# Algebra

Here is a list of all of the skills that cover algebra! These skills are organised by year, 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!

## Primary 6 skills

- B.9 Solve for a variable using properties of multiplication
- S.1 Write variable expressions
- S.2 Write variable expressions: word problems
- S.3 Evaluate variable expressions with whole numbers
- S.4 Evaluate variable expressions with decimals
- S.5 Identify terms and coefficients
- S.6 Identify equivalent expressions

## Secondary 1 skills

- I.3 Solve equations with variable exponents
- K.2 Write equations for proportional relationships from tables
- K.5 Write equations for proportional relationships from graphs
- K.7 Interpret graphs of proportional relationships
- Q.6 Evaluate variable expressions for number sequences
- Q.7 Write variable expressions for arithmetic sequences
- R.1 Write variable expressions
- R.2 Write variable expressions: word problems
- R.3 Evaluate linear expressions
- R.4 Evaluate absolute value expressions
- R.5 Evaluate multi-variable expressions
- R.6 Evaluate nonlinear expressions
- R.7 Add and subtract like terms
- R.8 Identify terms and coefficients
- R.9 Sort factors of expressions
- R.10 HCF of monomials
- R.11 Factors of linear expressions
- R.14 Identify equivalent linear expressions
- R.15 Solve equations using properties
- R.16 Write equivalent expressions using properties
- R.17 Add, subtract and multiply linear expressions
- S.1 Which x satisfies an equation?
- S.2 Write an equation from words
- S.3 Model and solve equations using algebra tiles
- S.4 Write and solve equations that represent diagrams
- S.5 Solve one-step equations
- S.6 Solve two-step equations
- S.7 Solve equations: word problems
- S.8 Solve equations involving like terms
- S.9 Solve equations: complete the solution
- T.1 Solutions to inequalities
- T.3 Solve one-step inequalities
- U.1 Does (x, y) satisfy the equation?
- U.2 Identify independent and dependent variables
- U.3 Find a value using two-variable equations
- U.4 Solve word problems involving two-variable equations
- U.5 Complete a table for a two-variable relationship
- U.6 Write a two-variable equation
- U.7 Identify the graph of an equation
- U.8 Graph a two-variable equation
- U.9 Interpret a graph: word problems
- U.10 Write an equation from a graph using a table
- V.1 Find the gradient from a graph
- V.2 Find the gradient from two points
- V.4 Find the gradient from an equation
- V.5 Graph a line using gradient
- V.7 Identify linear and nonlinear functions

## Secondary 2 skills

- F.3 Solve equations with variable exponents
- F.8 Multiplication with exponents
- F.9 Division with exponents
- F.10 Multiplication and division with exponents
- F.11 Power rule
- F.18 Solve equations involving squares and square roots
- F.21 Solve equations involving cubes and cube roots
- I.2 Write equations for proportional relationships from tables
- I.5 Write equations for proportional relationships from graphs
- I.8 Interpret graphs of proportional relationships
- V.6 Evaluate variable expressions for number sequences
- V.7 Write variable expressions for arithmetic sequences
- W.1 Write variable expressions
- W.2 Write variable expressions from diagrams
- W.3 Write variable expressions: word problems
- W.4 Evaluate one-variable expressions
- W.5 Evaluate multi-variable expressions
- W.6 Evaluate absolute value expressions
