet with answers: Pdf – Factoring By Grouping by Kuta Software.

5C Factorising monic quadratic trinomials

Monic quadratic trinomials are expressions where the leading coefficient is equal to 1. For example, x² + 7x + 12 is a monic quadratic trinomial because the coefficient of x² is 1 (implied). These trinomials are the simplest to factor. [A trinomial is a mathematical expression consisting of three terms. In algebraic terms, it is often in standard form ax² + bx + c. A quadratic is a polynomial equation where the highest power of the variable is 2 – otherwise known as having an order 2 or ‘of the second degree’.] Watch the appropriate videos linked from 1A above to refresh your memory about basic factorising.

1. Instruction: Video – Year 10 Maths – Factorising Monic Quadratic Expressions (8 mins) by Jo Anna Morrison.
2. Alternate Instruction with examples: Video – Factorisation of monic quadratic trinomials | Year 10 Quadratic Equations (16 mins) by LMKMaths.
3. Instruction example: Video – Simplifying Algebraic Fractions in Monic Expressions by Quadratic Factorise (Approx 4 mins) by iiTutor.com
4. Online lesson with examples: Web Page – 1.08 Factorising monic quadratic trinomials by Mathspace.
5. Online practice with solutions: Web Page – Factorising Monic Quadratic Trinomials – Questions by ClassMathematics.
6. Worksheet with answers Pdf –  Factorising Quadratics (a = 1 so a monic quadratic trinomial) – by EdExcel.  And here are the answers.

5D Factorising non-monic quadratic trinomials

(Many different algorithms work but it is not necessarily clear why they work. This is one area of maths where understanding is not a focus and as a result, often causes debate amongst teachers.)

1. Instruction: Video – Factorisation of non-monic (harder) quadratic trinomials – Year 10 Maths (15 mins) by LMKMaths.
2. Alternate Instruction: Video – Year 10 A Quadratics Factorising Non Monics Intro (2 mins) by High School Maths with Mr George.
3. Worked Example 1: Video – Year 10 A Quadratics Factorising Non Monics Example 1 (2.75 mins) MYJ by High School Maths with Mr George.
4. Worked Example 2: Video – Year 10 A Quadratics Factorising Non Monics Example 2 (2.75 mins) by High School Maths with Mr George.
5. Worked Example: Web Page –  Factorising quadratic using the ac method by Texas Wesleyan University.
6. Worksheet on the grouping method: Web Page – Scaffolded Factorisation Worksheet Grouping by StartingPointMaths.com.
7. Instruction, worksheet and solutions: Pdf –  Factoring using the traditional axc method by Metropolitan Community College.

5E Factorising by completing the square

As mentioned, there are many ways to factorise quadratics but up to now in the textbook, you won’t have learned how to factorise something like x² + 6x + 1 because there are no factors of 1 that add to 6. Instead, you can use your knowledge of perfect squares and the difference of perfect squares to help find factors using surds.

1. Instruction:  Video – Why is (a + b)² = a² + 2ab + b² (1 min) by Infinity Learn NEET. A quick and simple visual method using squares and rectangles to show why (a + b)² = a² + 2ab + b².
2. Instruction:  Video – Completing the Square (visual proof) (1.5 mins) by Mathematical Visual Proofs. This helps you understand how completing the square comes about and what it is equivalent to.
3. Instruction:  Video – back to our problem: x² + 6x + 1… Intro to completing the square (year 10) (7.5 mins) by Haywood’s Math.
4. An aside on factoring:  Video – Some quadratics cannot be factored!!! (5.6 mins) by NancyPi.
5. Instruction – journey summarised:  PDF – If you wish to go on the full journey of simple examples right through to the most complex example with the algorithm summarised towards the end.
6. Alternate Instruction – journey summarised: Web Page – And my favourite (after watching the videos above). This goes one more step by solving (which is covered in the next section) the factorised form as well. Solving Quadratic Equations By Completing The Square by Kate’s Math Lessons.
7. Worked problems: Web Page – Here are a couple of examples that factorise by completing the square but they then continue to solve for x (which is super easy once you’ve factorised).
8. Worked problems as well as a quiz with solutions. – Web Page – Completing the Square by MME.
9. Worksheet (with solutions) generator – PDF – Completing the Square by Interactive Maths. (Terrific resource).

5F Solving quadratic equations using factorisation

Now we are getting to the juicy bit… how to solve quadratic equations when they can be factorised.  After all, that is the point isn’t it… to solve for the unknown. (Remember, a quadratic equation has the highest power being 2 and can be written in standard form as follows: ax² + bx + c.)

1. Instruction:  Video – Introducing the null factor law and how we can use this to our advantage when solving quadratic. (2 mins) by Piece of Pi.
2. Alternate Instruction:  Web Page – The null factor law with examples by MathsTeacher.com.au
3. Instruction:  Video – Converting quadratic equations into standard form (Approx 5 mins) by Math Teacher Gon.
4. Instruction:  Video – Remove any common factors in the coefficients/constant first (if one exists) then factorise and solve using the null factor law (3.5 mins) by Quadratics with a common factor.
5. Worked examples: Video –  Solving Quadratic Equations by Factoring – Basic Examples (7.3 mins) by PatrickJMT.
6. Worked examples: Video – Solving Quadratic Equations by Factoring (22.5 mins) by GoTutor Math.
7. Worksheets and answers: Web Page –  Links to different worksheets by Mr Barton Maths
8. Worksheet with solutions: Web Page – Solving quadratic equations by factorising exam style by Corbett Maths. Here are the answers.
9. Worked examples of problem solving real life questions then a quiz: Web Page – Real Life Applications of Quadratic Equations by cK-12.

