# Higher 1 maths

Here is a list of all of the maths skills students learn in higher 1! 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!

## Equations and inequalities

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

## Functions

- B.1 Domain and range
- B.2 Identify functions
- B.3 Evaluate functions
- B.4 Find values using function graphs
- B.5 Complete a table for a function graph
- B.6 Find the gradient of a linear function
- B.7 Graph a linear function
- B.8 Write the equation of a linear function
- B.9 Linear functions over unit intervals

## Simultaneous equations

- C.1 Is (x, y) a solution to the simultaneous equations?
- C.2 Solve simultaneous equations by graphing
- C.3 Solve simultaneous equations by graphing: word problems
- C.4 Find the number of solutions to simultaneous equations
- C.5 Classify simultaneous equations
- C.6 Solve simultaneous equations using substitution
- C.7 Solve simultaneous equations using substitution: word problems
- C.8 Solve simultaneous equations using elimination
- C.9 Solve simultaneous equations using elimination: word problems
- C.10 Solve simultaneous equations using any method
- C.11 Solve simultaneous equations using any method: word problems
- C.12 Solve simultaneous equations in three variables using substitution
- C.13 Solve simultaneous equations in three variables using elimination
- C.14 Determine the number of solutions to a system of equations in three variables
- C.15 Solve non-linear simultaneous equations

## Inequalities and linear programming

## Matrices

- E.1 Matrix vocabulary
- E.2 Matrix operation rules
- E.3 Add and subtract matrices
- E.4 Multiply a matrix by a scalar
- E.5 Linear combinations of matrices
- E.6 Multiply two matrices
- E.7 Simplify matrix expressions
- E.8 Properties of matrices
- E.9 Solve matrix equations
- E.10 Determinant of a matrix
- E.11 Is a matrix invertible?
- E.12 Inverse of a matrix
- E.13 Identify inverse matrices
- E.14 Solve matrix equations using inverses

## Complex numbers

## Factorising

## Quadratic functions

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

## Polynomials

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

## Radical functions and expressions

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

## Rational exponents

## Rational functions and expressions

## Function operations

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

## Families of functions

## Logarithms

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

## Exponential and logarithmic functions

- P.1 Domain and range of exponential and logarithmic functions
- P.2 Evaluate exponential functions
- P.3 Match exponential functions and graphs
- P.4 Solve exponential equations by factorising
- P.5 Solve exponential equations using common logarithms
- P.6 Solve exponential equations using natural logarithms
- P.7 Solve logarithmic equations I
- P.8 Solve logarithmic equations II
- P.9 Identify linear and exponential functions
- P.10 Exponential functions over unit intervals
- P.11 Describe linear and exponential growth and decay
- P.12 Exponential growth and decay: word problems
- P.13 Compound interest: word problems
- P.14 Continuously compounded interest: word problems

## Parabolas

- Q.1 Identify the direction a parabola opens
- Q.2 Find the vertex of a parabola
- Q.3 Find the focus or directrix of a parabola
- Q.4 Find the axis of symmetry of a parabola
- Q.5 Write equations of parabolas in vertex form from graphs
- Q.6 Write equations of parabolas in vertex form using properties
- Q.7 Graph parabolas

## Circles

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

## Hyperbolas

- T.1 Find the centre of a hyperbola
- T.2 Find the vertices of a hyperbola
- T.3 Find the length of the transverse or conjugate axes of a hyperbola
- T.4 Find the equations for the asymptotes of a hyperbola
- T.5 Find the foci of a hyperbola
- T.6 Write equations of hyperbolas in standard form from graphs
- T.7 Write equations of hyperbolas in standard form using properties

## Angle measures

## Trigonometry

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

## Trigonometric functions

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

## Trigonometric identities

## Sequences

## Derivatives

- Z.1 Sum and difference rules
- Z.2 Product rule
- Z.3 Quotient rule
- Z.4 Power rule I
- Z.5 Power rule II
- Z.6 Find derivatives of polynomials
- Z.7 Find derivatives of rational functions
- Z.8 Chain rule
- Z.9 Find derivatives of exponential functions
- Z.10 Find derivatives of logarithmic functions
- Z.11 Find derivatives of radical functions
- Z.12 Find derivatives using the chain rule I
- Z.13 Find derivatives using the chain rule II

## Probability

- AA.1 Introduction to probability
- AA.2 Theoretical and experimental probability
- AA.3 Compound events: find the number of outcomes
- AA.4 Calculate probabilities of events
- AA.5 Factorials
- AA.6 Counting principle
- AA.7 Permutation and combination notation
- AA.8 Find probabilities using permutations and combinations
- AA.9 Find probabilities using two-way frequency tables
- AA.10 Identify independent events
- AA.11 Probability of independent and dependent events
- AA.12 Geometric probability
- AA.13 Find conditional probabilities
- AA.14 Independence and conditional probability
- AA.15 Find conditional probabilities using two-way frequency tables
- AA.16 Find probabilities using the addition rule
- AA.17 Identify discrete and continuous random variables
- AA.18 Write a discrete probability distribution
- AA.19 Graph a discrete probability distribution
- AA.20 Expected values of random variables
- AA.21 Write the probability distribution for a game of chance
- AA.22 Expected values for a game of chance
- AA.23 Choose the better bet
- AA.24 Find probabilities using the binomial distribution
- AA.25 Find probabilities using the normal distribution