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M1 MATHS

This is a totally free website for learning Years 7-12 Maths.

It can be used by students for independent learning, by schools as a supplement or substitute for a textbook, or as the basis of a school program.

Free support is offered to any teacher or school thinking of trialling the materials with students.

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    KNOWLEDGE Level 1 (Yr 7-10) Level 2 (Yr 7-10) Level 3 (Yr 7-10) Level 4 (Yr 7-10) Level 5 (Yr 7-10) Level 6 (Maths Methods)
    Number N1 N2 N3 N4 N5
    Algebra A1 A2 A3 A4 A5 A6
    Measurement M1 M2 M3 M4 M5 M6
    Geometry G1 G2 G3 G4
    Statistics S1 S2 S3 S4
    Probability P1 P2 P3 P4 P6
    Calculus C6

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N1:     Number - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is the pre-requisite modules.

N1-1 pdf   docx

Whole numbers

  • whole numbers to trillions
  • the terms: whole number, counting number, multiple, factor, even, odd, composite, prime, >, <
  • divisibility rules, products of prime factors
4 h
N1-2 pdf   docx

Fraction Meanings

  • understanding common fractions, decimal fractions and percentages
3 h
N1-3 pdf   docx

Fraction Conversions

  • converting between equivalent common fractions, between mixed numbers and improper fractions and between common fractions, decimal fractions and percentages
3 h N1-2
N1-4 pdf   docx

Negatives

  • understanding negative numbers and placing them on a number line
1 h
N1-5 pdf   docx

Calculators

  • using calculators to add, subtract, multiply and divide whole numbers, decimal fractions, common fractions and negative numbers
1 h N1-3 N1-4
N1-6 pdf   docx

Powers

  • whole number powers and square roots
  • expressing counting numbers as products of prime factors in power form
2 h N1-1 N1-5
N1-7 pdf   docx   Order of Operations
  • order of operations conventions
3 h
N1-8 pdf   docx

Common Fraction Operations 1

  • mental methods to perform simple operations on common fractions
  • approximation to perform more difficult operations
2 h N1-3
N1-9 pdf   docx

Decimal Operations 1

  • exact and approximate mental/written methods to add and subtract whole numbers and decimal fractions and multiply and divide whole numbers
3 h N1-3
N1-10 pdf   docx

Rounding and Approximation

  • rounding of numbers
  • approximate calculations
3 h N1-5, N1-9

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N2:     Number - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

N2-1 pdf   docx

Number Sets

  • the various sets of numbers
2 h
N2-2 pdf   docx

Fractions of Numbers

  • finding fractions (common, decimal and percent) of numbers
  • adding and subtracting percentages to/from numbers, including by multiplying
2 h
N2-3 pdf   docx

Rates

  • rates
4 h
N2-4 pdf  docx

Ratios

  • ratios
2 h N2-3
N2-5 pdf   docx

Decimal Operations 2

  • exact and approximate mental/written methods to multiply and divide whole numbers and decimal fractions
  • predicting when decimal fractions will terminate, recur and continue without recurrence
3 h N2-2
N2-6 pdf   docx

Negative Operations

  • mental/written methods to perform operations on positive and negative numbers
3 h
N2-7 pdf   docx

Common Fraction Operations 2

  • mental/written methods to add, subtract, multiply and divide common fractions
3 h

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N3:     Number - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.

N3-1 pdf   docx   Scientific Notation
  • scientific notation
2 h
N3-2 pdf   docx

Simple Interest

  • simple interest
3 h
N3-3 pdf   docx

Proportion

  • direct proportion
  • inverse proportion
2 h

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N4:     Number - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

N4-1 pdf   docx

Compound Interest

  • compound interest
3 h

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N5:     Number - Level 5

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 5 modules.

N5-1 pdf   docx

Simplifying Surds

  • simplifying expressions containing surds
2 h A5-4

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A1:     Algebra - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite modules.