5G Applications of quadratics

These generally are real-world word problems that can be modelled and solved using quadratic functions.

1. Worked examples: Video – Quadratic equations in everyday life. (Approx 5 mins) by Madeline Brandt. Covers the height of a fall, the equation of an arch and a horizontal distance problem.
2. Worked examples: Video – Applications of quadratic equations (8.5 mins) by Your Math Tutor. Covers three types of worded problems: throwing a ball/rock, building a fence and maximising revenue ($).
3. Worked examples: Video – Applications of quadratic (33 mins) by JensenMath. Covers rocket and ball paths, measurement questions and maximising revenue ($).
4. Worked examples: Video – Applications of quadratic (12.4 mins) by Andrea Hendricks. MYJ Covers geometric problems, area problems and a given model.
5. Worked examples: Web Page – Quadratic Equation Word Problems – Examples & Practice by expii. Covers area and projectile problems.
6. Worked examples with additional problems and solutions: Web Page – Applications involving quadratic equations by LibreTexts Mathematics. Covers number, geometry and projectile problems.
7. Worked examples with additional problems and solutions: Web Page – Quadratic Word Problems: Age and Numbers by BC Campus. Covers number, speed/distance and geometry problems.

5H Solving quadratic equations by completing the square

1. Instruction using examples:  Video – How to Solve By Completing the Square (17.5 mins) by NancyPi.
2. Worksheet with solutions: PDF – Solving Quadratic Equations By Completing the Square by Kuta Software.
3. Worksheet with solutions: PDF – Completing the Square Worksheet by Ms Warnock. Easy to medium questions.
4. Worksheet with solutions: PDF – Completing the Square Exam by MathsGenie. Medium to hard questions. The answers are here.

5I Solving quadratic equations using the quadratic formula

1. Instruction with example:  Video – The Quadratic Formula (Definition & example question) (11.6 mins) by Eddie Woo.
2. Instruction:  Video – Where does the quadratic formula come from? (3 mins) by FoggyMaths.
3. Question: Web Page – When do you use the quadratic formula? by Socratic Q&A.
4. Worked examples:  Video – How To Solve Quadratic Equations Using The Quadratic Formula (6 mins) by The Organic Chemistry Tutor.
5. Instruction:  Web page – Discriminant definition and review by Khan Academy.
6. Instruction with examples: Video – How To Determine The Discriminant of a Quadratic Equation (3 mins) by The Organic Chemistry Tutor.
7. Worksheet with solutions: PDF – Solve using the quadratic formula by Matawan-Aberdeen regional school district
8. Worksheet with solutions: PDF – Quadratic Formula exam style by MathGenie. Simple to difficult. And here are the answers.

Extra resources for this topic.

Workbook: Pdf – Factorising Algebraic Expressions by International Mathematics. This is a great workbook with lots of questions sets against each of the factorising areas plus a practice exam and revision assignment. Answers can be located from page 575 at this page on anyflip.
Workbook and worked solutions: Pdf – Arithmetic with Surds by Macquarie University including Expanding Expressions Involving Surds, Fractions involving surds, Rationalizing the denominator and Arithmetic with Surds including answers. MYJ

Chapter 6  Measurement

6A Review of length CONSOLIDATING

1. Instruction with examples: Video – Review of length. Full video for 6A in the textbook. (20.75 mins) by Math,you?
2. Practice: Worksheet and solutions – PDF – Converting metric units… length worksheet 2 by MathSalamanders.
3. Practice: Worksheet and solutions – PDF – Circles, Perimeters and Sectors (inc area but skip the area questions until you complete 6C if you are struggling) by Mathster.
4. Practice: Instruction, worked examples and more problems with solutions – Web Page – Perimeter of a sector. by Third Space Learning.

6B Pythagoras’ theorem

1. Instruction: Video – Pythagorean’s theorem and several proofs of its formulae. (5.25 mins) by TED-Ed (Betty Fei)
2. Instruction: Video – Rearranging the formula to make a or b the subject (algebraic rearrangement) (Approx 5 mins) by Quick Math.
3. Instruction with examples: Video – Pythagoras and exact value. (8 mins) by Australian Mathematics Curriculum.
4. Worked example: Video – Finding the hypotenuse (2 mins) by MathHelp.com
5. Worked examples: Video – Finding sides other than the hypotenuse (8 mins) by Tecmath.
6. Practice: Worksheet and solutions – PDF – Pythagoras (simple to difficult) by Corbett Maths. And here are the answers.
7. Practice: Worksheet and solutions – PDF – Pythagoras (simple to difficult) by Mrs Yost.

6C Review of area CONSOLIDATING

1. Instruction with examples: Video – 6C Review of area (24.75 mins) by Math,you?
2. Instruction with examples: Video – Quick review of the area of sectors (4 mins) by Mr Maison Net.
3. Instruction: Video – Geometry Surface Area Basic Area including various formulae (3.7 mins) by High School Maths with Mr George.
4. Worked examples: Video – How to find the Area of Compound Shapes #106 (4.5 mins) by Cognito.
5. Worked examples: Video – Area of composite shapes (6 mins) by TheLearningPod.
6. Practice: Worksheet and solutions – PDF – Area of Quadrilaterals and Triangles (simple) by DOBMaths.
7. Practice: Worksheet and solutions – PDF – Area of Sectors and Composite Shapes (simple) by DOBMaths
8. Practice: Worksheet and solutions – PDF – Area of compound shapes (medium) by Dr Austin Maths. And here are the answers.

