Year 7
Title  Description  
Dot Grid  Dots spaced at 1cm apart. Mainly for Pick’s formula and transformations (reflections, rotations & translations).  
Straight Line Geometry  Angles on straight lines and in triangles.  
Transformations  This worksheet explores the relationship between reflection and the other two transformations (translation and rotation). Includes solutions. 
Year 8
Title  Description  
Composite Figures  Exercises on calculating the area and perimeter of composite figures.  
Summary of Line Forms  In coordinate geometry, straight lines can be expressed in a variety of equation forms that are suited to different purposes and reveal different characteristics of the resultant graph.  
Explained Solution AT  2009 Assessment Task  
Graph Stories  Interpretation of the situation depicted by various twodimensional graphs.  
Inscribed Circles  Investigation of the areas of circles inscribed within different polygons. Informal introduction to the concept of a limit.  
Quadrilateral Properties  Proofs of quadrilateral properties, based only on the minimal definition of each quadrilateral.  
Rhombus Investigation  Proof that the diagonals in a rhombus are perpendicular.  
Set Theory Quiz  Topic test.  
Similarity Quiz  Topic test – includes sample solutions and marking guidelines.  
Spheres: Volume & SA  Investigation based on the approximations and experiments of Archimedes. 
Year 9
Title  Description  
Coordinate Geometry PreTest  This test assesses students for their grasp of year 8 coordinate geometry. Worked solutions included.  
Coordinate Geometry Proofs: Quad. Sufficiency Conditions  Incorporates understanding of foursided Euclidean figures with methods in coordinate geometry (gradients, distances, etc).  
Curve Sketching: Rational Functions  Steps for how to accurately draw the graphs of rational functions (for instance, y = (x+1) / ((x2)*(x4)) ).  
Deriving the Index Laws  The rules that apply when handling indices (exponents) are often learnt by rote without understanding where they come from. It’s straightforward to see that they all arise from the basic definition of exponentiation.  
Number System History  An overview of how our understanding and representation of numbers has progressed over the centuries.  
Oblique Asymptotes  Stepbystep guide of how to identify and locate the equations of asymptotes that are neither horizontal nor vertical.  
Solving Cubic Equations  Guide on how to find the roots of a thirddegree polynomial.  
Introduction to Solving Polynomial Equations  Includes derivation of Remainder and Factor Theorem.  
Polynomials Topic Test  Includes fully worked solutions.  
Synthetic Division  Once you learn it, you’ll never use long division to divide through polynomials again.  
Solving Quadratic Equations  Overview of factorising, completing the square and quadratic formula to solve seconddegree polynomials.  
Intercepts on Parallel Lines  Derivation of the geometric theorem, “parallel lines preserve the ratios of intercepts on transversals”.  
Weekly Quiz Template  9C (2010) template.  
Program Summary  Year 9 JRAHS program 
Videos
Recorded from actual lessons delivered in my classroom, sometimes divided up into sections for convenience. These can also be browsed through on the Maths playlist at WooTube. 


Polynomial Remainders  Worked example of a question related to remainders generated by dividing polynomials of certain degree, where the remainders themselves also happen to be polynomial expressions. 
Year 10
Title  Description  
Absolute Value Practice Tests  Two practice tests that assess your understanding of the core skills in the introduction to Absolute Value (i.e. evaluating expressions, solving inequalities, and simple graphing). Scanned solutions included.  
Algebra Revision  A quick refresher of Expanding & Factorising algebraic expressions.  
Combining Functions  Graphing functions that consist of different functions combined through the four basic operations.  
Constructions  Includes handdrawn solutions. This worksheet incorporates some circle properties learnt in years 89, so some of the later questions are inappropriate for a year 7 level.  
Coordinate Geometry Test  Topic test.  
Gradients of Perpendicular Lines (Proof)  An alternative proof for demonstrating that perpendicular gradients are negative reciprocals of each other.  
Graphing & Trigonometric Identities & Equations Test  Combined topic test.  
Perpendicular Distance Formula (Derivation)  Deriving the formula for the distance between a point and a line, by means of the standard distance formula and some fancy algebraic footwork.  
Probability Test  Topic test.  
Program Summary  Year 10 JRAHS program  
The Pythagorean Relationship  Includes derivation of the trigonometric identity and practice exercises.  
