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

## Functions

## Simultaneous equations

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

## Inequalities and linear programming

## Matrices

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

## Complex numbers

## Factorising

## Quadratic functions

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

## Polynomials

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

## Radical functions and expressions

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

## Rational exponents

## Rational functions and expressions

## Function operations

- M.1Add and subtract functions
- M.2Multiply functions
- M.3Divide functions
- M.4Composition of linear functions
- M.5Composition of linear and quadratic functions
- M.6Identify inverse functions
- M.7Find values of inverse functions from tables
- M.8Find values of inverse functions from graphs
- M.9Find inverse functions and relations

## Families of functions

## Logarithms

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

## Exponential and logarithmic functions

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

## Parabolas

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

## Circles

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

## Hyperbolas

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

## Angle measures

## Trigonometry

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

## Trigonometric functions

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

## Trigonometric identities

## Sequences

## Derivatives

## Probability

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