6D Surface area of prisms and cylinders

1. Instruction: Video – What is a prism? (2.4 mins) by MooMooMath and Science.
2. Instruction: Video – For fun…. how to make a 3D pull-up cylinder (20 seconds) by Science And Fun With Me.
3. Instruction: Video – What is a net concerning 3D shapes and maths? (Approx 3 mins) by Minity Maths.
   Total surface area is just the sum of all the surface areas of the faces.
4. Instruction: Video – What is the surface area of a cube? (Approx 3.7 mins) by The Maths Guy!
5. Instruction: Video – How to Find the Surface Area of a Rectangular Prism (Approx 5 mins) by Maths with Mr J.
6. Instruction: Video – How to Find the Surface Area of a Triangular Prism (Approx 6.7 mins) by Maths with Mr J.
7. Instruction: Video – Surface Area of a Cylinder (Approx 3 mins) by FuseSchool – Global Education.
8. Worked Example: Video – Finding the surface area of a composite solid (cylinder on top of a rectangular prism) (12.5 mins) by TeachingScience77
9. Worked Example: Video – Finding the surface area of a composite solid (Half a cylinder on top of a rectangular prism) (5 mins) by mrmaisonet
10. Worked Examples: PDF – Surface Area of Composite 3D Objects by JA Williams School.
11. Instruction, Worked Solutions and Practice: PDF– Links to various worksheets and solutions by Mr Barton Maths.
12. Instruction, Worked Solutions and Practice: Web Page – Surface Area and Volume of 3-D Shapes – Pick appropriate questions from this workbook by cimt.
13. Instruction, Worked Solutions and Practice: Web Page – Surface area of composite solids by MathSpace.

6E Surface area of pyramids and cones

1. Instruction: Video – Surface Area of Cones and Pyramids – but note that the fellow uses slightly different names for the elements of the equations but he means the same thing. Get used to different people calling the same thing by different names.  (about 4 mins) by Mario’s Math Tutoring.
2. Instruction: Video – How to find the surface area of pyramids and cones (about 14 mins) by Your Math Tutor.
3. Instruction and Practice: Web Page – Free unit of work by MathSpace.
4. Practice: Worksheet and solutions – PDF – general surface area as well as volume of shapes inc. pyramids and cones by Dobmaths.

6F Volume of prisms and cylinders

1. Instruction: Video – Volumes of Cylinders and Prisms (3.5 mins) by Cognito.
2. Instruction: Video – Volumes of Prisms & Cylinders (7 mins) by Eddie Woo.
3. Instruction: Video – How to find the volume of prisms and cylinders(11 mins) by Jim Barnard Math Tutorials.
4. Instruction and Practice: Free unit of work by MathSpace.
5. Instruction, Worked Solutions and Practice: PDF – Free unit of work by BigIdeasMath.
6. Practice: Worksheet and solutions – PDF – Volume of Prisms and Cylinders by KutaSoftware.com.

6G Volume of pyramids and cones

1. Instruction: Video – Experiment that proves the relationship between the volume of a pyramid or cone is a fraction of the volume of the prism or cylinder with the same base area. (5 mins) by Richard Pieper.
2. Instruction with examples: Video – Volume of Pyramids and Cones (5.4 mins) by Taylor Locke.
3. Instruction with examples and extra problems with answers: Web page – 9.05 Volume of pyramids and cones by MathSpace.
4. Practice: Worksheet and solutions – PDF – Volume of Pyramids and Cones by Kuta Software.

6H Surface area and volume of spheres

1. Instruction: Video – Volume and Surface Area of Spheres (3.3 mins) by Infinity Learn NEET
2. Alternative Instruction: Video – Volume and Surface Area of Spheres (2.5 mins) by Infinity Learn NEET
3. Worked examples: Video – Volume and Surface Area of Spheres – Mr Mathematics (5.7 mins) by Jonathan Robinson.
4. Worked examples: Video – Volume and Surface Area of Spheres (4 mins) by Cognito.
5. Practice: Worksheet and solutions – PDF – Volume of Surface Area of Spheres Worksheet with Answer Generator by Math-Aids.com.

6I Limits of accuracy EXTENDING

1. Instruction: Video – Limits of accuracy with measuring instruments. (4.6 mins) by Heather Whitehead. All measuring instruments have a limit of accuracy because of their length of precision.
2. Instruction: Video – Limits of accuracy – upper and lower bounds. (4.5 mins) by FuseSchool.
3. Instruction with examples: Video – Upper and Lower Bounds (8.25 mins) by The Maths Prof.
4. Practice: Worksheet and solutions – PDF – Limits of Accuracy by Mathster.
5. Practice: Worksheet and solutions – PDF – Exam style – GCSE Maths – Number – Rounding and Limits of Accuracy Worksheet by PMT Education. And here are the answers.

Additional practice.

1. Practice Workbook with Solutions: PDF – Volume and surface area of 3D shapes by EdExcel.
2. Practice Exam with Solutions: PDF – Surface Area and Volume by Dobmaths.