A1-1 pdf   docx

Relations 1

  • using relations given as tables, as graphs and as sets of ordered pairs
3 h
A1-2 pdf   docx

Relations 2

  • the terms 'variable', 'independent' and 'dependent'
  • converting between different forms of a relation
3 h A1-1
A1-3 pdf   docx

Patterns

  • recognising patterns in sequences of numbers
  • determining whether a relation has a pattern (from both tables and graphs)
  • knowing that relations with patterns can be expressed as formulae
3 h A1-2
A1-4 pdf   docx

Discrete vs Continuous Relations

  • distinguishing discrete and continuous relations
  • presenting them appropriately as tables and graphs
2 h A1-3
A1-5 pdf   docx

Substitution

  • substituting for the independent variable in a formula and doing the arithmetic to find the value of the dependent variable
  • converting from formulae to other forms of a relation
  • substituting into formulae with more than one independent variable
3 h A1-4
A1-6 pdf   docx

Equations

  • substituting for the dependent variable in a formula and solving the resulting equation to find the value of the independent variable
  • algebraic shorthand
7 h A1-5

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A2:     Algebra - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 2 modules.

A2-1 pdf   docx

Writing Equations

  • solving problems by modelling them with equations
3 h
A2-2 pdf   docx

Collecting Terms

  • collecting terms to solve equations
2 h A2-1
A2-3 pdf   docx

Expanding

  • expanding brackets to solve equations
3 h A2-2

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A3:     Algebra - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 3 modules.

A3-1 pdf   docx

Undoing the Unknown

  • undoing the unknown to solve equations
3 h
A3-2 pdf   docx

Choosing the Unknown

  • writing and solving equations where the choice of unknown is not obvious
2 h A3-1
A3-3 pdf   docx

Squares and Fractions

  • solving equations with squares and fractions
4 h A3-2
A3-4 pdf   docx

Rearranging Formulae

  • changing the subject of a formula
2 h A3-3
A3-5 pdf   docx

Solving by Graphing

  • using a graphics calculator or computer graphing program,
  • graphing relations and solving equations using a graphics calculator
2 h
A3-6 pdf   docx

Domain and Range

  • domain and range
2 h
A3-7 pdf   docx

Functions

  • functions and the language of functions
3 h A3-6
A3-8 pdf   docx

Linear Functions

  • general form and graph shape
  • using y=mx+c to convert between formulas, tables and graphs for linear functions
  • finding the formula for a linear function from the gradient and points on the line
  • equation solution methods
  • applications
  • finding equations of lines on the Cartesian plane
  • parallel and perpendicular lines
  • mid-point of a line segment
5 h A3-7 M3-3
A3-9 pdf   docx

Reciprocal Functions

  • general form and graph shape
  • equation solution methods
  • applications
2 h A3-8
A3-10 pdf   docx

Index Laws 1-5

  • using the index laws for natural number powers
4 h A3-3

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A4:     Algebra - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

A4-1 pdf   docx

Factorising

  • factorising with circles
  • expanding and factorising quadratics
5 h
A4-2 pdf   docx

Quadratic Functions

  • general form and graph shape
  • equation solution methods
  • applications
  • writing and solving quadratic equations
6 h A4-1
A4-3 pdf   docx

Simultaneous Equations - Linear

  • solving pairs of linear simultaneous equations by equating, graphing, substitution, elimination and calculator
6 h
A4-4 pdf   docx

Inequalities

  • solving single-unknown inequalities and graphing the solutions on a number line
1 h
A4-5 pdf   docx

Algebraic Fractions

  • manipulating algebraic fractions
3 h A4-1
A4-6 pdf   docx

Algebraic Proofs

  • algebraic proofs
2 h

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A5:     Algebra - Level 5

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 5 modules.

