Maths
A deeper level of understanding
All our content is directly connected to subjects from the NSW Board of Studies. We begin by explaining the concepts, then we proceed to simpler questions and eventually tackle questions similar to those in exams.
A fun learning environment
Our lessons are both enjoyable and interactive. We encourage group discussions, and students are welcome to ask as many questions as they wish!
What Will You Get?
Personalised Homework Questions
At LOGOS Academia, we make homework personal. We customize assignments to target each student's weak spots. Weekly, they get a special booklet full of practice questions meant to tackle their unique challenges head-on.
Answer Books
We start preparing you as early as Year 6 to structure your mathematical explanations. Just like organising paragraphs and sentences in English, we teach students to logically present their work in math using our effective answer book system!
Our Proven Lessons Breakdown
15 MIN
We go through any homework related issues, and ensure all students are comfortable.
45 MIN
We teach new material, developing theory, and slowing move up in difficulty until we are answering exam-style questions.
Subject Details
Week 1
INTEGERS
OPERATIONS AND BODMAS
- Apply the associative, commutative and distributive laws to aid mental and written computation
- Compare, order, add and subtract integers
- Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies
Week 2
INTEGERS
HCF AND LCM
- Identify and describe factors and multiples of whole numbers and use them to solve problems
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line
Week 3
ANGLES
TYPES OF ANGLES
- Construct angles using a protractor
- Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles use the results to find unknown angles
- Use the language, notation and conventions of geometry
- Recognise the geometrical properties of angles at a point
- Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal
Week 4
ANGLES
ANGLES ON PARALLEL LINES
- Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal
- Investigate conditions for two lines to be parallel
- Solve simple numerical problems using reasoning
Week 5
FRACTIONS, DECIMALS AND PERCENTEGES
OPERATIONS OF DECIMALS
- Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers
- Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies
- Round decimals to a specified number of decimal places
Week 6
FRACTIONS, DECIMALS AND PERCENTEGES
OPERATIONS OF FRACTIONS
- Solve problems involving addition and subtraction of fractions with the same or related denominators
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line
- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies
Week 7
FRACTIONS, DECIMALS AND PERCENTEGES
CONVERTING FRACTIONS AND DECIMALS
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies
- Express one quantity as a fraction of another, with and without the use of digital technologies
Week 8
FRACTIONS, DECIMALS AND PERCENTEGES
TERMINATING AND RECCURING DECIMALS
- Round decimals to a specified number of decimal places
- Investigate terminating and recurring decimals
- Connect fractions, decimals and percentages and carry out simple conversions
Week 9
FRACTIONS, DECIMALS AND PERCENTEGES
PERCENTAGES
- Make connections between equivalent fractions, decimals and percentages
- Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without the use of digital technologies
- Connect fractions, decimals and percentages and carry out simple conversions
Week 10
FRACTIONS, DECIMALS AND PERCENTEGES
CALCULLATING PERCENTAGES OF QUANTITIES
- Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without the use of digital technologies
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies
- Find percentages of quantities and express one quantity as a percentage of another, with and without the use of digital technologies
- Solve problems involving the use of percentages, including percentage increases and decreases, with and without the use of digital technologie
Week 1
ALGEBRA
WHAT IS A VARIABLE?​
- Introduce the concept of variables as a way of representing numbers using letters​
Week 2
ALGEBRA
COLLECTING LIKE-TERMS​
- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions​
- Simplify algebraic expressions involving the four operations ​
Week 3
ALGEBRA
EXPANDING​
- Extend and apply the distributive law to the expansion of algebraic expressions​
Week 4
ALGEBRA
FACTORISING​
- Factorise algebraic expressions by identifying algebraic factors
Week 5
ALGEBRA