Chapter 7 Parabolas and other graphs

7A Exploring parabolas

1. Instruction: Video – Exploring Parabolas – 10MM – 7A (13.5 mins) by MathBoy
2. Real World: Web Page –  Parabolas in the real world – Geogebra
3. Instruction, Worksheet, Practice and Answers: Web Page – Here is a short and succinct introduction to transforming parabolas. by Mathspace. It has a great little applet that you can tinker with to see what happens when you change the coefficients of the variables or the constant.  Don’t forget, you can always use the free Desmos graphing calculator tool online and enter an equation such as x² + x + 3 into the empty cell at the top left and tinker with the coefficient and constant values.
4. Interactive – Web Page – Super cool!!! Parabolas: General, Standard and Graphical Forms at Doenoet by Virginia Mae.
5. For a smile… – Instruction: Video – Everything You Need To Know About Parabolas In 2 Minutes (2 mins) by SimpleMathematics.
6. Instruction: Video – Key definitions for vertex, axis of symmetry, y-intercept, x-intercept/s, domain, range, and maximum/minimum value – (7.45 mins) by StudyPug.
7. Worksheet with solutions: Web Page –  Axis of symmetry and vertex worksheet by TopWorksheets.Com
8. Worksheet with solutions: Web Page – Identify properties of a quadratic function worksheet by Edia.

7B Sketching parabolas using transformations

1. Instruction, Worksheet, Practice and Answers: Web Page – Plot parabolas by Mathspace.
2. Instruction: Video – Introducing a sequence of four videos by Eddie Woo around graphing polynomials. This helps set the scene for parabolas and how the elements discussed above behave visually.
   1. Graphing Polynomials (1 of 4) – Graphing Techniques – Fundamental graphs. (8.75 mins) by Eddie Woo
   2. Graphing Polynomials (2 of 4) – Horizontal Translation (8.5 mins) by Eddie Woo
   3. Graphing Polynomials (3 of 4) – Vertical Translation (9 mins) by Eddie Woo
   4. Graphing Polynomials (4 of 4) – Dilation (14.33 mins) by Eddie Woo
3. Instruction: Video – Sketching Parabolas (approx 8 mins) MYJ by Heather Whitehead
4. Worksheet with solutions:  PDF – Using transformations to graph quadratic. By Needham.
5. Worksheet with solutions:  PDF – Characteristics of quadratics – By MathMonks.

7C Sketching parabolas using factorisation

1. Instruction with examples: Videos – A complete lesson on 7C Sketching Parabolas using Factorisation (28.6 mins) by Shane Underwood.
2. Alternate Instruction with examples: Video –  Sketching Parabolas Using Factorisation – 7C (19.5 mins) by Math Boy.
3. Instruction with example: Web Page – The top half provides instruction and a worked example of sketching parabolas using factorisation by Best Math.
4. Worksheet with solutions:  PDF – Quadratics and Parabolas in Factorised Form – sketching. by national5maths.co.uk.
5. Worksheet with solutions:  PDF – Sketching graphs of quadratics using factorisation by FridayMath.com

7D Sketching parabolas by completing the square

1. Instruction with examples: Video – Sketching Parabolas by Completing the Square – 7D (10.7 mins) by Math Boy.
2. Alternate Instruction with examples: Video – Sketching Parabolas by Completing the Square – 7D (22 mins) by Math,you?
3. Practice: Textbook –  Go to page 537 and select various questions. The answers are on 885 (Remember, we discussed the textbook we are using right back at the start of this page.)

7E Sketching parabolas using the quadratic formula

1. Worksheet with solutions:  PDF – Using transformations to graph quadratic. By Success Tutoring.
2. Worksheet with solutions:  PDF – Sketching Parabolas – By Class Mathematics.
3. Worksheet with solutions:  PDF – Revision of quadratics including factorisation and graphing. By Adelaide Uni.

7F Applications of parabolas

1. Instruction with examples: Video – Parabolas in real life. (2.25 mins) by Sadi I.
2. Instruction with examples: Video – Quadratics in the real world – part 1. (7 mins) by Lauren Kuhn—examples when the model function/equation is provided.
3. Instruction with examples: Video – Quadratics in the real world – part 2. (5.5 mins) by Lauren Kuhn. Examples of when you have to determine the model.
4. Instruction with example: Video – Setting up a quadratic model for a parabolic-shaped bridge with given certain data. (8 mins) By LSA SHS Math Dept.
5. Alternate Instruction with example: Video – Parabolic archway problem. (12 mins) by Jacopo Stifani.
6. Instruction with example: Video – Setting up a parabolic fencing problem (6.3 mins) by Gary Huang.
7. Instruction with example: Video – Setting up a parabolic worded revenue problem (4.7 mins) by NewbornAlgebraClass.
8. Instruction with example: Video – Kicking a football and modelling its trajectory using a quadratic. (44.25 mins) by High Peak Education.
9. Practice: Textbook –  Go to page 548 and select various questions. The answers are on 892 (Remember, we discussed the textbook we are using right back at the start of this page.)

7G Intersection of lines and parabolas

1. Instruction with examples: Video – Intersections of lines and parabolas (27.4 mins) by LMKMaths.
2. Instruction with examples: Video – Intersection of lines and parabolas (8 mins) by Currerazy about maths.
3. Practice: Worksheet and solutions – PDF – Simultaneous Equations: Advanced by Corbett Maths. And here are the solutions.