- W.7 Evaluate radical expressions
- W.8 Evaluate rational expressions
- W.9 Identify terms and coefficients
- W.10 Sort factors of expressions
- W.13 Simplify variable expressions using properties
- W.14 Add and subtract like terms
- W.15 Add, subtract and multiply linear expressions
- W.16 Factors of linear expressions
- W.17 Identify equivalent linear expressions
- X.1 Which x satisfies an equation?
- X.2 Write an equation from words
- X.3 Model and solve equations using algebra tiles
- X.4 Write and solve equations that represent diagrams
- X.6 Solve one-step equations
- X.7 Solve two-step equations
- X.8 Solve multi-step equations
- X.9 Solve equations involving like terms
- X.10 Solve equations with variables on both sides
- X.11 Solve equations: mixed review
- X.12 Solve equations: complete the solution
- Y.1 Solutions to inequalities
- Y.3 Solve one-step inequalities
- Y.4 Solve two-step inequalities
- Y.5 Solve multi-step inequalities
- Z.2 Does (x, y) satisfy the linear function?
- Z.3 Identify independent and dependent variables
- Z.6 Evaluate a linear function
- Z.7 Complete a table for a linear function
- Z.8 Complete a table and graph a linear function
- Z.9 Interpret the graph of a linear function: word problems
- Z.10 Find the gradient of a graph
- Z.11 Find the gradient from two points
- Z.13 Find the gradient of a linear equation
- Z.14 Identify linear and nonlinear functions
- Z.15 Graph a line using gradient
- Z.16 Graph a line from an equation in y=mx+c form
- Z.17 Write a linear function from a table
- Z.18 Convert a linear equation in standard form to y=mx+c form
- Z.19 Graph a line from an equation in standard form
- Z.20 Write linear functions: word problems
- Z.21 Gradients of parallel and perpendicular lines
- AA.1 Is (x, y) a solution to the simultaneous equations?
- AA.2 Solve simultaneous equations by graphing
- AA.3 Solve simultaneous equations by graphing: word problems
- AA.4 Find the number of solutions to simultaneous equations by graphing
- AA.5 Find the number of solutions to simultaneous equations
- AA.6 Solve simultaneous equations using substitution
- AA.7 Solve simultaneous equations using substitution: word problems
- AA.8 Solve simultaneous equations using elimination
- AA.9 Solve simultaneous equations using elimination: word problems
- BB.1 Identify monomials
- BB.2 Model polynomials with algebra tiles
- BB.3 Add and subtract polynomials using algebra tiles
- BB.4 Add and subtract polynomials
- BB.5 Add polynomials to find perimeter
- BB.6 Multiply monomials
- BB.7 Divide monomials
- BB.8 Multiply and divide monomials
- BB.9 Powers of monomials
- BB.10 Square and cube roots of monomials
- BB.11 Multiply polynomials using algebra tiles
- BB.12 Multiply binomials
- BB.13 Multiply polynomials to find area
- BB.14 Multiply trinomials
- CC.1 Factorise quadratics with leading coefficient 1
- CC.2 Factorise quadratics with other leading coefficients
- CC.3 Factorise quadratics: special cases
- CC.4 Factorise quadratics using algebra tiles
- CC.5 Characteristics of quadratic functions
- CC.6 Complete a function table: quadratic functions
- CC.7 Solve a quadratic equation using the zero product property
- CC.8 Solve a quadratic equation by factorising
- DD.2 Simplify rational expressions
- DD.3 Multiply and divide rational expressions
- DD.4 Add and subtract rational expressions
- DD.5 Solve rational equations