A5-1 pdf   docx

Polynomial Functions

  • general form and graph shape
  • equation solution methods
  • applications
3 h
A5-2 pdf   docx

Index Laws 6-10

  • zero, negative and fractional indices
  • converting between fractional indices and surds
3 h
A5-3 pdf   docx

Power Functions

  • general form and graph shape
  • equation solution methods
  • applications
2 h A5-2
A5-4 pdf   docx

Exponential Functions and Logs

  • general form and graph shape
  • equation solution methods and logs
  • applications
5 h A5-2
A5-5 pdf   docx

Simultaneous Equations - General

  • solving pairs of general simultaneous equations by equating, graphing and substitution
  • solving larger sets of simultaneous equations
6 h A5-3 A5-4
A5-6 pdf   docx

Finding Formulae for Functions

  • finding formulae for functions from known value pairs
3 h A5-5
A5-7 pdf   docx

Model Functions

  • finding model functions for data using technology
3 h A5-6 S5-1
A5-8 pdf   docx

Calculator Equation Solving

  • the equation solving function of a graphics calculator
1 h A5-1
A5-9 pdf   docx

Algebraic Transformations

  • how changes to formulae affect their graphs and vice versa
4 h
A5-10 pdf   docx

Further Relations

  • composition of functions
  • inverse functions and y^2 = x
  • discontinuities
  • rational functions
  • piecewise and step functions
  • absolute value functions
  • circles
5 h A6-1 M6-1
A5-11 pdf   docx

Trigonometric Functions

  • general form and graph shape of sinusoidal functions
  • applications of sinusoidal functions
  • drawing graphs of sinusoidal functions from the formulas and vice versa
  • non-sinusoidal trigonometric functions
5 h A6-1 M6-1
A5-12 pdf   docx

Trigonometric Equations

  • solving equations derived from trigonometric functions
5 h A6-4 M6-2
A5-13 pdf   docx

Logs

  • the meaning of logs
  • logarithmic functions
  • equations from logarithmic functions
  • the log laws
  • logarithmic scales
7 h

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A6:     Algebra - Maths Methods

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 6 modules.

A6-1 pdf   docx

Combinations and the Binomial Expansion

  • multiplication principle
  • permutations and combinations
  • expansion of (x+y)^n
  • Pascal’s triangle
6 h
A6-2 pdf   docx

Arithmetic Sequences

  • recursive and explicit formulae
  • sum to n terms
4 h
A6-3 pdf   docx

Geometric Sequences

  • recursive and explicit formulae
  • sum to n terms
  • sum to infinity
3 h A6-2

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M1:     Measurement - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite modules.

M1-1 pdf   docx

Dimensions, Size and Mass

  • dimensions and measures of size in 1D, 2D and 3D
  • measuring and estimating length, area, volume and mass
5 h G1-1
M1-2 pdf   docx

Time 1

  • reading and recording times to the nearest minute on digital and analogue clocks
  • the order of the months and how many days in each
  • calendars
  • simple timetables
2 h
M1-3 pdf   docx

Unit Conversion

  • converting between units for mass and length, between L, mL and cm3 and between units for time
2 h M1-1 M1-2
M1-4 pdf   docx

Length, Area and Volume 1

  • calculating perimeters of polygons
  • calculating areas of rectangles and volumes of rectangular prisms
2 h M1-1

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M2:     Measurement - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 2 modules.

M2-1 pdf   docx

Graduated Scales

  • reading graduated scales
2 h
M2-2 pdf   docx

Time 2

  • determining start time, finish time and duration of events given the other two
  • measuring and estimating duration of events
  • converting between 12h and 24h time
  • at a given local time, finding the time in other parts of the country in winter and in summer
  • estimating times in other parts of the world
  • more difficult timetables
5 h
M2-3 pdf   docx

Length, Area and Volume 2

  • perimeters of circles and sectors of circles
  • approximating areas of non-rectangular shapes using an enveloping rectangle
  • areas of parallelograms, trapeziums, triangles, circles and sectors of circles
  • surface areas (flat faces only)
  • volumes of prisms and cylinders
6 h G2-2 N2-6 S2-1

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M3:     Measurement - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 3 modules.