7H Graphs of circles

1. Instruction with examples: Video – 7H Graphs of circles (15.25 mins) by Maths with Miss Hunter.
2. Alternate Instruction with examples: Video –  Graphs of circles and semi-circles (28 mins) by LMKMaths.
3. Practice: Worksheet and solutions – Web Page – Graphing Equation of a Circle Worksheet Generator by Math-Aids.com.
4. Practice: Worksheet and solutions – PDF – Intersections of Circles & Lines – Homework by Mrs. Zarbnisky. And here are the answers.

7I Graphs of hyperbolas

1. Instruction with examples: Video – Graphs of hyperbolas and truncus’ (47 mins) by LMKMaths.
2. Instruction with examples: Video – Hyperbolic functions and their graphs (15.5 mins) by MathTutorMe.
3. Worked examples: Video – Sketching hyperbolas. (4.75 mins) by David Gould.
4. Worked examples: Video – Intersection of a line and a hyperbola. (4 mins) by ExamSolutions.
5. Worked examples: Video – Intersection of hyperbola and linear graphs (3.4 mins) MYJ by Ian Bailey-Mortimer.
6. Practice: Worksheet and solutions – PDF – Graphing and Properties of Hyperbolas by Kuta Software.
7. Practice: Worksheet and solutions – PDF – Graphing Hyperbolas by Edia.

7J Further transformations of graphs 10A

1. Instruction with examples: Video – Further transformations of graphs covering circles, exponentials and hyperbolas. (56 mins… it’s a long one!) by Math,you?
2. Practice: Textbook –  Go to page 580 and select various questions. The answers are on 899 (Remember, we discussed the textbook we are using right back at the start of this page.) MYJ

Extra resources

1. Practice: Questions with solutions – Web Page – Section 4.2 : Sketching parabolas by Paul’s Online Notes.
2. An aside: PDF –  If you are interested, here is a guide prepared for teachers of year 10 parabolas. It has lots of worked examples and takes you on a journey from the simple to the more difficult as well as applications. By AMSI.
3. Worked examples with more problems and solutions: – PDF – Sketching quadratics by Pearson EdExcel. MYJ
4. Practice: Questions with solutions – PDF – Grade 10 Academic Math Quadratics 2 Practice Test A by Mathwiz.ca.

Chapter 8  Probability

8A Review of probability CONSOLIDATING

1. Instruction: Video – Review of probability | Year 10 Probability includes definitions and some worked examples. ( Approx 16 mins) by LMKMaths. (Note: A trial is a single experiment, such as a single roll of a die, an outcome is a possible result of an experiment and a long-run proportion is the experimental probability for a sufficiently large number of trials.)
2. Instruction: Video – Theoretical Probability of Simple Events (7 mins) by Charly Baker.
3. Instruction: Video – Experimental Probability ( 5.5 mins) by Anywhere Math.
4. Worksheet with answers: PDF – Probability Worksheet #9 by Mr Calise.

8B Unions and intersections

1. Instruction: Video – Basics of Probability: Unions, Intersections, and Complements (15.25 mins) by jbstatistics.
2. Alternative option: Instruction: Video – Year 10 Maths 8B Unions and Intersections (23.25 mins) by Shane Underwood.
3. Alternative option: Instruction: Video – Set Notation (goes through unions, intersections, complements, and a Venn diagram).
4. Instruction with worked problems: Video –Two Way Tables (6 mins) by Miss D Maths.
5. Alternative option: Instruction with worked problems: Video –Two way tables + probability (higher) (7 mins) Yr 10 by Hodge Hill College.
6. Alternative option: Instruction with worked problems: Video – Two-way Tables – Year 10 (13.3 mins) by Teaching With Miss Dunford.
7. Instruction: Web Page – Venn Diagram Union And Intersection by Third Space Learning.
8. Worksheet with answers: PDF – Operations with sets – Union, Intersection and Complement by Glendale Community College.
9. Worksheet with answers: PDF– MATH 120 Section 8.2 Union, Intersection, Complement of Events & Odds by Montgomery College, and here are the answers.
10. Worksheet with answers: PDF – Two Way Tables by Corbett Maths.

8C The addition rule

1. Instruction: Video – Mutually Exclusive vs. Independent Events (4 mins) by Ace Tutors.
2. Instruction: Video – Addition Rule (OR) for Probability Explained! (9 mins) by Math Man McGreal.
3. Worked problem: Video – An example of the addition rule for probability (6 mins) by Dane McGuckian.
4. Worked problem: Video – Another example of the addition rule for probability (7 mins) by Dane McGuckian.
5. Worked problem: Video – And another example of the addition rule for probability (4.4 mins) by TwoSigma
6. Examples with problems and solutions: Web Page – The addition rule for probability by MathGoodies.com.
7. Worksheet with answers: Pdf – The addition rule of probability worksheet by Edia.

8D Conditional probability

1. Instruction: Video – Intro to Conditional Probability (11 mins) by Wrath of Math.
2. Instruction: Video – Conditional Probability With Venn Diagrams & Contingency Tables (Two-way Tables) (Approx 16.5 mins) by The Organic Chemistry Tutor.
3. Worked problem: Video – An example of Conditional Probability, part 1 128-1.8.a (Approx 10 mins) by HCCMathHelp
4. Worked problem: Video – An example of Conditional Probability, part 2 128-1.8.b (5.75 mins) by HCCMathHelp
5. Worked problem: Video – An example of Conditional Probability (1 of 7: A surprising example) (Approx 10.5 mins) by Eddie Woo.
6. Worksheet with answers: PDF – Conditional Probability (Higher) worksheet. PhysicsAndMathsTutor.Com. Here are the worked solutions.
7. Worksheet with answers: PDF – Conditional Probability Practice Questions. CorbettMaths.

