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ACT Year 12 Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Year 12
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Fractions Multiplying and dividing to obtain equivalent fractions
Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.
3 Fractions Reducing fractions to lowest equivalent form
Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.
4 Fractions Adding and subtracting fractions with different denominators
Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.
5 Fractions Multiplying fractions
Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.
6 Fractions Multiplying mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.
7 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
8 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
9 Fractions Finding reciprocals of fractions and mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).
10 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
11 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
12 Rules properties Using Order of Operation procedures (BIDMAS) with Fractions
Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.
13 Decimals Adding decimals with a different number of decimal places
Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.
14 Decimals Subtracting decimals with a different number of places
Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.
15 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
16 Decimals Dividing decimal fractions by whole numbers
Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers.
17 Decimals Multiplication of decimals by decimals to two decimal places
Objective: On completion of the lesson the student will be able to multiply decimals to two digits.
18 Decimals Dividing numbers by a decimal fraction
Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction.
19 Percentages Introduction to percentages, including relating common fractions to percentages
Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.
20 Percentages Changing fractions and decimals to percentages using tenths and hundredths
Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.
21 Percentages Changing percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
22 Percentages One quantity as a percentage of another
Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.
23 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
24 Algebraic expressions Algebraic expressions.
Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.
25 Algebraic expressions Substitution into algebraic expressions.
Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.
26 Algebraic expressions Directed numbers: addition and subtraction.
Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.
27 Algebraic expressions Directed numbers: multiplication and division.
Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.
28 Algebraic expressions Simplifying algebraic expressions: adding like terms.
Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.
29 Algebraic expressions Simplifying algebraic Expressions: subtracting like terms.
Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.
30 Rules for indices/exponents Adding indices when multiplying terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.
31 Rules for indices/exponents Subtracting indices when dividing terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base.
32 Rules for indices/exponents Multiplying indices when raising a power to a power
Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.
33 Rules for indices/exponents Multiplying indices when raising to more than one term
Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.
34 Geometry-angles Measuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
35 Geometry-angles Adjacent angles
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
36 Geometry-angles Complementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
37 Algebraic expressions Simplifying Algebraic expressions: combining addition and subtraction.
Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.
38 Algebraic expressions Simplifying algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.
39 Algebraic expressions Simplifying algebraic expressions: division
Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions.
40 Algebraic expressions Expanding algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.
41 Algebraic expressions Expanding algebraic expressions: negative multiplier
Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier.
42 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
43 Geometry-angles Vertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
44 Geometry-angles Angles at a Point.
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.
45 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
46 Geometry-problems Additional questions involving parallel lines
Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.
47 Algebraic equations Solving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
48 Algebraic equations Solving equations containing multiplication and division
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.
49 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
50 Algebraic equations Solving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
51 Geometry-triangles Angle sum of a triangle
Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.
52 Geometry-triangles Exterior angle theorem
Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.
53 Special triangles Special triangles
Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.
54 Geometry-quadrilaterals Quadrilaterals
Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.
55 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
56 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
57 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
58 Rules for indices/exponents Terms raised to the power of zero
Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.
59 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.
60 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.
61 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.
62 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.
63 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.
64 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.
65 Rules for indices/exponents Negative Indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.
66 Fractional indices/exponents Fractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
67 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.
68 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.
69 Algebra-inequalities Solving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
70 Fractional indices/exponents Complex fractions as indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.
71 Scientific notation Scientific notation with larger numbers
Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation.
72 Scientific notation Scientific notation with small numbers
Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.
73 Geometry-circles The equation of a circle: to find radii of circles
Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.
74 Geometry-circles The semicircle: to select the equation given the semi circle and vice versa
Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.
75 Scientific notation Changing scientific notation to numerals
Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.
76 Significant figures Significant figures
Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.
77 Geometry-parabola The parabola: to describe properties of a parabola from its equation
Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.
78 Geometry problems More difficult exercises involving parallel lines
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log
79 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.
80 Geometry-polygons Angles of regular polygons
Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.
81 Statistics Frequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
82 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
83 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
84 Statistics The range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
85 Statistic-probability The mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
86 Statistic-probability The mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
87 Statistic-probability The median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
88 Trigonometry-ratios Trigonometric ratios.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
89 Trigonometry-ratios Using the calculator.
Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.
90 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
91 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
92 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
93 Trigonometry-ratios Unknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
94 Trigonometry-compass Bearings – the compass.
Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.
95 Trigonometry-elevation Angles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.
96 Graphing binomials Binomial products.
Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression.
97 Graphing binomials Binomial products with negative multiplier
Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.
98 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
99 Statistic-probability Calculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.
100 Trigonometry-practical Trigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
101 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.
102 Graphing binomials Binomial products [non-monic].
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.
103 Squaring binomial Squaring a binomial. [monic]
Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial.
104 Squaring binomial Squaring a binomial [non-monic].
Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials.
105 Factorising Expansions leading to the difference of two squares
Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares.
106 Algebraic expressions-products Products in simplification of algebraic expressions
Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing.
107 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
108 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
109 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
110 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
111 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
112 Statistic-probability Rolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.
113 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.
114 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.
115 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.
116 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.
117 Quadratic trinomials Quadratic trinomials [monic] – Case 1.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
118 Factorising quads Factorising quadratic trinomials [monic] – Case 2.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
119 Factorising quads Factorising quadratic trinomials [monic] – Case 3.
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.
120 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
121 Trigonometry-sine rule The sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
122 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
123 Trigonometry-areas The area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
124 Statistic-probability Tree diagrams – not depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.
125 Statistic-probability Tree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.
126 Matrices Basic concepts – Matrices
Objective: On completion of the lesson the student will have had an introduction to matrices
127 Matrices Addition and subtraction of matrices
Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations.
128 Matrices Scalar matrix multiplication
Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.
129 Matrices Multiplication of one matrix by another matrix
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.
130 Matrices Translation in the number plane
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
131 Factorising quads Factorising quadratic trinomials [monic] – Case 4.
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.
132 Factorising quads Factorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
133 Factorising quads Factorisation of non-monic quadratic trinomials – moon method
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
134 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.
135 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.
136 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
137 Matrices Translation by matrix multiplication
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.
138 Statistics – grouped data Calculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
139 Statistics – Range and dispersion Range as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.
140 Statistics – Spread Measures of spread
Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.
141 Statistics – Standard deviation Standard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.
142 Statistics – Standard deviation Normal distribution
Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.
143 Statistics – Interquartile range Measures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range
144 Exam Exam – Year 12
Objective: Exam