M3-1 pdf   docx  

Pythagoras

  • using Pythagoras theorem to find any side of a right-angle triangle in 2- and 3-dimensional situations
3 h
M3-2 pdf   docx

Trigonometry

  • using tangent, sine and cosine ratios to find side lengths and angles in right-angle triangles
  • solving problems using trigonometry including those involving direction and angles of elevation/depression
6 h M3-1
M3-3 pdf   docx

Slope

  • slope as an angle
  • gradient
2 h M3-2
M3-4 pdf   docx

Length, Area and Volume 3

  • perimeters, areas and volumes of compound shapes
  • distinguishing length, area and volume formulae by inspection
  • the effect on length, area and volume of multiplying the dimensions of a shape
8 h M3-1

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M4:     Measurement - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 4 modules.

M4-1 pdf   docx

Length, Area and Volume 4

  • converting between different units for area and volume
  • volumes of pyramids, cones and spheres
  • surface areas of cylinders, cones and spheres
  • approximating volumes of irregular 3D shapes
4 h

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M5:     Measurement - Level 5

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 6 modules.

M5-1 pdf   docx

Unit Circle and Trig Identities

  • sines, cosines and tangents in terms of the unit circle
  • identities: tan theta = sin theta/cos theta, Pythagorean identity, sin theta = cos (90 - theta)
4 h
M5-2 pdf   docx

Solving Triangles

  • cosine and sine rules
  • area formulae
5 h M5-1

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M6:     Measurement - Maths Methods

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 6 modules.

M6-1 pdf   docx

Radians

  • radians, conversion between radians and degrees and the radian values of common angles
5 h M5-1 M5-2 A5-13
M6-2 pdf   docx

Exact Trig Values

  • exact values of the trig functions of multiples of 30 and 45 degrees
3 h M6-1

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G1:     Geometry - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite modules.

G1-1 pdf   docx

Drawings

  • plans and elevations, perspective drawings, cross sections and nets
3 h M1-1
G1-2 pdf   docx

Angles

  • estimating, measuring and constructing angles
  • the meaning of turn and angle
2 h
G1-3 pdf   docx

Position

  • describing position using eight compass points, distance and bearing, coordinates and latitude and longitude
2 h G1-1

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G2:     Geometry - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 2 modules.

G2-1 pdf   docx

Maps and Scales

  • making and reading maps and plans with legends and scales
2 h
G2-2 pdf   docx

Geometric Figures

  • conventions for labelling geometric figures
  • geometric theorems
5 h G2-2
G2-3 pdf   docx

Properties of Polygons

  • polygon names
  • internal angles
  • types of triangles and their properties
  • types of quadrilateral and their properties
5 h G2-3
G2-4 pdf   docx

Geometric Vocabulary

  • words used in geometry
2 h
G2-5 pdf   docx

Transformations and Symmetry

  • translations, reflections, rotations and dilations of points and shapes
  • reflectional and rotational symmetry
3 h G2-1 G2-2
G2-6 pdf   docx

Congruence

  • the meaning of congruence
  • tests for congruence of triangles
3 h G2-5

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G3:     Geometry - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 3 modules.

G3-1 pdf   docx

Similarity

  • the meaning of similarity
  • tests for similarity
  • applications of similar triangles
3 h

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G4:     Geometry - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 5 modules.

G4-1 pdf   docx

Geometric Proofs

  • proving geometric statements using chains of reasoning
  • circle theorems
4 h

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S1:     Statistics - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite modules.

S1-1 pdf   docx

Data Displays 1

  • reading varied data displays
  • reading and drawing tables, picture graphs, dot plots, bar graphs, scatter graphs and line graphs
6 h
S1-2 pdf   docx

Data Summary

  • mean, median, mode and range
2 h

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S2:     Statistics - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 2 modules.

S2-1 pdf   docx

Data Collection

  • data and surveys
  • extracting data
2 h

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S3:     Statistics - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 3 modules.