8E Two-step experiments using tables

1. Instruction: Video – Two-step experiments using tables (18 mins) by LMK Maths.
2. Instruction: Video – With or Without Replacement (6.75 mins) by Quick Math.
3. Instruction: Video – Showing sample space for a two-step experiment with an array (with replacement) (3.4 mins) by Mr H Vids.
4. Instruction: Video – Showing the sample space for a two-step experiment without replacement (3 mins) by Mr H Vids.
5. Instruction: Video – Probability – Creating A Sample Space Using A Table (Approx 2.5 mins) by Rachel Colwill.
6. Instruction: Video – Probability – Showing ‘Sample Space’ in a table (3 mins) by S McF.
7. Sequence of learning: Web Page – List outcomes in a sample space diagram (two-way table) and calculate probabilities by Oak National Academy.
8. Worksheet with answers: PDF – Two-way tables by Corbett Maths.
9. Worksheet with answers: PDF – Two-way tables – Exam Style. by Corbett Maths. Answers to this.

8F Using tree diagrams

1. Instruction: Video – What are tree diagrams (4.5 mins) by Minity Maths.
2. Instruction: Video – Multi step experiments using tree diagrams (30 mins) by LMK Maths.
3. Instruction, worked examples and problems with solutions: Web Page – Probability Tree diagram by Third Space Learning.
4. Worksheet with answers: PDF – Tree diagrams worksheet by Corbett Maths. Answers can be found here.
5. Worksheet with answers: PDF – Probability Trees Exam by Maths Genie. Answers can be found here.

8G Independent events

1. Instruction: Video – What is independence (probability)? (1.5 mins) by IntuitiveML
2. Instruction: Video – Probability of independent events (15.25 mins) by LMKMaths.
3. Instruction with example: Video – Probability Independence Test (Approx 3 mins) by G Conlon.
4. Instruction with examples: Video – Independent Probability (WITH Replacement) (9.6 mins) by Natalie DeBaldo.
5. Worksheet with answers: PDF – Exam style independent probability worksheet by Corbett Maths. And here are the answers.
6. Instruction, examples with problems and solutions: Web Page – Probability of A and B for Independent Events by RadfordMathematics.

More general probability resources:

1. Practice exam with answers: PDF – General conditional probability exam by Maths Genie. Here are the answers.
2. Practice exam with answers: PDF – Tree diagram, etc. probability exam by Maths Genie. Here are the answers.

Chapter 9  Statistics

9A Collecting and using data

1. Instruction: Video – What is a survey? (Approx 2 mins) by LearnFree.
2. Instruction: Video – Collecting and using data: population/sample, classifying data and representative samples. (9 mins) by Hakea Math & Science.
3. Alternate Instruction: Video – Collecting data: population/sample, classifying data with examples. (6 mins) by Miss D Maths.
4. Instruction: Video – What is a representative sample? (2.4 mins) by Stats4SD.
5. Definitions: PDF – Basic Statistics Vocabulary by University of Montana.
6. Worksheet with answers: PDF – Types of Data. by DobMaths.
7. Instruction and interactive quiz with answers: Web Page – Types of Data in Statistics. by BYJU’s
8. Workbook with answers: PDF – Statistics Practice Booklet. Do the first worksheet to practice Populations and Samples. by washoeschools.net (Answers at the end of the booklet.)

9B Review of statistical graphs CONSOLIDATING

1. Instruction: Video – Review of statistical graphs (8.3 mins) by Maths Factory.
2. Instruction: Video – What graph types do you choose based on the variables you are investigating? (13 mins) by PhysicsHigh.
3. Instruction: Video – Revision of measures of centre: mean, median and mode. (5.7 mins) by Maths with Mr. J.
4. For interest Instruction: Video – Science of Data Visualization | Bar, scatter plot, line, histograms, pie, box plots, bubble chart (Approx 7 mins) by Prof. Ryan Ahmed.
5. Practice: Textbook –  Go to page 665 and select various questions. The answers are on 916 (Remember, we discussed the textbook we are using right back at the start of this page.)

9C Summary statistics

Summary statistics give you information about your data. This section is interested in summary statistics related to measures of spread and location.

1. Instruction with worked example:Video – Five number summary / five figure summary (4 mins) by Joel Speranza Math.
2. Instruction with a worked example:Video – Measures of spread (3 mins) by Joel Speranza Math.
3. Instruction with worked examples: Video – Summary Statistics for Year 10 (13.3 mins) by Hakea Math & Science.
4. Worksheet with answers: PDF – Five number summary by https://www.mathworksheets4kids.com
5. Worksheet with answers: PDF – Interquartile range and range worksheet by Cazoom Maths.

