# Essential Maths Help & Practice

Aligned with your class and textbook, our comprehensive help on Essential Mathematics covers all topics that you would see in your maths class, whether it's the Australian curriculum for Essential Mathematics, Externally Set Tasks (EST), ATAR course exam.

In the video lessons, our Essential maths tutors walk you through all topics like Trigonometry, Simultaneous equations, Operations with Surds, Derivatives, Congruent triangles, Linear programming, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest essential maths problems. Then, reinforce your understanding with tons of essential maths practice.

All our lessons are taught by experienced essential maths teachers. Let's finish your homework in no time, and ACE that final.

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##### 1Adding and Subtracting Fractions

##### 2Multiplying and Dividing Fractions

##### 3Pythagorean Theorem

##### 4Percents

##### 5Surds

##### 6Algebraic Expressions

##### 7Introduction to Relations and Functions

##### 8Linear Functions

- 8.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 8.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 8.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 8.4Gradient intercept form: y = mx + b
- 8.5General form: Ax + By + C = 0
- 8.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 8.7Rate of change
- 8.8Graphing linear functions using table of values
- 8.9Graphing linear functions using x- and y-intercepts
- 8.10Graphing from slope-intercept form y=mx+b
- 8.11Graphing linear functions using a single point and gradient
- 8.12Word problems of graphing linear functions
- 8.13Parallel and perpendicular lines in linear functions
- 8.14Applications of linear relations
- 8.15Perpendicular line equation

- 8.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 9Simultaneous Equations

- 9.1Determining number of solutions to linear equations
- 9.2Solving simultaneous linear equations by graphing
- 9.3Solving simultaneous linear equations by elimination
- 9.4Solving simultaneous linear equations by substitution
- 9.5Money related questions in linear equations
- 9.6Unknown number related questions in linear equations
- 9.7Distance and time related questions in linear equations
- 9.8Rectangular shape related questions in linear equations
- 9.9Simultaneous linear-quadratic equations
- 9.10Simultaneous quadratic-quadratic equations
- 9.11Solving 3 variable simultaneous equations by substitution
- 9.12Solving 3 variable simultaneous equations by elimination
- 9.13Solving 3 variable simultaneous equations with no solution, infinite solutions
- 9.14Word problems relating 3 variable simultaneous equations

- 9.1Determining number of solutions to linear equations
##### 10Factorisation

##### 11Quadratic Functions

- 11.1Introduction to quadratic functions
- 11.2Transformations of quadratic functions
- 11.3Quadratic function in general form:
*y = ax^2 + bx + c* - 11.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 11.5Completing the square
- 11.6Converting from general to vertex form by completing the square
- 11.7Shortcut: Vertex formula
- 11.8Graphing quadratic functions: General form VS. Vertex form
- 11.9Finding the quadratic functions for given parabolas
- 11.10Applications of quadratic functions

- 11.1Introduction to quadratic functions
##### 12Solving Quadratic Equations

##### 13Inequalities

- 13.1Express linear inequalities graphically and algebraically
- 13.2Solving one-step linear inequalities
- 13.3Solving multi-step linear inequalities
- 13.4Compound inequalities
- 13.5Solving absolute value inequalities
- 13.6Graphing linear inequalities in two variables
- 13.7Graphing simultaneous inequalities
- 13.8Solving quadratic inequalities in one variable

- 13.1Express linear inequalities graphically and algebraically
##### 14Algebraic Fractions

- 14.1Simplifying algebraic fractions and restrictions
- 14.2Adding and subtracting algebraic fractions
- 14.3Multiplying algebraic fractions
- 14.4Dividing algebraic fractions
- 14.5Solving equations with algebraic fractions
- 14.6Applications of equations with algebraic fractions
- 14.7Simplifying complex fractions
- 14.8Partial fraction decomposition

- 14.1Simplifying algebraic fractions and restrictions
##### 15Reciprocal Functions

##### 16Angles, Lines, and Transversals

##### 17Scale Factors and Similarity

##### 18Properties of Triangles

##### 19Congruent Triangles

##### 20Functions

##### 21Rational Functions

##### 22Indices

- 22.1Indices: Product rule
*(a^x)(a^y) = a^(x+y)* - 22.2Indices: Division rule (a^x / a^y) = a^(x-y)
- 22.3Indices: Power rule
*(a^x)^y = a^(x * y)* - 22.4Indices: Negative exponents
- 22.5Indices: Zero exponent:
*a^0 = 1* - 22.6Indices: Rational exponents
- 22.7Combining laws of indices
- 22.8Scientific notation
- 22.9Convert between radicals and rational exponents
- 22.10Solving for indices

- 22.1Indices: Product rule
##### 23Exponential Functions

##### 24Logarithmic Functions

- 24.1What is a logarithm?
- 24.2Converting from logarithmic form to exponential form
- 24.3Evaluating logarithms without a calculator
- 24.4Common logarithms
- 24.5Natural log: ln
- 24.6Evaluating logarithms using change-of-base formula
- 24.7Converting from exponential form to logarithmic form
- 24.8Solving exponential equations with logarithms
- 24.9Product rule of logarithms
- 24.10Quotient rule of logarithms
- 24.11Combining product rule and quotient rule in logarithms
- 24.12Evaluating logarithms using logarithm rules
- 24.13Solving logarithmic equations
- 24.14Graphing logarithmic functions
- 24.15Finding a logarithmic function given its graph

- 24.1What is a logarithm?
##### 25Trigonometric Ratios and Angle Measure

- 25.1Angle in standard position
- 25.2Coterminal angles
- 25.3Reference angle
- 25.4Find the exact value of trigonometric ratios
- 25.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 25.6Unit circle
- 25.7Converting between degrees and radians
- 25.8Trigonometric ratios of angles in radians
- 25.9Radian measure and arc length

- 25.1Angle in standard position
##### 26Sine Rule and Cosine Rule

##### 27Trigonometric Graphs

##### 28Inverse Trigonometric Functions

##### 29Bearings

##### 30Series

##### 31Growth and Decay

##### 32Conics

##### 33Probability

##### 34Limits

##### 35Derivatives

##### 36Derivative Applications

##### 37Integrals

##### 38Integral Applications