# Fifth year maths

Here is a list of all of the maths skills students learn in fifth year! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. To start practising, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Numbers

## Consumer maths

## Scientific notation

## Equations

## Inequalities

- E.1 Graph a linear inequality in one variable
- E.2 Graph a linear inequality in the coordinate plane
- E.3 Write inequalities from graphs
- E.4 Write a linear inequality: word problems
- E.5 Solve linear inequalities
- E.6 Graph solutions to linear inequalities
- E.7 Solve absolute value inequalities
- E.8 Graph solutions to absolute value inequalities
- E.9 Graph solutions to quadratic inequalities
- E.10 Solve quadratic inequalities

## Functions

## Simultaneous equations

- G.1 Is (x, y) a solution to the simultaneous equations?
- G.2 Solve simultaneous equations by graphing
- G.3 Solve simultaneous equations by graphing: word problems
- G.4 Find the number of solutions to simultaneous equations
- G.5 Solve simultaneous equations using substitution
- G.6 Solve simultaneous equations using substitution: word problems
- G.7 Solve simultaneous equations using elimination
- G.8 Solve simultaneous equations using elimination: word problems
- G.9 Solve simultaneous equations using any method
- G.10 Solve simultaneous equations using any method: word problems
- G.11 Solve simultaneous equations in three variables using substitution
- G.12 Solve simultaneous equations in three variables using elimination
- G.13 Determine the number of solutions to a system of equations in three variables
- G.14 Solve non-linear simultaneous equations

## Inequalities and linear programming

## Complex numbers

## Argand plane

## Factorising

## Quadratic functions

- L.1 Characteristics of quadratic functions
- L.2 Complete a function table: quadratic functions
- L.3 Find a quadratic function
- L.4 Graph a quadratic function
- L.5 Match quadratic functions and graphs
- L.6 Solve a quadratic equation using square roots
- L.7 Solve a quadratic equation using the zero product property
- L.8 Solve a quadratic equation by factorising
- L.9 Complete the square
- L.10 Solve a quadratic equation using the quadratic formula
- L.11 Using the discriminant

## Polynomials

- M.1 Polynomial vocabulary
- M.2 Add and subtract polynomials
- M.3 Multiply polynomials
- M.4 Divide polynomials using long division
- M.5 Divide polynomials using synthetic division
- M.6 Evaluate polynomials using synthetic division
- M.7 Solve polynomial equations
- M.8 Write a polynomial from its roots
- M.9 Find the roots of factorised polynomials
- M.10 Rational root theorem
- M.11 Complex conjugate theorem
- M.12 Conjugate root theorems
- M.13 Match polynomials and graphs
- M.14 Pascal's triangle
- M.15 Pascal's triangle and the Binomial Theorem
- M.16 Binomial Theorem I
- M.17 Binomial Theorem II

## Radical functions and expressions

- N.1 Roots of integers
- N.2 Roots of rational numbers
- N.3 Find roots using a calculator
- N.4 Nth roots
- N.5 Simplify radical expressions with variables I
- N.6 Simplify radical expressions with variables II
- N.7 Multiply radical expressions
- N.8 Divide radical expressions
- N.9 Add and subtract radical expressions
- N.10 Simplify radical expressions using the distributive property
- N.11 Simplify radical expressions using conjugates
- N.12 Domain and range of radical functions
- N.13 Solve radical equations

## Rational exponents

## Rational functions and expressions

## Function operations

- Q.1 Add and subtract functions
- Q.2 Multiply functions
- Q.3 Divide functions
- Q.4 Composition of linear functions: find a value
- Q.5 Composition of linear functions: find an equation
- Q.6 Composition of linear and quadratic functions: find a value
- Q.7 Composition of linear and quadratic functions: find an equation
- Q.8 Identify inverse functions
- Q.9 Find values of inverse functions from tables
- Q.10 Find values of inverse functions from graphs
- Q.11 Find inverse functions and relations

## Logarithms

- R.1 Convert between exponential and logarithmic form: rational bases
- R.2 Convert between natural exponential and logarithmic form
- R.3 Convert between exponential and logarithmic form: all bases
- R.4 Evaluate logarithms
- R.5 Evaluate natural logarithms
- R.6 Change of base formula
- R.7 Identify properties of logarithms
- R.8 Product property of logarithms
- R.9 Quotient property of logarithms
- R.10 Power property of logarithms
- R.11 Properties of logarithms: mixed review
- R.12 Evaluate logarithms: mixed review

## Exponential and logarithmic functions

- S.1 Domain and range of exponential and logarithmic functions
- S.2 Evaluate exponential functions
- S.3 Match exponential functions and graphs
- S.4 Solve exponential equations by factorising
- S.5 Solve exponential equations using common logarithms
- S.6 Solve exponential equations using natural logarithms
- S.7 Solve logarithmic equations I
- S.8 Solve logarithmic equations II
- S.9 Identify linear and exponential functions
- S.10 Exponential functions over unit intervals
- S.11 Describe linear and exponential growth and decay
- S.12 Exponential growth and decay: word problems

