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### NT Year 10 Extension Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Year 10 Extension
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Area Larger areas: square metre, hectare, square kilometre.
Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit.
3 Area Area of a trapezium.
Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.
4 Area Area of a rhombus.
Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.
5 Area Area of a circle.
Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.
6 Area Area of regular polygons and composite figures.
Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.
7 Surface area Surface area of a cube/rectangular prism.
Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.
8 Surface area Surface area of a cylinder and sphere.
Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.
9 Capacity Converting between volume and capacity using millilitres and litres
Objective: On completion of the lesson the student will be able to convert between units of capacity.
10 Volume/capacity Problems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
11 Volume Finding the volume of prisms
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.
12 Volume Volume of a cylinder and sphere.
Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.
13 Money Problems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
14 Sequences and Series-Compound interest Compound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
15 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
16 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.
17 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.
18 Surds Introducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.
19 Surds Some rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.
20 Surds Simplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.
21 Surds Creating entire surds
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds
22 Surds Adding and subtracting like surds
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.
23 Surds Expanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
24 Surds Binomial expansions
Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.
25 Surds Conjugate binomials with surds
Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds.
26 Surds Rationalising the denominator
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds.
27 Surds Rationalising binomial denominators
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions.
28 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.
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.
30 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.
31 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.
32 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.
33 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
34 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.
35 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.
36 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.
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 Geometry-quadrilaterals Using the Properties of a Parallelogram
Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram.
41 Geometry-quadrilaterals Proving a Shape is a Parallelogram
Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram.
42 Geometry-quadrilaterals Properties of the Rectangle, Square and Rhombus
Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values.
43 Geometry-quadrilaterals Properties of the Trapezium and Kite
Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.
44 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.
45 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.
46 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.
47 Pythagoras Find the hypotenuse
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.
48 Pythagoras Pythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
49 Pythagoras Find the hypotenuse Part 2
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds.
50 Pythagoras Calculating a leg of a right-angled triangle
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
53 Coordinate Geometry-straight line The straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
54 Coordinate Geometry-slope, etc. Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
55 Coordinate Geometry-equation of line General form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
56 Coordinate Geometry-intercept Slope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
57 Conic sections The parabola x. = 4ay
Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.
58 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.
59 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.
60 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.
61 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.
62 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.
63 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.
64 Fractional indices/exponents Fractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
65 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.
66 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.
67 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.
68 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.
69 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
70 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.
71 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.
72 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
73 Algebraic equations Solving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
74 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
75 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
76 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.
77 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.
78 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.
79 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.
80 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.
81 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.
82 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.
83 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.
84 Graphing binomials Binomial products [non-monic].
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.
85 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.
86 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.
87 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.
88 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.
89 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
90 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.
91 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.
92 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.
93 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 understand simple quadratic equations.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
101 Quadratic equations Completing the square
Objective: On completion of the lesson the student will understand the process of completing the square.
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
106 Graphing-cubic curves Graphing cubic curves
Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.
107 Absolute value equations Absolute value equations
Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio
108 Rect.hyperbola The rectangular hyperbola.
Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.
109 Exponential function The exponential function.
Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.
110 Log functions Logarithmic functions.
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
111 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.
112 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
113 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
114 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.
115 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.
116 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.
117 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
118 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
119 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.
120 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.
121 Statistics using a calculator Statistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
122 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.
123 Statistics Stem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
124 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
125 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
126 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.
127 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
128 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.
129 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.
130 Statistic-probability The complementary result ..
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.
131 Statistic-probability P[A or B] When A and B are both mutually and NOT mutually exclusive
Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.
132 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
133 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.
134 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.
135 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.
136 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.
137 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.
138 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.
139 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.
140 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.
141 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.
142 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.
143 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.
144 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.
145 Co-ordinate Geometry-Two point formula Two point formula: equation of a line which joins a pair of points.
Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.
146 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.
147 Co-ordinate Geometry-Parallel lines equations Parallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.
148 Co-ordinate Geometry-Perpendicular lines Perpendicular lines.
Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.
149 Co-ordinate Geometry-Inequalities Inequalities on the number plane.
Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.
150 Exam Exam – Year 10 Extension
Objective: Exam