## Secondary 3 skills

- B.3 Evaluate variable expressions involving integers
- B.7 Evaluate variable expressions involving rational numbers
- J.3 Simplify variable expressions using properties
- K.1 Write variable expressions
- K.2 Simplify variable expressions involving like terms and the distributive property
- K.3 Identify equivalent linear expressions
- K.4 Write variable equations
- K.5 Does x satisfy the equation?
- K.6 Which x satisfies an equation?
- K.7 Solve equations using order of operations
- L.1 Model and solve equations using algebra tiles
- L.2 Write and solve equations that represent diagrams
- L.3 Solve one-step linear equations
- L.4 Solve two-step linear equations
- L.5 Solve advanced linear equations
- L.6 Solve equations with variables on both sides
- L.7 Solve equations: complete the solution
- L.8 Find the number of solutions
- L.9 Create equations with no solutions or infinitely many solutions
- L.10 Solve linear equations: word problems
- L.11 Solve linear equations: mixed review
- M.3 Identify solutions to inequalities
- M.4 Solve one-step linear inequalities: addition and subtraction
- M.5 Solve one-step linear inequalities: multiplication and division
- M.6 Solve one-step linear inequalities
- M.7 Graph solutions to one-step linear inequalities
- M.8 Solve two-step linear inequalities
- M.9 Graph solutions to two-step linear inequalities
- M.10 Solve advanced linear inequalities
- M.11 Graph solutions to advanced linear inequalities
- N.1 Matrix vocabulary
- N.2 Matrix operation rules
- N.3 Add and subtract matrices
- N.4 Multiply a matrix by a scalar
- N.5 Multiply two matrices
- P.4 Rate of travel: word problems
- P.5 Weighted averages: word problems
- Q.4 Evaluate variable expressions for number sequences
- Q.5 Write variable expressions for arithmetic sequences
- Q.6 Write variable expressions for geometric sequences
- R.7 Evaluate a function
- R.8 Evaluate a function: plug in an expression
- R.10 Complete a function table from an equation
- R.11 Interpret the graph of a function: word problems
- S.3 Graph a proportional relationship
- S.4 Write direct variation equations
- S.5 Write and solve direct variation equations
- T.1 Identify linear functions
- T.2 Find the gradient of a graph
- T.3 Find the gradient from two points
- T.5 Find the gradient and y-intercept of a linear equation
- T.6 Graph an equation in y=mx+c form
- T.7 Write an equation in y=mx+c form from a graph
- T.8 Write an equation in y=mx+c form
- T.9 Write an equation in y=mx+c form from a table
- T.10 Write an equation in y=mx+c form from a word problem
- T.11 Linear equations: solve for y
- T.12 Write linear functions to solve word problems
- T.13 Complete a table and graph a linear function
- T.15 Write equations in standard form
- T.16 Standard form: find x- and y-intercepts
- T.17 Standard form: graph an equation
- T.18 Equations of horizontal and vertical lines
- T.19 Graph a horizontal or vertical line
- T.20 Point-gradient form: graph an equation
- T.21 Point-gradient form: write an equation
- T.22 Point-gradient form: write an equation from a graph
- T.23 Gradients of parallel and perpendicular lines
- T.24 Write an equation for a parallel or perpendicular line
- U.1 Is (x, y) a solution to the simultaneous equations?
- U.2 Solve simultaneous equations by graphing
- U.3 Solve simultaneous equations by graphing: word problems
- U.4 Find the number of solutions to simultaneous equations by graphing
- U.5 Find the number of solutions to simultaneous equations
- U.6 Solve simultaneous equations using substitution
- U.7 Solve simultaneous equations using substitution: word problems
- U.8 Solve simultaneous equations using elimination
- U.9 Solve simultaneous equations using elimination: word problems
- V.4 Multiplication with exponents
- V.5 Division with exponents
- V.6 Multiplication and division with exponents
- V.7 Power rule
- Y.1 Identify monomials
- Y.2 Multiply monomials
- Y.3 Divide monomials
- Y.4 Multiply and divide monomials
- Y.5 Powers of monomials
- Z.1 Polynomial vocabulary
- Z.2 Model polynomials with algebra tiles
- Z.3 Add and subtract polynomials using algebra tiles
- Z.4 Add and subtract polynomials
- Z.5 Add polynomials to find perimeter
- Z.6 Multiply a polynomial by a monomial
- Z.7 Multiply two polynomials using algebra tiles
- Z.8 Multiply two binomials
- Z.9 Multiply two binomials: special cases
- Z.10 Multiply polynomials
- AA.1 HCF of monomials
- AA.2 Factorise out a monomial
- AA.3 Factorise quadratics with leading coefficient 1
- AA.4 Factorise quadratics with other leading coefficients
- AA.5 Factorise quadratics: special cases
- AA.6 Factorise quadratics using algebra tiles
- AA.7 Factorise by grouping
- AA.8 Factorise polynomials
- BB.1 Characteristics of quadratic functions
- BB.2 Complete a function table: quadratic functions
- BB.3 Graph a quadratic function
- BB.4 Solve a quadratic equation using square roots
- BB.5 Solve a quadratic equation using the zero product property
- BB.6 Solve a quadratic equation by factorising
- BB.7 Complete the square
- BB.8 Solve a quadratic equation by completing the square
- BB.9 Solve a quadratic equation using the quadratic formula
- BB.10 Using the discriminant
- CC.1 Identify linear, quadratic and exponential functions from graphs
- CC.2 Identify linear, quadratic and exponential functions from tables
- CC.3 Write linear, quadratic and exponential functions
- DD.2 Simplify rational expressions
- DD.3 Multiply and divide rational expressions
- DD.4 Divide polynomials
- DD.5 Add and subtract rational expressions
- DD.6 Solve rational equations