9D Box Plots (Also called Box and Whisker Plots)

1. Instruction: Video – Box and Whisker Plot Explained. (6.5 mins) by Mashup Math.
2. Instruction: Video – Parts of a Box and Whisker Plot (Box Plot) (4.7 mins) by Math with Mr J.
3. Instruction: Video – How to Make a Boxplot with Outliers (6.4 mins) by Midnight Math Tutor.
4. Instruction: Video – How to compare & contrast data sets using parallel box-plots in statistics (6.7 mins) by The Maths Studio.
5. Instruction: Web Page – 14.05 Compare data sets by MathSpace. Stop when you get to Different graphs of the same data.
6. Worksheet with answers: PDF – Box Plots by Corbett Maths. Here are the answers for this worksheet.
7. Worksheet with answers: PDF – Interpreting a Box & Whisker Plot by Livingston.
8. Worksheet with answers: PDF – GCSE (1 – 9) Box Plots by MathsGenie and here are the answers.

9E Standard deviation

1. Instruction: Video – The Standard Deviation (and Variance) Explained Simply (7.75 mins) by Datatab.
2. Instruction with worked examples: Video – Calculating the standard deviation ( 4.3 mins) by Kirkman’s Academy.
3. Instruction: Video – Learn Standard Deviation – Formula & Examples | Step-by-Step (12.6 mins) by Math and Science.
4. Worked examples:  Video – Variance and Standard Deviation: Sample and Population Practice Statistics Problems (13 mins) by Statistics Dojo.
5. Practice: Worksheet with answers – PDF – Standard Deviation Worksheet by GlowScotland.

9F Time-series data

1. Instruction: Video – Time Series Data (4.5 mins) by Miss D Maths.
2. Alternate Instruction: Video – Time Series Data (4.5 mins) by Hakea Math & Science.
3. Practice: Textbook –  Go to page 697 and select various questions. The answers are on 920 (Remember, we discussed the textbook we are using right back at the start of this page.)

9G Bivariate data and scatter plots

1. Instruction: Video – Introduction to Bivariate data and explanatory (independent) and response (dependent) variables (8.75 mins) by Joel Speranza
2. Instruction: Video – Interpreting Scatterplots: Association, Strength & Outliers (5.7 mins) by Joel Speranza
3. Instruction and exercises: Web Page  – 6.02 Scatterplots by Mathspace.
4. Worksheets with answers: Web Page – Various worksheets and answers can be found from this page on Mr Barton Maths.
5. Worksheet with answers: PDF – Constructing Scatter Plots by Education.com
6. Worksheet with answers: Doc – Scatter Plots Worksheet Including Understanding the Dependent (response) and Independent (explanatory) Variables by Jensen.

9H Line of best fit by eye

1. Instruction: Video – Line of best fit by eye. (5 mins) by Mr Kettle’s Maths.
2. Alternate Instruction: Video – Line of best fit by eye. (Approx 9 mins) by Sheldon Collier.
3. Practice: Textbook –  Go to page 716 and select various questions. The answers are on 921 (Remember, we discussed the textbook we are using right back at the start of this page.)

9I Linear regression using technology

1. Instruction: Video – Simple Linear Regression – Explained Simply (2 mins) by RegenerativeToday
2. Instruction: Video – All about regression and how it can be applied to machine learning and AI. (4.5 mins) by What’s AI by Louis-François Bouchard.
3. Instruction with worked problem: Video – Year 10 Statistics Bivariate Regression Line Example 1 (Approx 7 mins) by High School Maths with Mr George.
4. Instruction with worked problem: Video – Linear Regression with calculator & Summary of Statistics (17 mins) using a Casio FX-82AU Plus II calculator.
5. Instruction with worked problem: Video – Linear Regression (7.7 mins) using Excel.
6. Instruction with worked problem: Video – Linear Regression (10.5 mins) using the TI NSpire CX calculator.
7. Instruction with worked problem: Video – Classpad for scatter plots and linear regression (Approx 4 mins) using the ClassPad.

Chapter 10 Logarithms and polynomials

10A Introducing logarithms

1. Instruction: Video – Logarithms explained (3.5 mins) by Steve Kelly on TED-Ed.
2. Alternate Instruction: Video – Logarithms explained Bob Ross style (9 mins) by Tibees. This is a little out there in terms of an explanation but I think is a little more interesting. (3.5 million views and counting tells me it might be more understandable by the masses too.)
   And because people can struggle a little with logs, I am linking even more videos here.
3. Instruction: Video – Introduction to Logarithms (1 of 2: Definition) (8 mins) by Eddie Woo.
4. Instruction: Video – Introduction to Logarithms (2 of 2: Numerical examples) (4 mins) by Eddie Woo.
5. Practice: Worksheet with solutions – PDF – Basic logarithms worksheet by Chino Valley Unified School District. Here are the solutions but you’ll need to go to the correct page (3rd and 4th pages).
6. Practice: Worksheet with solutions – PDF – Intro to logarithms by FlippedMath.com. (Don’t worry about the graphing questions or the extension at the end of the paper.)

10B Laws of logarithms

1. Instruction: Video – Laws Of Logarithms (Only 2 mins) by StudySession.
2. Worked Example: Video – Logarithm Addition With Same Base Example (1.3 mins) by StudySession.
3. Worked Example: Video – Logarithm Subtraction With Same Base Example (1.5 mins) by StudySession.
4. Worked Example: Video – Solve For X Logarithmic Equation Example 1 (2.25 mins) by StudySession.
5. Instruction: Video – Log_a1 = 0 (a ≠ 1) using a⁰ = 1 (0.5 mins) by Clarity Education (Note they simply use b instead of an a in their proof.)
6. Instruction: Video – Log_aa = 1 using a¹ = a (0.7 mins) by Clarity Education (Note they simply use b instead of an a in their proof.)
7. Instruction: Video – Log_a  1/x = Log_a x^-1 = –Log_ax from law 3. (1 mins) by Clarity Education (Note they have used b instead of an a for the base and they have used a instead of an x for the variable.)
8. Practice: Exercises – Textbook – Select a variety of questions from the textbook (mentioned at the top of this page) on page 745 and the answers are on page 927.

