Specialist Mathematics Yr12 by Texas Instruments

Units 3 and 4 Specialist Mathematics are completely prescribed and consists of six areas of study, Functions and Graphs, Calculus, Algebra, Vectors, Mechanics and Probability and Statistics. Students are expected to be able to apply techniques, routines and processes involving rational, real and complex arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs, differentiation, anti-differentiation and integration and inference with and without the use of technology. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated through each unit as applicable.

For more information on the Specialist Mathematics course, visit the VCAA website.

VIC: Specialist Mathematics Yr12 Classroom Activities	Download
Functions and Graphs
Functions and Graphs Test 2A Automated, self-check or print, the choice is yours, regardless of your choice this free assessment resource will save you time. TI-Navigator users send the test to students and have Navigator automatically complete all the corrections and data analysis. TI-Nspire users can have students immediately see their results. Even if you don’t have access to TI-Navigator or TI-Nspire use our PDF version of the test, in any case, this resource will save you time.	Download96
Circular Functions Test 3A This assessment resource is suitable for Chapter Three of the Cambridge VCE Year 12 Specialist Mathematics textbook. The assessment resource is available as a TI-Nspire file or PDF. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided. The companion PDF provides the same questions in a printed format.	Download31
$Absolute Value Thumb$ Absolute Value Worksheet designed to help students explore the absolute value function focusing specifically on notation such as f(\|x\|) and \|f(x)\|.	Download294
The Matrix Part 1 The focus of this activity is to help build conceptual understanding of transformations. This activity includes three video tutorial links, an interactive TI-nspire file, student questions, teacher answers, notes and recommendations. Students build an intuitive understanding of transforming points, a plane and ultimately simple functions all through a very visual and numeric environment. Students then use matrices and build understanding of the importance of the determinant.	Download15
Algebra
Circles on the Complex Plane Students start with the familiar real number line and basic geometry to develop a deeper understanding of circle equations on the complex plane.	Download54
Fundamental Theorem of Algebra Students generate random polynomials and observe the distribution of the zeros on the complex plane. From the distributions students are able to draw conclusions about the zeros, and therefore roots, of a polynomial in order to gain a better visual understanding of the Fundamental Theorem of Algebra.	Download55
Complex Numbers Test 1A Automated, self-check or print, the choice is yours, regardless of your choice this free assessment resource will save you time. TI-Navigator users send the test to students and have Navigator automatically complete all the corrections and data analysis. TI-Nspire users can have students immediately see their results. Even if you don’t have access to TI-Navigator or TI-Nspire use our PDF version of the test, in any case, this resource will save you time.	Download73
Preliminary Test 1A This assessment resource is suitable for Chapter One of the Cambridge VCE Year 12 Specialist Mathematics textbook. The assessment resource is available as a TI-Nspire file or PDF. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided. The companion PDF provides the same questions in a printed format.	Download19
Complex Numbers Test 4A This assessment resource is suitable for Chapter Four of the Cambridge VCE Year 12 Specialist Mathematics textbook. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided. The companion PDF provides the same questions in a printed format. Whichever option you chose, this free assessment resource will save	Download45
Taylor Polynomials The modulus and argument form of a complex number can be written in two ways, but how are they connected? ‘CIS’ format is a straight forward application of trigonometry, but what about e ? In this activity students explore the Taylor expansion of e^x and compare it with the Taylor expansion of cos(x) + sin(x) revealing a small difference relating to an alternating sequence of negative signs which can be adjusted using i. The activity removes the mystery and replaces it with a beautifully connected piece of mathematics	Download36
Calculus
Volume of a Football Students use calculus (solid of revolution) in both Cartesian and Parametric form to determine the volume of an ellipse when it is rotated around the axis to form an ellipsoid (football). Students also use arc-length to check measurements.	Download12
Melon Volume There are several ways you can work out the volume of a watermelon. This activity explores three different ways and in the process, improves student understanding of the approximation approach (slices) and the calculus formula.	Download4
Kicking Goals Watch Paul discusses the kick, we discuss the calculus and more. There is no doubt, a kick directly in front of goals is more likely to be successful, but where is the best place if you are near the boundary line? This activity starts with shooting for goals in soccer before heading out to the MCG and a magnificent kick from the boundary by AFL great, Paul Salmon. Did he find the best spot from where to launch his kick?	Download15