SUBSTITUTION​
- Create algebraic expressions and evaluate them by substituting a given value for each variable​
Week 6
EQUATIONS
SOLVING LINEAR EQUATIONS​
- Solve simple linear equations
- Solve linear equations using algebraic techniques and verify solutions by substitution​
Week 7
LINEAR RELATIONSHIPS
AN INTRODUCTION TO LINEAR RELATIONSHIPS
- Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point​
- Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates​
Week 8
LINEAR RELATIONSHIPS
PLOT LINEAR RELATIONSHIPS ON THE CARTESIAN PLANE, WITH AND WITHOUT THE USE OF DIGITAL TECHNOLOGIES 1​
- Plot linear relationships on the Cartesian plane, with and without the use of digital technologies​
Week 9
LINEAR RELATIONSHIPS
SOLVE LINEAR QUEATIONS USING GRAPHICAL TECHNIQUES​
- Solve linear equations using graphical techniques
Week 10
CONGRUENCY
CONGRUENCY​
- Define congruence of plane shapes using transformations
- Develop the conditions for congruence of triangles
- Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning​
Week 1
INDICES
WHAT ARE INDICES?​
- Investigate index notation and represent whole numbers as products of powers of prime numbers​
Week 2
INDICES
SQUARE ROOTS AND PERFECT SQUARES​
- Investigate and use square roots of perfect square numbers
Week 3
LENGTH
PERIMETER​
- Find perimeters of parallelograms, trapeziums, rhombuses and kites​
Week 4
LENGTH
CIRCLES AND CIRCUMFERENCE​
- Investigate the concept of irrational numbers, including π
- Investigate the relationship between features of circles, such as the circumference, radius and diameter use formulas to solve problems involving circumference​
Week 5
AREA
SQUARES, RECTANGLES, PARALLELOGRAMS, AND TRIANGLES​
- Choose appropriate units of measurement for area and convert from one unit to another​
- Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving​
Week 6
AREA
TRAPEZIUMS, KITES AND RHOMBUSES​
- Find areas of trapeziums, rhombuses and kites​
Week 7
AREA
CIRCLES​
- Investigate the relationship between features of circles, such as the area and the radius use formulas to solve problems involving area​
Week 8
VOLUME
UNITS OF MEASUREMENT FOR VOLUME​
- Draw different views of prisms and solids formed from combinations of prisms​
- Choose appropriate units of measurement for volume and convert from one unit to another​
Week 9
VOLUME
CALCULATING VOLUME OF PRISMS AND CYLIINDERS​
- Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general use formulas to solve problems involving volume​
- Calculate the volumes of cylinders and solve related problems
Week 10
TIME
DURATION​
- Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone​
- Solve problems involving international time zones
Week 1
PROBABILITY
CALCULATING PROBABILITIES OF OUTCOMES​
- Construct sample spaces for single-step experiments with equally likely outcomes​
- Assign probabilities to the outcomes of events and determine probabilities for events​
Week 2
PROBABILITY
COMPLEMENTARY EVENTS​
- Identify complementary events and use the sum of probabilities to solve problems​
Week 3
DATA
AN INTRODUCTION TO STATISTICS AND DATA ANALYSIS​
- Construct and compare a range of data displays, including stem-and-leaf plots and dot plots
Week 4
DATA
MEAN, MODE, MEDIAN, RANGE​
- Calculate mean, median, mode and range for sets of data and interpret these statistics in the context of data​
- Describe and interpret data displays using mean, median and range
Week 5
PYTHAGORA'S THEOREM
C2=A2+B2
- Investigate Pythagora's theorem and its application to solving simple problems involving right-angled triangles​
Week 6
PYTHAGORA'S THEOREM
SOLVE PROBLEMS INVOLVING PYTHAGORA'S THEOREM​
- Investigate Pythagora's theorem and its application to solving simple problems involving right-angled triangles​
Week 7
PROPERTIES OF GEOMTRICAL FIGURE
TRIANGLES AND QUADRILATERALS​
- Classify triangles according to their side and angle properties and describe quadrilaterals​
Week 8
PROPERTIES OF GEOMTRICAL FIGURE
ANGLE SUM OF TRIANGLE AND QUADRILATERAL​
- Identify line and rotational symmetries
- Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral​
Week 9
ALGEBRA
EXPANDING, SIMPLIFYING AND SOLVING​
- Apply the four operations to simple algebraic fractions with numerical denominators​
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate​
- Solve linear equations
Week 10
ALGEBRA
FACTORISING AND HARDER EQUATIONS​
- Factorise algebraic expressions by taking out a common algebraic factor
- Solve linear equations involving simple algebraic fractions
Week 1
