| 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 |
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. |
| 3 |
Statistics |
Frequency histograms and polygons |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. |
| 4 |
Statistics |
Relative frequency |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. |
| 5 |
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. |
| 6 |
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. |
| 7 |
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. |
| 8 |
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 |
| 9 |
Statistic-probability |
Cumulative frequency |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. |
| 10 |
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. |
| 11 |
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. |
| 12 |
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. |
| 13 |
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. |
| 14 |
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. |
| 15 |
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. |
| 16 |
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 |
| 17 |
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. |
| 18 |
Statistics |
Scatter Diagrams |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. |
| 19 |
Coordinate Geometry-point slope |
Point slope form of a line |
| Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. |
| 20 |
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. |
| 21 |
Sequences and Series |
General sequences. |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. |
| 22 |
Sequences and Series |
Finding Tn given Sn. |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. |
| 23 |
Arithmetic Progression |
The arithmetic progression |
| Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts. |
| 24 |
Arithmetic Progression |
Finding the position of a term in an A.P. |
| Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression. |
| 25 |
Arithmetic Progression |
Given two terms of A.P., find the sequence. |
| Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms |
| 26 |
Arithmetic Progression |
Arithmetic means |
| Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means. |
| 27 |
Arithmetic Progression |
The sum to n terms of an A.P. |
| Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems. |
| 28 |
Geometric Progression |
The geometric progression. |
| Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts. |
| 29 |
Geometric Progression |
Finding the position of a term in a G.P. |
| Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems. |
| 30 |
Geometric Progression |
Given two terms of G.P., find the sequence. |
| Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression. |
| 31 |
Sequences and Series-Geometric means |
Geometric means. |
| Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means. |
| 32 |
Sequences and Series-Sum of gp |
The sum to n terms of a G.P. |
| Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P). |
| 33 |
Sequences and Series-Sigma notation |
Sigma notation |
| Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. |
| 34 |
Sequences and Series-Sum-infinity |
Limiting sum or sum to infinity. |
| Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems. |
| 35 |
Sequences and Series-Recurring decimal infinity |
Recurring decimals and the infinite G.P. |
| Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number. |
| 36 |
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. |
| 37 |
Sequences and Series-Superannuation |
Superannuation. |
| Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P. |
| 38 |
Sequences and Series-Time payments |
Time payments. |
| Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan. |
| 39 |
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 |
| 40 |
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. |
| 41 |
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. |
| 42 |
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. |
| 43 |
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. |
| 44 |
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. |
| 45 |
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. |
| 46 |
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. |
| 47 |
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. |
| 48 |
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. |
| 49 |
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. |
| 50 |
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. |
| 51 |
Pythagoras |
Pythagorean triples |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. |
| 52 |
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. |
| 53 |
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. |
| 54 |
Pythagoras |
Proofs of Pythagoras theorem |
| Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem |
| 55 |
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 |
| 56 |
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. |
| 57 |
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. |
| 58 |
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. |
| 59 |
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. |
| 60 |
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. |
| 61 |
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. |
| 62 |
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. |
| 63 |
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. |
| 64 |
Geometry – triangles |
Triangle inequality theorem |
| Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. |
| 65 |
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. |
| 66 |
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. |
| 67 |
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. |
| 68 |
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. |
| 69 |
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. |
| 70 |
Surface area |
Surface area of a triangular/trapezoidal prism. |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. |
| 71 |
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. |
| 72 |
Surface area |
Surface area of pyramids |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. |
| 73 |
Surface area |
Surface area of cones |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul |
| 74 |
Surface area |
Surface area of composite solids |
| Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. |
| 75 |
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. |
| 76 |
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. |
| 77 |
Volume |
Volume of pyramids and cones. |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. |
| 78 |
Volume |
Composite solids. |
| Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately. |
| 79 |
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. |
| 80 |
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. |
| 81 |
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. |
| 82 |
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. |
| 83 |
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. |
| 84 |
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. |
| 85 |
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. |
| 86 |
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. |
| 87 |
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. |
| 88 |
Quadratic equations |
Solving simultaneous quadratic equations graphically |
| 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.. |
| 89 |
Calculus |
Limits |
| Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. |
| 90 |
Calculus=1st prin |
Differentiation from first principles. |
| Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve. |
| 91 |
Calculus=1st prin |
Differentiation of y = x to the power of n. |
| Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n. |
| 92 |
Calculus-differential, integ |
Meaning of dy over dx – equations of tangents and normals. |
| Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve. |
| 93 |
Calculus-differential, integ |
Function of a function rule, product rule, quotient rule. |
| Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule. |
| 94 |
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. |
| 95 |
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. |
| 96 |
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. |
| 97 |
Calculus – Curve sketching |
Curve sketching |
| Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve. |
| 98 |
Calculus – Maxima minima |
Practical applications of maxima and minima |
| Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems. |
| 99 |
Calculus – Integration |
Integration – anti-differentiation, primitive function |
| Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions. |
| 100 |
Functions |
Definition, domain and range |
| Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range. |
| 101 |
Functions |
Notation and evaluations |
| Objective: On completion of the lesson the student will be understand different notations for functions. |
| 102 |
Functions |
More on domain and range |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation. |
| 103 |
Functions |
Domain and range from graphical representations |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations. |
| 104 |
Functions |
Evaluating and graphing piecewise functions |
| Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. |
| 105 |
Functions |
Functions combinations |
| Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. |
| 106 |
Functions |
Composition of functions |
| Objective: On completion of the lesson the student will understand composition of functions or a function of a function. |
| 107 |
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. |
| 108 |
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 |
| 109 |
Matrices |
Basic concepts – Matrices |
| Objective: On completion of the lesson the student will have had an introduction to matrices |
| 110 |
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. |
| 111 |
Matrices |
Scalar matrix multiplication |
| Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. |
| 112 |
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. |
| 113 |
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. |
| 114 |
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. |
| 115 |
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. |
| 116 |
Vectors |
Vectors |
| Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. |
| 117 |
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. |
| 118 |
Vectors |
2 vector addition in 2 and 3D (stage 2) |
| Objective: On completion of the lesson the student will understand and use component forms for vector resolution. |
| 119 |
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. |
| 120 |
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. |
| 121 |
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. |
| 122 |
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. |
| 123 |
Exam |
Exam – Year 12 – Further Mathematics Units 3 and 4 |
| Objective: Exam |
