# Class XI maths

Here is a list of all of the maths skills students learn in class XI! 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!

## Consumer maths

## Single-variable inequalities

- B.1 Graph inequalities
- B.2 Write inequalities from graphs
- B.3 Identify solutions to inequalities
- B.4 Solve one-step linear inequalities: addition and subtraction
- B.5 Solve one-step linear inequalities: multiplication and division
- B.6 Solve one-step linear inequalities
- B.7 Graph solutions to one-step linear inequalities
- B.8 Solve two-step linear inequalities
- B.9 Graph solutions to two-step linear inequalities
- B.10 Solve advanced linear inequalities
- B.11 Graph solutions to advanced linear inequalities
- B.12 Graph compound inequalities
- B.13 Write compound inequalities from graphs
- B.14 Solve compound inequalities
- B.15 Graph solutions to compound inequalities
- B.16 Graph solutions to quadratic inequalities
- B.17 Solve quadratic inequalities

## Relations and functions

- C.1 Relations: convert between tables, graphs, mappings and lists of points
- C.2 Domain and range of relations
- C.3 Identify independent and dependent variables
- C.4 Identify functions
- C.5 Identify functions: vertical line test
- C.6 Find values using function graphs
- C.7 Evaluate a function
- C.8 Evaluate a function: plug in an expression
- C.9 Complete a function table from a graph
- C.10 Complete a function table from an equation
- C.11 Interpret the graph of a function: word problems

## Linear functions

- D.1 Find the slope of a graph
- D.2 Find the slope from two points
- D.3 Find a missing coordinate using slope
- D.4 Slope-intercept form: find the slope and y-intercept
- D.5 Slope-intercept form: graph an equation
- D.6 Slope-intercept form: write an equation from a graph
- D.7 Slope-intercept form: write an equation
- D.8 Slope-intercept form: write an equation from a table
- D.9 Slope-intercept form: write an equation from a word problem
- D.10 Write linear functions to solve word problems
- D.11 Complete a table and graph a linear function
- D.12 Write equations in standard form
- D.13 Standard form: find x- and y-intercepts
- D.14 Standard form: graph an equation
- D.15 Equations of horizontal and vertical lines
- D.16 Graph a horizontal or vertical line
- D.17 Slopes of parallel and perpendicular lines
- D.18 Write an equation for a parallel or perpendicular line
- D.19 Transformations of linear functions

## Linear inequalities

- E.1 Does (x, y) satisfy the inequality?
- E.2 Linear inequalities: solve for y
- E.3 Graph a linear inequality in the coordinate plane
- E.4 Linear inequalities: word problems
- E.5 Is (x, y) a solution to the system of inequalities?
- E.6 Solve systems of linear inequalities by graphing
- E.7 Solve systems of linear and absolute value inequalities by graphing

## Complex numbers

## Argand plane

## Factorising

## Quadratic functions

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

## Polynomials

- J.1 Polynomial vocabulary
- J.2 Add and subtract polynomials
- J.3 Multiply polynomials
- J.4 Divide polynomials using long division
- J.5 Divide polynomials using synthetic division
- J.6 Evaluate polynomials using synthetic division
- J.7 Solve polynomial equations
- J.8 Write a polynomial from its roots
- J.9 Find the roots of factorised polynomials
- J.10 Rational root theorem
- J.11 Complex conjugate theorem
- J.12 Conjugate root theorems
- J.13 Match polynomials and graphs
- J.14 Fundamental Theorem of Algebra
- J.15 Pascal's triangle
- J.16 Pascal's triangle and the Binomial Theorem
- J.17 Binomial Theorem I
- J.18 Binomial Theorem II

## Parabolas

- K.1 Identify the direction a parabola opens
- K.2 Find the vertex of a parabola
- K.3 Find the focus or directrix of a parabola
- K.4 Find the axis of symmetry of a parabola
- K.5 Write equations of parabolas in vertex form from graphs
- K.6 Write equations of parabolas in vertex form using properties
- K.7 Convert equations of parabolas from general to vertex form
- K.8 Find properties of a parabola from equations in general form
- K.9 Graph parabolas

## Circles

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

## Ellipses

- M.1 Find the center, vertices, or co-vertices of an ellipse
- M.2 Find the length of the major or minor axes of an ellipse
- M.3 Find the foci of an ellipse
- M.4 Write equations of ellipses in standard form from graphs
- M.5 Write equations of ellipses in standard form using properties
- M.6 Convert equations of ellipses from general to standard form
- M.7 Find properties of ellipses from equations in general form

## Hyperbolas

- N.1 Find the center of a hyperbola
- N.2 Find the vertices of a hyperbola
- N.3 Find the length of the transverse or conjugate axes of a hyperbola
- N.4 Find the equations for the asymptotes of a hyperbola
- N.5 Find the foci of a hyperbola
- N.6 Write equations of hyperbolas in standard form from graphs
- N.7 Write equations of hyperbolas in standard form using properties
- N.8 Convert equations of hyperbolas from general to standard form
- N.9 Find properties of hyperbolas from equations in general form

## Rational functions and expressions

## Function operations

- P.1 Add and subtract functions
- P.2 Multiply functions
- P.3 Divide functions
- P.4 Composition of linear functions: find a value
- P.5 Composition of linear functions: find an equation
- P.6 Composition of linear and quadratic functions: find a value
- P.7 Composition of linear and quadratic functions: find an equation

## Angle measures

## Trigonometry

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

## Trigonometric functions

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

## Problem solving

## Logic

## Sequences and series

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

## Introduction to limits

## Calculate limits

## Limits involving infinity

## Limits and rational functions

## Continuity

- BB.1 Identify graphs of continuous functions
- BB.2 Determine continuity using graphs
- BB.3 Determine one-sided continuity using graphs
- BB.4 Find and analyse points of discontinuity using graphs
- BB.5 Determine continuity on an interval using graphs
- BB.6 Determine the continuity of a piecewise function at a point
- BB.7 Make a piecewise function continuous
- BB.8 Intermediate Value Theorem

## Introduction to derivatives

## Calculate derivatives

- DD.1 Sum and difference rules
- DD.2 Product rule
- DD.3 Quotient rule
- DD.4 Power rule I
- DD.5 Power rule II
- DD.6 Find derivatives of polynomials
- DD.7 Find derivatives of rational functions
- DD.8 Find derivatives of trigonometric functions I
- DD.9 Find derivatives of trigonometric functions II
- DD.10 Chain rule
- DD.11 Find derivatives of radical functions
- DD.12 Find derivatives using the product rule
- DD.13 Find derivatives using the quotient rule I
- DD.14 Find derivatives using the quotient rule II
- DD.15 Find derivatives using the chain rule I
- DD.16 Find derivatives using the chain rule II

## Probability

- EE.1 Introduction to probability
- EE.2 Theoretical and experimental probability
- EE.3 Compound events: find the number of outcomes
- EE.4 Calculate probabilities of events
- EE.5 Permutations
- EE.6 Counting principle
- EE.7 Permutation and combination notation
- EE.8 Find probabilities using permutations and combinations
- EE.9 Find probabilities using two-way frequency tables
- EE.10 Identify independent events
- EE.11 Probability of independent and dependent events
- EE.12 Geometric probability
- EE.13 Find conditional probabilities
- EE.14 Independence and conditional probability
- EE.15 Find conditional probabilities using two-way frequency tables
- EE.16 Find probabilities using the addition rule
- EE.17 Find probabilities using the normal distribution