ALGEBRA
SIMPLIFYING ALGEBRAIC EXPRESSIONS
- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
- Simplify algebraic expressions involving the four operations
- Create algebraic expressions and evaluate them by substituting a given value for each variable
Week 2
ALGEBRA
EXPANSION AND FACTORISATION
- Create algebraic expressions and evaluate them by substituting a given value for each variable
- Extend and apply the distributive law to the expansion of algebraic expressions
- Factorise algebraic expressions by identifying numerical factors
- Factorise algebraic expressions by identifying algebraic factors
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Expand binomial products using a variety of strategies
Week 3
RIGHT-ANGLED TRIANGLES (PYTHAGORAS)
APPLICATIONS OF PYTHAGORAS' THEOREM
- Investigate Pythagoras' theorem and its application to solving simple problems involving right-angled triangles
- Investigate the concept of irrational numbers
Week 4
FRACTIONS, DECIMALS AND PERCENTEGES
FRACTIONS AND DECIMALS (REVIEW)​
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line
- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies
- Express one quantity as a fraction of another, with and without the use of digital technologies
- Round decimals to a specified number of decimal places
- Investigate terminating and recurring decimals
Week 5
FRACTIONS, DECIMALS AND PERCENTEGES​
PERCENTEGES​
- Connect fractions, decimals and percentages and carry out simple conversions
- Represent events in two-way tables and Venn diagrams and solve related problems​
- Investigate the concept of irrational numbers, including π​
- Find percentages of quantities and express one quantity as a percentage of another, with and without the use of digital technologies
- Solve problems involving the use of percentages, including percentage increases and decreases, with and without the use of digital technologie
Week 6
PROBABILITY
PROBABILITY
- Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and'
- Represent events in two-way tables and Venn diagrams and solve related problems​
Week 7
AREA
CIRCLE
- Investigate the relationship between features of circles, such as the area and the radius use formulas to solve problems involving area
Week 8
REVISION
REVISION
- Exam Revision
Week 9
AREA AND SURFACE AREA
AREA
- Choose appropriate units of measurement for area and convert from one unit to another
- Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving
- Find areas of trapeziums, rhombuses and kites
Week 10
TIME
TIME
- Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone
- Solve problems involving international time zones
Week 1
VOLUME
PRISMS
- Draw different views of prisms and solids formed from combinations of prisms
- Choose appropriate units of measurement for volume and convert from one unit to another
- Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general use formulas to solve problems involving volume
Week 2
VOLUME
CYLINDERS
- Calculate the volumes of cylinders and solve related problems
Week 3
EQUATIONS
SOLVING EQUATIONS
- Solve simple linear equations
- Solve linear equations using algebraic techniques and verify solutions by substitution
- Solve simple quadratic equations
Week 4
INDICES
INDICES LAWS
- Use index notation with numbers to establish the index laws with positive-integer indices and the zero index
Week 5
LINEAR RELATIONSHIPS
- Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point
Week 6
INDICES
INDICES LAWS​
- Extend and apply the index laws to variables, using positive-integer indices and the zero index
Week 7
EQUATIONS
- Solve linear equations
- Solve linear equations involving simple algebraic fractions
- Substitute values into formulas to determine an unknown
- Solve complex linear equations involving algebraic fractions
Week 8
LINEAR RELATIONSHIPS
- Plot linear relationships on the Cartesian plane, with and without the use of digital technologies
- Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates
Week 9
LINEAR RELATIONSHIPS
- Solve linear equations using graphical techniques
- Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software
Week 10
FINANCIAL MATHEMATICS
- Investigate and calculate the Goods and Services Tax (GST), with and without the use of digital technologies
Week 1
FINANCIAL MATHEMATICS
- Investigate and calculate 'best buys', with and without the use of digital technologies
Week 2
FINANCIAL MATHEMATICS
- Solve problems involving profit and loss, with and without the use of digital technologies