S3-1 pdf   docx   xlsx

Spreadsheets

  • using spreadsheets to store data, to calculate and to produce graphs
4 h S2-1 N2-7
S3-2 pdf   docx

Data Displays 2

  • reading varied data displays
  • reading and drawing grouped tables, compound bar graphs, histograms, stem and leaf plots and pie charts
5 h
S3-3 pdf   docx

Critiquing

  • critiquing data collection, data representation and conclusions drawn from data
3 h S3-1
S3-4 pdf   docx

Data Types

  • numerical, categorical and ordinal data
  • univariate, bivariate and multivariate data
  • time series
1 h S3-1
S3-5 pdf   docx

Data Distributions

  • distribution shape
  • unimodal and bimodal distributions
  • normal distributions
  • skewed distributions
2 h

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S4:     Statistics - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 4 modules.

S4-1 pdf   docx

Quantiles and Spread

  • quantiles and ogives
  • five-number summaries, box plots
  • inter-quartile range
  • standard deviation
5 h
S4-2 pdf   docx

Linear Regression

  • trends in data, regression lines, interpolation and extrapolation
  • correlation
  • causality
3 h

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P1:     Probability - Level 1

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The second last column is the estimated time required to work through the module; the last column is any pre-requisite modules.

P1-1 pdf   docx

Probability

  • the meaning of probability
  • finding approximate probabilities using data (from experiment and pre-existing) and understanding the reliability of the approximations
  • estimating probabilities by guesswork
  • finding exact probability using indifference, deciding when it applies
  • calculating expected frequency
8 h N1-3

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P2:     Probability - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 2 modules.

P2-1 pdf   docx

Compound Events

  • addition and multiplication rules
5 h
P2-2 pdf   docx

Two-way Tables

  • using two-way tables to determine probabilities
1 h P2-1
P2-3 pdf   docx

Venn Diagrams

  • using Venn diagrams to determine numbers and probabilities
3 h

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P3:     Probability - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 3 modules.

P3-1 pdf   docx

Tree Diagrams

  • using tree diagrams to determine probabilities
3 h

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P4:     Probability - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 4 modules.

P4-1 pdf   docx

Complex Probabilities

  • using the addition and multiplication rules in combination
4 h

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P6:     Probability - Maths Methods

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 6 modules.

P6-1 pdf   docx

Sets

  • set terminology and notation
2 h
P6-2 pdf   docx

Conditional Probability

  • conditional probability
3 h
P6-3 pdf   docx

Discrete Random Variables

  • discrete random variables
  • discrete probability distributions
  • expected value and variation
5 h
P6-4 pdf   docx

Binomial Distributions

  • binomial probabilities
5 h P6-3 A6-1
P6-5 pdf   docx

Continuous Random Variables

  • continuous random variables
5 h P6-3 C6-10
P6-6 pdf   docx

Normal Distributions

  • normal distributions
5 h P6-5
P6-7 pdf   docx

Confidence Intervals for Proportions

  • confidence intervals for proportions
4 h P6-4

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C6:     Calculus - Maths Methods

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is any pre-requisite Level 6 modules.

C6-1 pdf   docx

Velocity Graphically

  • displacement vs time graphs: high/low, rising/falling, steeper/flatter
  • gradient = velocity
  • gradient of secant = average velocity
  • gradient of tangent = instantaneous velocity
4 h
C6-2 pdf   docx

Velocity Algebraically

  • velocity at a given time using reducing intervals
  • velocity at given time using an unspecified interval, dt
  • velocity at any time
6 h C6-1
C6-3 pdf   docx

Velocity by Rule

  • differentiating at^n and sums of such terms by rule
6 h C6-2
C6-4 pdf   docx

Other Relations

  • calculus with relations other than between time, displacement and velocity
  • generic x-y relations
4 h C6-3
C6-5 pdf   docx

Applications of Derivatives

  • small increments
  • tangents and normals
  • finding a point with a given gradient
  • optimisation
  • turning points and curve sketching
8 h C6-4
C6-6 pdf   docx

