# Fifth Year Maths Help & Practice

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##### 1Number System and Radicals

##### 2Exponents

##### 3Linear Inequalities

##### 4Quadratic Equations and Inequalities

##### 5Introduction to Relations and Functions

##### 6Solving Simultaneous Equations

- 6.1Determining number of solutions to linear equations
- 6.2Solving simultaneous equations by graphing
- 6.3Solving simultaneous equations by elimination
- 6.4Solving simultaneous equations by substitution
- 6.5Money related questions in linear equations
- 6.6Unknown number related questions in linear equations
- 6.7Distance and time related questions in linear equations
- 6.8Rectangular shape related questions in linear equations

- 6.1Determining number of solutions to linear equations
##### 7Inequalities in two variables

##### 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 Quadratic Functions

##### 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
##### 11Operations of Polynomials

##### 12Polynomial Functions

- 12.1What is a polynomial function?
- 12.2Polynomial long division
- 12.3Polynomial synthetic division
- 12.4Remainder theorem
- 12.5Factor theorem
- 12.6Rational zero theorem
- 12.7Characteristics of polynomial graphs
- 12.8Multiplicities of polynomials
- 12.9Imaginary zeros of polynomials
- 12.10Determining the equation of a polynomial function
- 12.11Applications of polynomial functions
- 12.12Solving polynomial inequalities
- 12.13Fundamental theorem of algebra
- 12.14Descartes' rule of signs

- 12.1What is a polynomial function?
##### 13Radicals

##### 14Radical Functions

##### 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
##### 16Rational Expressions

- 16.1Simplifying rational expressions and restrictions
- 16.2Adding and subtracting rational expressions
- 16.3Multiplying rational expressions
- 16.4Dividing rational expressions
- 16.5Solving rational equations
- 16.6Applications of rational equations
- 16.7Simplifying complex fractions
- 16.8Partial fraction decomposition

- 16.1Simplifying rational expressions and restrictions
##### 17Reciprocal Functions

##### 18Function Operations

- 18.1Function notation
- 18.2Operations with functions
- 18.3Adding functions
- 18.4Subtracting functions
- 18.5Multiplying functions
- 18.6Dividing functions
- 18.7Composite functions
- 18.8Inequalities of combined functions
- 18.9Inverse functions
- 18.10One to one functions
- 18.11Difference quotient: applications of functions

- 18.1Function notation
##### 19Logarithmic Functions

- 19.1What is a logarithm?
- 19.2Converting from logarithmic form to exponential form
- 19.3Evaluating logarithms without a calculator
- 19.4Common logarithms
- 19.5Natural log: ln
- 19.6Evaluating logarithms using change-of-base formula
- 19.7Converting from exponential form to logarithmic form
- 19.8Solving exponential equations with logarithms
- 19.9Product rule of logarithms
- 19.10Quotient rule of logarithms
- 19.11Combining product rule and quotient rule in logarithms
- 19.12Evaluating logarithms using logarithm rules
- 19.13Solving logarithmic equations
- 19.14Graphing logarithmic functions
- 19.15Finding a logarithmic function given its graph

- 19.1What is a logarithm?
##### 20Exponential Growth and Decay

##### 21Trigonometry

- 21.1Angle in standard position
- 21.2Coterminal angles
- 21.3Reference angle
- 21.4Find the exact value of trigonometric ratios
- 21.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 21.6Unit circle
- 21.7Converting between degrees and radians
- 21.8Trigonometric ratios of angles in radians
- 21.9Radian measure and arc length
- 21.10Law of sines
- 21.11Law of cosines
- 21.12Applications of the sine law and cosine law

- 21.1Angle in standard position
##### 22Bearings

##### 23Graphing Trigonometric Functions

##### 24Applications of Trigonometric Functions

##### 25Trigonometric Identities

##### 26Scale Factors and Similarity

##### 27Circle Geometry

##### 28Conics

##### 29Surface Area and Volume

##### 30Sequences and series

##### 31Probability

##### 32Permutations and Combinations

##### 33Statistics

##### 34Data and Graphs