Week 3
RATIOS AND RATES
- Recognise and solve problems involving simple ratios
- Solve a range of problems involving ratios and rates, with and without the use of digital technologies
Week 4
RATIOS AND RATES
- Investigate, interpret and analyse graphs from authentic data
Week 5
RATIOS AND RATES
- Solve problems involving direct proportion explore the relationship between graphs and equations corresponding to simple rate problems
Week 6
PROPERTIES OF GEOMETRICAL FIGURES 1
- Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral
- Use the properties of special triangles and quadrilaterals to solve simple numerical problems with appropriate reasoning
Week 7
PROPERTIES OF GEOMETRICAL FIGURES 2
- Define congruence of plane shapes using transformations
- Develop the conditions for congruence of triangles
- Formulate proofs involving congruent triangles and angle properties
- Use the enlargement transformation to explain similarity
Week 8
PROPERTIES OF GEOMETRICAL FIGURES 2
FURTHER CONGRUENCY
- Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Week 9
ANGLE RELATIONSHIPS
USE THE LANGUAGE, NOTATION AND CONVENTIONS OF GEOMETRY
- Use the language, notation and conventions of geometry
- Recognise the geometrical properties of angles at a point
- Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal
Week 10
ALGEBRA
SIMPLIFY ALGEBRAIC EXPRESSIONS INVOLVING THE FOUR OPERATIONS
- Apply the order of operations to simplify a range of algebraic expressions, including those involving mixed operations
Week 1
DATA COLLECTION AND REPRESENTATION
- Descriptive Statistics and Bivariate Data Analysis
- Construct and compare a range of data displays, including stem-and-leaf plots and dot plots
- Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including 'skewed', 'symmetric' and 'bi-modal'
Week 2
STATISTICAL ANALYSIS
SINGLE VARIABLE DATA ANALYSIS
- Determine quartiles and interquartile range
- Construct and interpret box plots and use them to compare data se
- Сompare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
- Descriptive Statistics and Bivariate Data Analysis
Week 3
SURFACE
CYLINDERS
- Calculate the surface areas of cylinders and solve related problems
Week 4
VOLUME
CYLINDERS
- Volume of cylinders
Week 5
ALGEBRAIC TECHNIQUES
FACTORISING
- Expand binomial products and factorise monic quadratic expressions using a variety of strategies
Week 6
ALGEBRAIC TECHNIQUES​
FACTORISING
- Factorising involving indices
Week 7
INDICES
- Apply index laws to numerical expressions with integer indices
Week 8
ALGEBRA
ALGEBRAIC TECHNIQUES
- Apply the four operations to simple algebraic fractions with numerical denominators
- Apply the four operations to algebraic fractions with pronumerals in the denominator
Week 9
ALGEBRA
ALGEBRAIC TECHNIQUES
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Factorise algebraic expressions by taking out a common algebraic factor
- Expand binomial products and factorise monic quadratic expressions using a variety of strategies
Week 10
EQUATIONS
HARDER SIMULTANEOUS EQUATIONS
- Solve problems involving linear equations, including those derived from formulas
- Solve linear simultaneous equations, using algebraic and graphical techniques, including with the use of digital technologies
Week 1
FINANCIAL MATHEMATICS
SIMPLE INTEREST
- Solve problems involving earning money
- Solve problems involving simple interest
Week 2
AREA AND SURFACE AREA
APPLICATIONS OF AREA
- Solve problems involving the surface areas of right prisms
- Calculate the surface areas of cylinders and solve related problems
- Solve problems involving surface area for a range of prisms, cylinders and composite solids
Week 3
VOLUMES
APPLICATIONS OF VOLUMES
- Solve problems involving the volumes of right prisms
- Solve problems involving volume for a range of prisms, cylinders and composite solids
Week 4
ALGEBRAIC TECHNIQUES
SOLVE LINEAR EQUATIONS
- Solve linear equations
- Solve linear equations involving simple algebraic fractions
- Solve simple quadratic equations using a range of strategies
- Solve complex linear equations involving algebraic fractions
Week 5
ALGEBRAIC TECHNIQUES
FACTORISING
- Factorise algebraic expressions by taking out a common algebraic factor
- Expand binomial products and factorise monic quadratic expressions using a variety of strategies
- Solve simple quadratic equations using a range of strategies
- Solve a wide range of quadratic equations derived from a variety of contexts
Week 6
EQUATIONS
SOLVE PROBLEMS INVOLVING LINEAR EQUATION