Chain, Product and Quotient Rules

  • chain, product and quotient rules
7 h C6-5
C6-7 pdf   docx

Other Derivatives

  • the derivatives of sin x, cos x, a^x, e^x, ln x
5 h M6-3 C6-6
C6-8 pdf   docx

Mastering Differentiation

  • differentiating all functions fluently
12 h C6-7
C6-9 pdf   docx

Differential Equations

  • differential equations
10 h C6-8
C6-10 pdf   docx

Integration

  • definite integrals and the fundamental theorem of calculus
  • solving problems with integration
  • area under and between curves
  • trapezoidal rule
  • indefinite integrals
14 h C6-9
C6-11 pdf   docx

Pert

  • differential equations of the form dA/dt = rA
4 h C6-10
C6-12 pdf   docx

Higher-order Derivatives

  • second and higher-order derivatives
3 h C6-10
C6-13 pdf   docx

Graph Sketching

  • sketching graphs of polynomial and rational functions using knowledge of function shape, extreme behaviour, discontinuities, axis intercepts, stationary points and spot values
4 h A6-8 C6-8
C6-14 pdf   docx

Optimisation

  • finding the value of a control quantity which gives the optimum value of an objective quantity
6 h C6-8

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Extra Knowledge Modules

These are modules on topics which aren't in the Australian curriculum for Years 7 to 10 or for Maths Methods, but which might be of interest to students

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly.

The second last column is the estimated time required to work through the module; the last column is the level at which it could be studied.

E1 pdf   docx

Complex Numbers

Real and imaginary numbers. Imaginary numbers involve the square root of -1. Part of Specialist Maths.

9 h 6
E2 pdf   docx

Vectors

Quantities involving more than one number. Geometric vectors are used a lot in dynamics and physics. Part of Specialist Maths.

8 h 6
E3 pdf   docx

Statistics from Grouped Data

Calculating statistics from grouped data.

3 h 5
E4 pdf   docx

Linear Programming

A method for making optimal decisions given certain constraints.

3 h 5
E5 pdf   docx

Loci and Conic Sections

Graphs of relations that produce the shape of sections through a cone, shapes which occur commonly in nature.

4 h 6
E6 pdf   docx

Further Methods of Proof

Proof by deduction, exhaustion, contradiction and induction. Part of Specialist Maths.

3 h 6
E7 pdf   docx

Simpson's Rule

A more accurate adaptation of the trapezoidal rule. Part of Specialist Maths.

2 h 6
E8 pdf   docx

Confidence Intervals for Means

As for proportions, but applied to means. Part of Specialist Maths.

3 h 6

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Skills

There is just one module for each of the skills. Each module covers all levels.

Click on the required format. Word documents need to be downloaded and opened in Word to display properly.

Mental Arithmetic   pdf   docx                     Problem Solving   pdf   docx                     Investigating   pdf   docx                     Communication   pdf   docx

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Australian Curriculum Correlation

Click the links below for a list of syllabus elements along with the M1 Maths module relevant to each.

Word documents need to be downloaded and opened in Word to display properly.

Australian Curriculum

Years 7-10 Maths   pdf   docx Years 11-12 Maths Methods   pdf   docx

Queensland Syllabuses

Years 11-12 Essential Maths  pdf   docx Years 11-12 Maths Methods   pdf   docx
Years 11-12 General Maths   pdf   docx Years 11-12 Specialist Maths   pdf   docx

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Years 7-10 Programs

Below are some suggested structures for maths programs for Australian schools based on the M1 Maths materials.

Click on the required format. Word documents need to be downloaded and opened in Word to display properly.

Curriculum-paced   pdf   docx                                       Student-paced   pdf   docx                                       Progress Tracker   xlsx

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Years 7-10 Level Tests

The links below are to Knowledge tests and Skills test for each level from Level 1 to Level 5. The tests were produced by writing a question or two from each of the modules at that level, plus a scattering of questions from earlier levels.

There will eventually be four versions of each test. However, not all have been written to date. The others will be added shortly.

These tests can be used as school tests. A version should be picked at random and minor changes made (e.g. changing some of the numbers, maybe changing the problems and the investigation). Students can then still use the versions below for test preparation / practice without invalidating the tests. The tests are not high stakes after all.

Alternatively, schools might decide to write their own tests from scratch. In that case, the tests below can be used as models.

