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### Unit 3DMAT – Yr12 (Opt 8-9) Mathematics

# TOPIC TITLE
1 Self Assessment Self Assessment – Unit 3DMAT – Yr12 (Opt 8-9)
Objective: Assessment
2 Algebra- formulae Equations resulting from substitution into formulae.
Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.
3 Algebra- formulae Changing the subject of the formula.
Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.
4 Simultaneous equns Simultaneous equations
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.
5 Simultaneous equns Elimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.
6 Simultaneous equns Elimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.
7 Algebra-factorising Simplifying easy algebraic fractions.
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.
8 Algebraic fractions Simplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
9 Algebra-negative indices Algebraic fractions resulting in negative indices.
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.
10 Factorisation Factorisation of algebraic fractions including binomials.
Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.
11 Algebraic fractions-binomial Cancelling binomial factors in algebraic fractions.
Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.
12 Absolute value or modulus Solving for the variable
Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value.
13 Absolute value or modulus Solving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
14 Algebra-highest common factor Highest common factor.
Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.
15 Factors by grouping Factors by grouping.
Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.
16 Difference of 2 squares Difference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
17 Common fact and diff Common factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
24 Sum/diff 2 cubes Sum and difference of two cubes.
Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.
25 Algebraic fractions Simplifying algebraic fractions.
Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.
26 Simultaneous equns Applications of simultaneous equations
Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.
27 Simultaneous equations Number of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
28 Linear systems Optimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
29 Linear systems Linear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
30 Linear systems Row-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
31 Linear systems Gauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.
32 Calculus-differential, integ Increasing, decreasing and stationary functions.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.
33 Calculus First Derivative – turning points and curve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.
34 Calculus-2nd derivative The second derivative – concavity.
Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.
35 Calculus – Computation volumes Computation of volumes of revolution
Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.
36 Geometry-reasoning Further difficult exercises involving formal reasoning
Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.
37 Geometry-congruence Congruent triangles, Test 1 and 2
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent.
38 Geometry-congruence Congruent triangles, Test 3 and 4
Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.
39 Geometry-congruence Proofs and congruent triangles.
Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.
40 Similar triangles Similar triangles
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar.
41 Similar triangles Using similar triangles to calculate lengths
Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles.
42 Overlapping triangles Examples involving overlapping triangles
Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles.
43 Geometry – triangles Triangle inequality theorem
Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.
44 Circle Geometry Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.
Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro
45 Circle Geometry Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.
Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.
46 Circle Geometry Theorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.
47 Circle Geometry Theorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’
48 Circle Geometry Theorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.
49 Circle Geometry Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.
Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.
50 Circle Geometry Theorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.
51 Circle Geometry Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
52 Logic Inductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
53 Logic Definition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
54 Logic Indirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
55 Logic Mathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
56 Logic Conditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
57 Circle Geometry-chords Theorem – The products of the intercepts of two intersecting chords are equal.
Objective: On completion of the lesson the student will be able to prove that ‘The product of the intercepts of two intersecting chords are equal.’, and use this result to complete questions that require this knowledge.
58 Circle Geometry-tangents Theorem – The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point. [Including Alternate Proof]
Objective: On completion of the lesson the student will be able to prove and apply ‘The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point ‘, and use this result to complete q
59 Circle Geometry-cyclic quads Theorem – If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic.
Objective: On completion of the lesson the student will be able to prove that a quadrilateral is cyclic using the supplementary angles theorem.
60 Circle Geometry-subtending Theorem – If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic.
Objective: On completion of the lesson the student will be able to prove that ‘ If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic’, and use this result to complete the ques
61 Circle Geometry Theorem – When circles touch, the line of the centres passes through the point of contact.
Objective: On completion of the lesson the student will be able to prove that ‘ When two circles touch, the line of the centres passes through the point of contact’, and use this result to complete questions that require it.
62 Circle Geometry-non-collinear Theorem – Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points.
Objective: On completion of the lesson the student will be able to prove that ‘ Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points’, and use this knowled
63 Exam Exam – Unit 3DMAT – Yr12 (Opt 8-9)
Objective: Exam