- Substitute values into formulas to determine an unknown
- Solve problems involving linear equations, including those derived from formulas
Week 7
EQUATIONS
LINEAR INEQUALITIES
- Solve linear inequalities and graph their solutions on a number line
Week 8
REVISION
REVISION
- Revision
Week 9
EQUATIONS
SOLVE SIMULTANEOUS EQUATIONS WITH LINEAR EQUATIONS, INCLUDING WORD PROBLEMS
- Solve linear simultaneous equations, using algebraic and graphical techniques, including with the use of digital technologies
Week 10
EQUATIONS
SOLVE SIMULTANEOUS EQUATIONS WITH NON-LINEAR EQUATIONS, INCLUDING WORD PROBLEMS
- Solve simultaneous equations, where one equation is non-linear, using algebraic and graphical techniques, including the use of digital technologies
- Graph simple non-linear relationships, with and without the use of digital technologies, and solve simple related equations
Week 1
INDICES
INDICE LAWS
- Simplify algebraic products and quotients using index laws
- Apply index laws to numerical expressions with integer indices
- Apply index laws to algebraic expressions involving integer indices
Week 2
INDICES
UNDERSTANDING SURDS
- Define rational and irrational numbers and perform operations with surds and fractional indices
Week 3
INDICES
RATIONALISING SURDS
- Define rational and irrational numbers and perform operations with surds and fractional indices
Week 4
EQUATIONS
UNDERSTANDING THE DISCRIMINANT
- Solve a wide range of quadratic equations derived from a variety of contexts
Week 5
EQUATIONS
SOLVING EQUATIONS (REVISION)
- Solve simple cubic equations
- Rearrange literal equations
Week 6
AREA AND SURFACE AREA
CYLINDERS AND PRISMS
Week 7
FINANCIAL MATHEMATICS
COMPOUND INTEREST
- Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies
Week 8
TRIGONOMETRY
WORKING MATHEMATICALLY WITH TRIGONOMETRY
- Apply Pythagoras' theorem and trigonometry to solve three-dimensional problems in right-angled triangles
Week 9
TRIGONOMETRY
USE THE UNIT CIRCLE TO DEFINE TRIGONOMETRIC FUNCTIONS, AND GRAPH THEM, WITH AND WITHOUT THE USE OF DIGITAL TECHNOLOGIES
- Use the unit circle to define trigonometric functions, and graph them, with and without the use of digital technologies
Week 10
TRIGONOMETRY
EXACT VALUES
- Use the unit circle to define trigonometric functions, and graph them, with and without the use of digital technologies
- Solve simple trigonometric equations
Week 1
TRIGONOMETRY
THE SINE RULE
- Establish the sine, cosine and area rules for any triangle and solve related problems
Week 2
TRIGONOMETRY
THE COSINE RULE + GENERAL NON-RIGHT ANGLED TRIGONOMETRY PROBLEMS
- Establish the sine, cosine and area rules for any triangle and solve related problems
Week 3
TRIGONOMETRY
BEARINGS
- Solve right-angled triangle problems, including those involving direction and angles of elevation and depression
Week 4
LINEAR RELATIONSHIPS
FINDING THE EQUATION OF A LINE
- Interpret and graph linear relationships using the gradient-intercept form of the equation of a straight line
Week 5
LINEAR RELATIONSHIPS
MID-POINT, DISTANCE. PARALLEL AND PERPENDICULAR
- Find the midpoint and gradient of a line segment (interval) on the Cartesian plane
- Find the distance between two points located on the Cartesian plane
- Sketch linear graphs using the coordinates of two points
- Solve problems using various standard forms of the equation of a straight line
Week 6
LINEAR RELATIONSHIPS
PARALLEL AND PERPENDICULAR AND HARDER PROBLEMS
- Solve problems involving parallel and perpendicular lines
Week 7
NON-LINEAR RELATIONSHIPS
THE PARABOLA 1
- Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations
Week 8
NON-LINEAR RELATIONSHIPS
THE PARABOLA 2
- Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations
Week 9
NON-LINEAR RELATIONSHIPS
THE HYPERBOLA, CUBIC AND EXPONENTIAL FUNCTIONS
- Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations
- Describe, interpret and sketch cubics, other curves and their transformations
- Describe, interpret and sketch functions
Week 10
NON-LINEAR RELATIONSHIPS
THE CIRCLE
Week 1
PROBABILITY
CALCULATE RELATIVE FREQUENCIES
- List all outcomes for two-step chance experiments, with and without replacement, using tree diagrams or arrays assign probabilities to outcomes and determine probabilities for events
Week 2
PROBABILITY
CONDITIONAL PROBABILITY
- Describe the results of two- and three-step chance experiments, with and without replacement, assign probabilities to outcomes, and determine probabilities of events investigate the concept of independence
