# Year 11 Maths Help & Practice

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##### 1Solving Linear Equations

##### 2Linear Inequalities

##### 3Quadratic Equations and Inequalities

##### 4Solving Simultaneous Equations

- 4.1Determining number of solutions to linear equations
- 4.2Solving simultaneous equations by graphing
- 4.3Solving simultaneous equations by elimination
- 4.4Solving simultaneous equations by substitution
- 4.5Money related questions in linear equations
- 4.6Unknown number related questions in linear equations
- 4.7Distance and time related questions in linear equations
- 4.8Rectangular shape related questions in linear equations

- 4.1Determining number of solutions to linear equations
##### 5Linear programming

##### 6Introduction to Relations and Functions

##### 7Direct Variation

##### 8Imaginary and Complex Numbers

- 8.1Introduction to imaginary numbers
- 8.2Complex numbers and complex planes
- 8.3Adding and subtracting complex numbers
- 8.4Complex conjugates
- 8.5Multiplying and dividing complex numbers
- 8.6Distance and midpoint of complex numbers
- 8.7Angle and absolute value of complex numbers
- 8.8Polar form of complex numbers
- 8.9Operations on complex numbers in polar form

- 8.1Introduction to imaginary numbers
##### 9Factorising Polynomial

##### 10Quadratic Functions

- 10.1Characteristics of quadratic functions
- 10.2Transformations of quadratic functions
- 10.3Quadratic function in general form:
*y = ax^2 + bx + c* - 10.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 10.5Completing the square
- 10.6Converting from general to vertex form by completing the square
- 10.7Shortcut: Vertex formula
- 10.8Graphing parabolas for given quadratic functions
- 10.9Finding the quadratic functions for given parabolas
- 10.10Applications of quadratic functions

- 10.1Characteristics of quadratic functions
##### 11Polynomial Functions

- 11.1What is a polynomial function?
- 11.2Polynomial long division
- 11.3Polynomial synthetic division
- 11.4Remainder theorem
- 11.5Factor theorem
- 11.6Rational zero theorem
- 11.7Characteristics of polynomial graphs
- 11.8Multiplicities of polynomials
- 11.9Imaginary zeros of polynomials
- 11.10Determining the equation of a polynomial function
- 11.11Applications of polynomial functions
- 11.12Solving polynomial inequalities
- 11.13Fundamental theorem of algebra
- 11.14Descartes' rule of signs

- 11.1What is a polynomial function?
##### 12Radicals

##### 13Radical Functions

##### 14Exponents

##### 15Exponential Functions

- 15.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 15.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 15.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 15.4Exponents: Negative exponents
- 15.5Exponents: Zero exponent:
*a^0 = 1* - 15.6Exponents: Rational exponents
- 15.7Graphing exponential functions
- 15.8Graphing transformations of exponential functions
- 15.9Finding an exponential function given its graph

- 15.1Exponents: Product rule
##### 16Logarithmic Functions

- 16.1What is a logarithm?
- 16.2Converting from logarithmic form to exponential form
- 16.3Evaluating logarithms without a calculator
- 16.4Common logarithms
- 16.5Natural log: ln
- 16.6Evaluating logarithms using change-of-base formula
- 16.7Converting from exponential form to logarithmic form
- 16.8Solving exponential equations with logarithms
- 16.9Product rule of logarithms
- 16.10Quotient rule of logarithms
- 16.11Combining product rule and quotient rule in logarithms
- 16.12Evaluating logarithms using logarithm rules
- 16.13Solving logarithmic equations
- 16.14Graphing logarithmic functions
- 16.15Finding a logarithmic function given its graph

- 16.1What is a logarithm?
##### 17Applications of Exponential and Logarithmic Functions

- 17.1Exponential growth and decay by a factor
- 17.2Exponential decay: Half-life
- 17.3Exponential growth and decay by percentage
- 17.4Finance: Compound interest
- 17.5Continuous growth and decay
- 17.6Logarithmic scale: Richter scale (earthquake)
- 17.7Logarithmic scale: pH scale
- 17.8Logarithmic scale: dB scale
- 17.9Finance: Future value and present value

- 17.1Exponential growth and decay by a factor
##### 18Conics

##### 19Introduction to Trigonometry

- 19.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 19.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 19.3Use tangent ratio to calculate angles and side (Tan = $\frac{o}{a}$ )
- 19.4Combination of SohCahToa questions
- 19.5Solving expressions using 45-45-90 special right triangles
- 19.6Solving expressions using 30-60-90 special right triangles
- 19.7Word problems relating ladder in trigonometry
- 19.8Word problems relating guy wire in trigonometry
- 19.9Other word problems relating angles in trigonometry

- 19.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 20Trigonometric Ratios and Angle Measure

##### 21Bearings

##### 22Graphing Trigonometric Functions

##### 23Applications of Trigonometric Functions

##### 24Trigonometric Identities

##### 25Circle Geometry

##### 26Sequences and Series

##### 27Introduction to Probability

##### 28Probability

##### 29Statistics

##### 30Limits

- 30.1Finding limits from graphs
- 30.2Continuity
- 30.3Finding limits algebraically - direct substitution
- 30.4Finding limits algebraically - when direct substitution is not possible
- 30.5Infinite limits - vertical asymptotes
- 30.6Limits at infinity - horizontal asymptotes
- 30.7Intermediate value theorem
- 30.8Squeeze theorem

- 30.1Finding limits from graphs
##### 31Derivatives

- 31.1Definition of derivative
- 31.2Power rule
- 31.3Gradient and equation of tangent line
- 31.4Chain rule
- 31.5Derivative of trigonometric functions
- 31.6Derivative of exponential functions
- 31.7Product rule
- 31.8Quotient rule
- 31.9Implicit differentiation
- 31.10Derivative of inverse trigonometric functions
- 31.11Derivative of logarithmic functions
- 31.12Higher order derivatives
- 31.13Position velocity acceleration

- 31.1Definition of derivative
##### 32Introduction to Matrices

##### 33Determinants and Inverses of Matrices

- 33.1The determinant of a 2 x 2 matrix
- 33.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
- 33.3The inverse of a 2 x 2 matrix
- 33.4The inverse of 3 x 3 matrices with matrix row operations
- 33.5The inverse of 3 x 3 matrix with determinants and adjugate
- 33.62 x 2 invertible matrix
- 33.7Solving linear systems using Cramer's Rule
- 33.8Solving linear systems using 2 x 2 inverse matrices

- 33.1The determinant of a 2 x 2 matrix