Click on the required format. Word documents need to be downloaded and opened in Word to display properly.

    Version A Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx pdf   docx pdf   docx pdf   docx pdf   docx
    Skills pdf   docx pdf   docx pdf   docx pdf   docx pdf   docx

    Version B Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx        
    Skills pdf   docx        

    Version C Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx        
    Skills pdf   docx        

    Version D Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx        
    Skills pdf   docx        

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Fun and Games

These are fun activities and games which can be played as a class or by small groups. They help develop or reinforce the concepts addressed in the learning modules. Click the preferred format in the first column to download instructions and materials for that activity. Word documents need to be downloaded and opened in Word to display properly. The instructions are designed primarily for teachers to allow them to conduct the activity with a class.

Activity

Format

Relevance

Description

Bingo

pdf   docx

Mental arithmetic (all levels)

A game of bingo where students have to perform simple mental computations to work out the numbers called

Goodies and Baddies

pdf   docx

General

A quiz game between one half of the class and the other. The questions can be made up to suit the needs of the class.

Group Problem Solving

pdf   docx

Problem solving – persistence and cooperation

A competition in which students work in groups to try to solve more problems correctly than the other groups

Mind Reading

pdf   docx

Problem solving

A simple magic trick for students to work out

Twenty

pdf   docx

Problem solving

A strategy game for students to work out so they can succeed in the challenge of beating the teacher

Last One Standing

pdf   docx

General

A quick class game that rehearses recollection of facts and mental arithmetic skills Can be used as a break and leg stretch

4-Corner Quiz

pdf   docx

General

This is a fun quiz involving movement that can be used to revise and reinforce any topic

Target

pdf   docx

Number sense, mental arithmetic, estimation, order of operations

A card game in which students use numbers to make an expression as close in value as possible to a given target number

Back to Back

pdf   docx

Geometry, Communication

An activity where students have to give clear and precise mathematical instructions

Protractor Golf

pdf   docx

Estimating and measuring angles and distances

A game for two in which students aim for holes on a paper golf course by estimating then measuring direction and distance

Walk the Plank

pdf   docx

Adding and subtracting positive and negative numbers

A simulation of walking the plank using addition and subtraction of positive and negative numbers to decide which direction and how far to go

Fraction Line

pdf   docx

Fraction meanings and fractions of numbers

A game where one half of the class competes against the other half to best estimate given fractions of the way along a line

Fraction Dominoes

pdf   docx

Fraction conversion

A game of dominoes to develop fluency with recognising different expressions of the same fraction and with fraction conversion

Millionaire

pdf   docx pdf   docx

Fractions of numbers

A board game that rehearses fractions among other things

Stomp

pdf   docx

Number facts and mental arithmetic

A board game for two

Greedy Pig

pdf   docx

Probability

A game mostly for fun, but which helps develop intuitive ideas of probability It can be used with all levels

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Find...

To search for a particular string, word or phrase on this web page, press Ctrl+F.

For more detailed instructions, see below for the browser you are using .

To find modules which mention 'equation', search for 'equation'. If you want also to find 'equate', 'equating' etc., search for 'equat'.

    Chrome

Press Ctrl+F (or click on the white upward arrow on an orange background on the far right of the address bar, then choose 'Find...')

You will get a small dialogue box near the top right of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Up and Down arrows in the dialogue box to move to other occurrences.

    Safari

Press Ctrl+F

You will get a small box with a magnifying glass near the top right of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Enter key to scroll through other occurrences.

    Firefox

Press Ctrl+F (or click on the three horizontal bars on the far right of the address bar, then choose 'Find in This Page...')

You will get a small dialogue box near the bottom left of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Up and Down arrows in the dialogue box to move to other occurrences.

    Edge

Press Ctrl+F (or click on the three dots on the far right of the address bar, then choose 'Find on Page...')

You will get a small dialogue box near the top left of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Left and Right arrows in the dialogue box to move to other occurrences.

    Other Browsers

Most other browsers work in very similar ways. It shouldn't be hard to find the search function.

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