10C Solving exponential equations using logarithms

1. Instruction with examples: Video – Solving exponential equations using logarithms. (14 mins) by LMKMaths.
2. Worked Examples: Video – Solving Exponential Equations With Different Bases Using Logarithms (11 mins) by The Organic Chemistry Tutor.
3. Worked Example: Video – Year 10 A Exponential Equations Example 5 (4.5 mins) by High School Maths with Mr George.
4. Practice: Worksheet with answers – PDF – Solving Exponential Equations with Logarithms by Kuta Software.
5. Practice: Worksheet with answers – Web Page – Solving Exponential Equations including examples by Paul’s Online Notes.
6. Practice: Worksheet with answers – Web Page – Solving Exponential Equations worksheet generator by Edia.
7. Practice: Worksheet with answers – PDF – Solving Exponential Equations by Paula Kelly mmc.

10D Introducing polynomials

1. Instruction: Video –  What are polynomials? (2.5 mins) by FuseSchool.
2. Instruction with examples: Video – Polynomials – (38.25 mins) by LMKMaths.
3. Examples: Video – What are polynomials used for? Real-life situations. (5.5 mins) by Teach Me Animated Math.
4. Instruction with examples: Video – Are these polynomials or not? (4.6 mins) by Brian McLogan.
5. Instruction: Video – What is a function? (9.4 mins) by Eddie Woo.
6. Practice: Exercises – Textbook – Select a variety of questions from the textbook (mentioned at the top of this page) on page 755 and the answers are on page 928.

10E Expanding and simplifying polynomials

1. Instruction: Video – Expanding polynomials (Foil Method Algebra, Binomials, Trinomials, Polynomials, Multiplication With Exponents) and simplifying. (18 mins) by The Organic Chemistry Tutor.
2. Practice: Exercises – Textbook – Select a variety of questions from the textbook (mentioned at the top of this page) on page 761 and the answers are on page 929.

10F Division of polynomials and Applications and problem-solving

1. To do the division of polynomials, you need to understand the long-division algorithm which can be remembered using the Dad, Mum, Sister, Brother and Rover the dog analogy where Dad is Divide, Mum is Multiply, Sister is Subtract, Brother is Bring Down and Rover stands for Repeat or Remainder.   This video looks at it using normal numbers.  (4.5 mins) by Math Magician.
2. Instruction with example: Video – Long Division With Polynomials – The Easy Way! (12.2 mins) by The Organic Chemistry Tutor.
3. Alternate Instruction with example: Video – Long Division of Polynomials (6.5 mins) by 1st Class Maths.
4. Practice: Worksheet with answers – PDF – Dividing polynomials by Kuta Software.
5. Practice: Examples and problems with answers – PDF – Division of polynomials by Hunter College.

10G The remainder and factor theorems

1. Instruction with examples: Video – The remainder and factor theorems (31.75 mins) by LMKMaths.
2. Practice: Exercises – Textbook – Select a variety of questions from the textbook (mentioned at the top of this page) on page 769 and the answers are on page 930.

10H Solving polynomial equations

1. Instruction with examples: Video – Solving Polynomial Equations (1 of 2: Using the factor theorem) (9.3 mins) by Eddie Woo.
2. Instruction with examples: Video – Solving Polynomial Equations (2 of 2: Determining solutions) (8.6 mins) by Eddie Woo.
3. Instruction with examples: Video – Remainder Theorem and Synthetic Division of Polynomials (10.5 mins) by The Organic Chemistry Tutor.
4. Instruction with example: Video – Reminder of the Null Factor Law. (2 mins) by Piece of Pi.
5. Practice: Exercises – Textbook – Select a variety of questions from the textbook (mentioned at the top of this page) on page 775 and the answers are on page 930.

10I Graphs of polynomials

Here is a sequence of graphing by Eddie Woo and whilst he has recorded these teaching a higher grade maths class, the majority of it is still relevant to this year 10 topic.

1. Instruction: Video – Graphing Polynomials (1 of 4: Fundamental graphs) (8.75 mins) by Eddie Woo. (I’ve copied the video to start at 152 seconds as it is more relevant from this point on.)
2. Instruction: Video – Graphing Polynomials (2 of 4: Horizontal translation) (8.5 mins) by Eddie Woo.  This refers to the free online Desmos graphing tool which is fabulous for visualising functions.
3. Instruction: Video – Graphing Polynomials (3 of 4: Vertical translation) (9 mins) by Eddie Woo. 
4. Instruction: Video – Graphing Polynomials (4 of 4: Dilation) (14.3 mins) by Eddie Woo.
5. Worked Example: Video – Sketching a cubic function (8 mins) by Maths Learning Centre UofA.
6. Worked Examples: Video – Sketching cubics (6 mins) by Haywood’s Math.
7. Worked Examples: Video – Sketching Polynomials (Quartic Equations) (12.5 mins) by A Level Maths Tutor.
8. Practice: Exercises – Textbook – Select a variety of questions from the textbook (mentioned at the top of this page) on page 782 and the answers are on page 931.