## Angle measures

## Trigonometry

- U.1 Pythagoras' Theorem and its converse
- U.2 Special right triangles
- U.3 Trigonometric ratios: sin, cos and tan
- U.4 Trigonometric ratios: csc, sec and cot
- U.5 Trigonometric ratios in similar right triangles
- U.6 Find trigonometric ratios using the unit circle
- U.7 Sin, cos and tan of special angles
- U.8 Csc, sec and cot of special angles
- U.9 Find trigonometric functions using a calculator
- U.10 Inverses of sin, cos and tan
- U.11 Inverses of csc, sec and cot
- U.12 Solve trigonometric equations I
- U.13 Solve trigonometric equations II
- U.14 Trigonometric ratios: find a side length
- U.15 Trigonometric ratios: find an angle measure
- U.16 Solve a right triangle
- U.17 Law of Sines
- U.18 Law of Cosines
- U.19 Solve a triangle
- U.20 Area of a triangle: sine formula
- U.21 Area of a triangle: Law of Sines

## Trigonometric functions

- V.1 Find properties of sine functions
- V.2 Write equations of sine functions from graphs
- V.3 Write equations of sine functions using properties
- V.4 Graph sine functions
- V.5 Find properties of cosine functions
- V.6 Write equations of cosine functions from graphs
- V.7 Write equations of cosine functions using properties
- V.8 Graph cosine functions
- V.9 Graph sine and cosine functions

## Trigonometric identities

## Similarity

- Y.1 Identify similar figures
- Y.2 Similarity ratios
- Y.3 Similarity statements
- Y.4 Side lengths and angle measures in similar figures
- Y.5 Similar triangles and indirect measurement
- Y.6 Perimeters of similar figures
- Y.7 Similarity rules for triangles
- Y.8 Similar triangles and similarity transformations
- Y.9 Similarity of circles
- Y.10 Triangle Proportionality Theorem
- Y.11 Areas of similar figures

## Two-dimensional figures

- Z.1 Polygon vocabulary
- Z.2 Perimeter
- Z.3 Area of triangles and quadrilaterals
- Z.4 Area and perimeter in the coordinate plane I
- Z.5 Area and perimeter in the coordinate plane II
- Z.6 Area and circumference of circles
- Z.7 Area of compound figures
- Z.8 Area between two shapes
- Z.9 Area and perimeter of similar figures

## Circles

- AA.1 Parts of a circle
- AA.2 Central angles
- AA.3 Arc measure and arc length
- AA.4 Area of sectors
- AA.5 Circle measurements: mixed review
- AA.6 Arcs and chords
- AA.7 Tangent lines
- AA.8 Perimeter of polygons with an inscribed circle
- AA.9 Inscribed angles
- AA.10 Angles in inscribed right triangles
- AA.11 Angles in inscribed quadrilaterals

## Circles in the coordinate plane

- BB.1 Find the centre of a circle
- BB.2 Find the radius or diameter of a circle
- BB.3 Write equations of circles in standard form from graphs
- BB.4 Write equations of circles in standard form using properties
- BB.5 Convert equations of circles from general to standard form
- BB.6 Find properties of circles from equations in general form
- BB.7 Graph circles

## Surface area and volume

- CC.1 Introduction to surface area and volume
- CC.2 Surface area of prisms and cylinders
- CC.3 Surface area of pyramids and cones
- CC.4 Volume of prisms and cylinders
- CC.5 Volume of pyramids and cones
- CC.6 Surface area and volume of spheres
- CC.7 Introduction to similar solids
- CC.8 Surface area and volume of similar solids
- CC.9 Surface area and volume review

## Logic

## Sequences and series

- EE.1 Classify formulas and sequences
- EE.2 Find terms of an arithmetic sequence
- EE.3 Find terms of a geometric sequence
- EE.4 Find terms of a recursive sequence
- EE.5 Evaluate formulas for sequences
- EE.6 Write a formula for an arithmetic sequence
- EE.7 Write a formula for a geometric sequence
- EE.8 Write a formula for a recursive sequence
- EE.9 Sequences: mixed review
- EE.10 Introduction to sigma notation
- EE.11 Identify arithmetic and geometric series
- EE.12 Find the sum of a finite arithmetic or geometric series
- EE.13 Introduction to partial sums
- EE.14 Partial sums of arithmetic series
- EE.15 Partial sums of geometric series
- EE.16 Partial sums: mixed review
- EE.17 Convergent and divergent geometric series
- EE.18 Find the value of an infinite geometric series
- EE.19 Write a repeating decimal as a fraction

## Probability

- FF.1 Introduction to probability
- FF.2 Theoretical and experimental probability
- FF.3 Compound events: find the number of outcomes
- FF.4 Calculate probabilities of events
- FF.5 Permutations
- FF.6 Counting principle
- FF.7 Permutation and combination notation
- FF.8 Find probabilities using permutations and combinations
- FF.9 Find probabilities using two-way frequency tables
- FF.10 Identify independent events
- FF.11 Probability of independent and dependent events
- FF.12 Geometric probability
- FF.13 Find conditional probabilities
- FF.14 Independence and conditional probability
- FF.15 Find conditional probabilities using two-way frequency tables
- FF.16 Find probabilities using the addition rule
- FF.17 Expected values of random variables
- FF.18 Write the probability distribution for a game of chance
- FF.19 Expected values for a game of chance
- FF.20 Choose the better bet
- FF.21 Find probabilities using the binomial distribution

## Statistics

## Data and graphs

## Constructions

- II.1 Construct the midpoint or perpendicular bisector of a segment
- II.2 Construct an angle bisector
- II.3 Construct a congruent angle
- II.4 Construct a perpendicular line
- II.5 Construct parallel lines
- II.6 Construct an equilateral triangle or regular hexagon
- II.7 Construct a square
- II.8 Construct a tangent line to a circle
- II.9 Construct the circumcenter or incenter of a triangle
- II.10 Construct the inscribed or circumscribed circle of a triangle
- II.11 Construct the centroid or orthocenter of a triangle