Quadratic Theory Revision  Advanced year 9 level quadratic questions, to refresh the memory and prepare for the year 10 topic.  
Sum & Product of Roots  Derivation of Viète’s formulas for quadratic and cubic equations.  
Trigonometry & Bearings  Exercises for consolidation of trigonometry in the context of bearings. Diagrams essential!  
Trigonometric Functions & the Unit Circle  Investigation of the relationship between the sine, cosine and tangent ratios and the unit circle, by means of coordinate geometry techniques.  
Trigonometry Review  Short series of questions designed to review the core skills and formulae in Year 10 Trigonometry.  
Scans  Handwritten solutions to exercises or tests set in class.  
Radian Measure (Fitzpatrick, 2U Ex 17(b))  
Graphing Trigonometric Functions  Introduces amplitude, period, domain and range in the context of the graphs for sin, cos and tan.  
Intercepts on Circles: Challenging Questions  Activity that consolidates understanding of the relationship between intercepts on chords, tangents and secants. Includes solutions. 
Year 11
Title  Description  
Calculating Tangents & Normals  Using calculus, we can now find the equation of a tangent or normal to any differentiable function at any point within its domain.  
Chain Rule  For differentiating functions within functions. Includes instances of how the chain rule plays out for exponentiated functions, exponentials, logarithms and trigonometric functions.  
Deriving Powers of x  Derivation of the result for dy/dx when y = x^n, where n is a constant.  
Differentiating ‘Unnatural’ Exponentials  Derivation of the result for dy/dx when y = a^x, where a is an arbitrary constant.  
Linear Trigonometric Equations  Illustrated worked solutions for finding angles that satisfy particular trigonometric equations.  
Locus of a Parabola  Finding the focus and directrix of a parabola, given its equation.  
Primitives  Introduction to the techniques required to find a function given its derivative.  
Trigonometric Expansions  Geometric deductive proofs of the sin(a+b) and tan(a+b) expansions. NB: this is 3Unit content.  
Trigonometry Review Worksheet  Includes questions and scanned handwritten solutions.  
Yr 11 2U Sample HalfYearly Test  Includes questions and scanned handwritten solutions.  
Quadratic Theory Topic Test  Includes questions and scanned handwritten solutions.  
Radian Measure Topic Test  Includes questions and scanned handwritten solutions. 
Year 12
Title  Description  
Exponential Growth & Decay  These questions are selected from past HSC papers and worked solutions are provided.  
Motion (JRAHS Questions)  Selected questions on the Motion topic from past JRAHS exams.  
2Unit Program Summary  Summary of the JRAHS Mathematics Program for the HSC 2Unit course. For full details on each dot point, see the full program on the intranet.  
Simpson’s Rule  This worksheet illustrates the use of Simpson’s Rule with examples of both the basic form (2 subintervals) and the expanded form (3+ subintervals). Also includes a comparison with integration as a method of calculating areas under curves.  
Marking Schemes  Each of the files below includes fully worked solutions for the relevant question, as well as a detailed marking scheme that describes where marks were allocated for each part.  
2Unit, 2008 Term 4, Q4  
2Unit, 2009 Term 1, Q1 

2Unit, 2009 Term 2, Q3  
2Unit, 2009 Trial, Q1  
Scans  Handwritten solutions to exercises or tests set in class.  
Rates of Change  
Rates of Change (Yr 12 Cambridge, 2U Ex 6F) 
Good morning here in Mexico and I think midnight in Australia Professor Woo: It gives me great pleasure to write from Tamaulipas, Mexico, I teach high school, working with students aged 15 to 18 years old. The class that my students and I share is differential calculus. I found you via a video on youtube ” the derivative, a visual approach ,” and I wonder , I found that after you mention that ” real learning real teaching ” and I agree with you. I downloaded some of their worksheets to work with my students. I will give credit to you, Professor Woo . Thank you very much for your input and I agree with you about how we share students and one professor of mathematics, so that students learn mathematics must present situations of context.
Best Regards
Eduardo Gomez de la Fuente
Agricultural Technology Center School No. 55
Padilla , Tamaulipas, Mexico
Eduardo, I’m really honoured to read about how my videos and resources have been helpful to you and your students! Thanks for writing to let me know, and good luck to you and your classes in the future. 🙂