Bezier Curves (Advanced) It starts with an envelope, progressed to a curve and then a whole world of mathematics opens up. From the humble parabola, the curve is transformed and explored using algebra, parametric equations, rotations, calculus (including implicit differentiation); this activity has got the lot! Hours of enjoyment.	Download28
Slope Fields and Differential Equations Students use the interactive TI-nspire file and support video to gain an understanding of slope fields and differential equations. Students use a slope vector to manually produce a slope field and specific solution followed by the more automated option using the inbuilt calculator functionality. Students solve differential equations by hand and on TI-Nspire.	Download65
Solid of Revolution Liquid flows into a vase at a constant rate, sketch a graph of height vs time. Ever thought of actually doing this experiment to help students see that their sketch graphs really are correct? This activity links to a YouTube video so students can collect the data and use this to verify their sketch graph. The activity also includes modelling the curve and then eventually rotating it around the axis to produce a 3D image of the vase!	Download65
Astroid Students start by considering the motion of a point on the wheel of a bicycle. With the aid of interactive diagrams in the TI-Nspire document, students go on to explore the case when the wheel rotating inside another resulting in a hypocycloid. Students generate the parametric form of the equation, use compound and double angle formulas to generate the equivalent Cartesian equations and use calculus to analyse features of the curves, including gradient and arc length.	Download43
Trigonometry Powers In this activity students have the opportunity to learn a useful integration technique to help establish a rule for the integral of sine, cosine and tangent raised to increasing integer powers. A teacher slide presentation is provided to help work through the technique.	Download5
Differentiation Test 6A This assessment resource is suitable for Chapter Six of the Cambridge VCE Year 12 Specialist Mathematics textbook. The assessment resource is available as a TI-Nspire file or PDF. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided. The companion PDF provides the same questions in a printed format.	Download33
Arc Length and Surface Area Students calculate arc length of functions and surface area as functions are rotated around the x and y axis.	Download7
Probability and Statistics
Linear Transformations of a Random Variable This activity presents an intuitive approach to Linear Transformations of a random variable. If your students don’t understand E(aX+b) or Var(aX+b) then this is a good place to start. By building on a simple familiar example students can validate their intuition using the tables, graphs, spreadsheets and notation to build an better understanding of E(aX+b) and Var(aX+b).	Download21
Frank’s Farm When should linear transformations be applied to the combination of random variables? Frank has steers and heifers to sell, their weights are randomly distributed. What is the probability that four randomly selected steers and two heifers will exceed the required weight? What about the required price? A program is provided for students to simulate the problem so they can compare their theoretical calculations with the simulations.	Download33
Calculator BlackJack In the game of Blackjack, players continually draw cards until they can gain a score as close to 21 as possible, without going bust. In Calculator-Blackjack the random number generator is used to produce numbers between 0 and 1, these numbers are summed with the aim to keep this sum less than 1. On average how many cards do you think a player might have drawn to end up bust? This question is explored through statistics and sampling distributions. The answer to the question may surprise you!	Download56
Vectors
Vectors In Component Form Students experiment with an interactive 2 dimensional vector and observe the corresponding changes to its representation in i and j component form.	Download109
Scalar Resolute (Vectors) Understand the concept of scalar resolute, generate and use the formula for scalar resolute and solve related problems. Students learn how to define vectors in terms of matrices, calculate the dot product and magnitude required for the scalar resolute.	Download77
Vectors Test 2A This assessment resource is suitable for Chapter Two of the Cambridge VCE Year 12 Specialist Mathematics textbook. The assessment resource is available as a TI-Nspire file or PDF. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). Whichever option you chose, this free assessment resource will save you time.	Download53
Investigations
String Art This resource provides the foundation for a complete investigation incorporating, pseudo-coding, parametric and cartesian equations (relations), differential calculus including implicit and chain rule, proof and much more.	Download

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Functions and Graphs Test 2A

Circular Functions Test 3A

Absolute Value

The Matrix Part 1

Circles on the Complex Plane

Fundamental Theorem of Algebra

Complex Numbers Test 1A

Preliminary Test 1A

Complex Numbers Test 4A

Taylor Polynomials

Volume of a Football

Melon Volume

Kicking Goals

Bezier Curves (Advanced)

Slope Fields and Differential Equations

Solid of Revolution

Astroid

Trigonometry Powers

Differentiation Test 6A

Arc Length and Surface Area

Linear Transformations of a Random Variable

Frank’s Farm

Calculator BlackJack

Vectors In Component Form

Scalar Resolute (Vectors)

Vectors Test 2A

String Art

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