## Secondary 4 skills

- B.3 Evaluate variable expressions involving integers
- B.7 Evaluate variable expressions involving rational numbers
- D.1 Model and solve equations using algebra tiles
- D.2 Write and solve equations that represent diagrams
- D.3 Solve one-step linear equations
- D.4 Solve two-step linear equations
- D.5 Solve advanced linear equations
- D.6 Solve equations with variables on both sides
- D.7 Solve equations: complete the solution
- D.8 Find the number of solutions
- D.9 Create equations with no solutions or infinitely many solutions
- D.10 Solve linear equations: word problems
- D.11 Solve linear equations: mixed review
- E.3 Identify solutions to inequalities
- E.4 Solve one-step linear inequalities: addition and subtraction
- E.5 Solve one-step linear inequalities: multiplication and division
- E.6 Solve one-step linear inequalities
- E.7 Graph solutions to one-step linear inequalities
- E.8 Solve two-step linear inequalities
- E.9 Graph solutions to two-step linear inequalities
- E.10 Solve advanced linear inequalities
- E.11 Graph solutions to advanced linear inequalities
- F.1 Identify linear functions
- F.2 Find the gradient of a graph
- F.3 Find the gradient from two points
- F.5 Find the gradient and y-intercept of a linear equation
- F.6 Graph an equation in y=mx+c form
- F.7 Write an equation in y=mx+c form from a graph
- F.8 Write an equation in y=mx+c form
- F.9 Slope-intercept form: write an equation from a table
- F.10 Slope-intercept form: write an equation from a word problem
- F.11 Write linear functions to solve word problems
- F.12 Complete a table and graph a linear function
- F.14 Write equations in standard form
- F.15 Standard form: find x- and y-intercepts
- F.16 Standard form: graph an equation
- F.17 Equations of horizontal and vertical lines
- F.18 Graph a horizontal or vertical line
- F.19 Point-gradient form: graph an equation
- F.20 Point-gradient form: write an equation
- F.21 Point-gradient form: write an equation from a graph
- F.22 Gradients of parallel and perpendicular lines
- F.23 Write an equation for a parallel or perpendicular line
- 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 by graphing
- G.5 Find the number of solutions to simultaneous equations
- G.6 Solve simultaneous equations using substitution
- G.7 Solve simultaneous equations using substitution: word problems
- G.8 Solve simultaneous equations using elimination
- G.9 Solve simultaneous equations using elimination: word problems
- H.1 Matrix vocabulary
- H.2 Matrix operation rules
- H.3 Add and subtract matrices
- H.4 Multiply a matrix by a scalar
- H.5 Multiply two matrices
- I.4 Multiplication with exponents
- I.5 Division with exponents
- I.6 Multiplication and division with exponents
- I.7 Power rule
- K.4 Evaluate variable expressions for number sequences
- K.5 Write variable expressions for arithmetic sequences
- K.6 Write variable expressions for geometric sequences
- L.1 Polynomial vocabulary
- L.2 Model polynomials with algebra tiles
- L.3 Add and subtract polynomials using algebra tiles
- L.4 Add and subtract polynomials
- L.5 Add polynomials to find perimeter
- L.6 Multiply and divide monomials
- L.7 Powers of monomials
- L.8 Multiply a polynomial by a monomial
- L.9 Multiply two polynomials using algebra tiles
- L.10 Multiply two binomials
- L.11 Multiply two binomials: special cases
- L.12 Multiply polynomials
- L.13 Pascal's triangle
- L.14 Pascal's triangle and the Binomial Theorem
- L.15 Binomial Theorem I
- L.16 Binomial Theorem II
- M.1 HCF of monomials
- M.2 Factorise out a monomial
- M.3 Factorise quadratics with leading coefficient 1
- M.4 Factorise quadratics with other leading coefficients
- M.5 Factorise quadratics: special cases
- M.6 Factorise quadratics using algebra tiles
- M.7 Factorise by grouping
- M.8 Factorise polynomials
- N.1 Characteristics of quadratic functions
- N.2 Complete a function table: quadratic functions
- N.3 Graph a quadratic function
- N.5 Solve a quadratic equation using square roots
- N.6 Solve a quadratic equation using the zero product property
- N.7 Solve a quadratic equation by factorising
- N.8 Complete the square
- N.9 Solve a quadratic equation by completing the square
- N.10 Solve a quadratic equation using the quadratic formula
- N.11 Using the discriminant
- O.1 Identify linear, quadratic and exponential functions from graphs
- O.2 Identify linear, quadratic and exponential functions from tables
- O.3 Write linear, quadratic and exponential functions
- P.2 Simplify rational expressions
- P.3 Multiply and divide rational expressions
- P.4 Divide polynomials
- P.5 Add and subtract rational expressions
- P.6 Solve rational equations
- GG.2 Rate of travel: word problems
- GG.3 Weighted averages: word problems

## Higher 1 skills

- 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
- 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
- D.1 Is (x, y) a solution to the system of inequalities?
- D.2 Solve systems of inequalities by graphing
- D.3 Solve systems of linear and absolute value inequalities by graphing
- D.4 Find the vertices of a solution set
- D.5 Linear programming
- 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
- F.1 Introduction to complex numbers
- F.2 Add and subtract complex numbers
- F.3 Complex conjugates
- F.4 Multiply complex numbers
- F.5 Divide complex numbers
- F.6 Add, subtract, multiply and divide complex numbers
- F.7 Absolute values of complex numbers
- F.8 Powers of i
- G.1 Factorise out a monomial
- G.2 Factorise quadratics
- G.3 Factorise quadratics using algebra tiles
- G.4 Factorise using a quadratic pattern
- G.5 Factorise by grouping
- G.6 Factorise sums and differences of cubes
- G.7 Factorise polynomials
- 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.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
- 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.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
- J.12 Domain and range of radical functions
- J.13 Solve radical equations
- L.1 Rational functions: asymptotes and excluded values
- L.2 Evaluate rational expressions I
- L.3 Evaluate rational expressions II
- L.4 Simplify rational expressions
- L.5 Multiply and divide rational expressions
- L.6 Add and subtract rational expressions
- L.7 Solve rational equations
- Y.4 Evaluate variable expressions for sequences
- Y.5 Write variable expressions for arithmetic sequences
- Y.6 Write variable expressions for geometric sequences

## Higher 2 skills

- C.3 Graph a quadratic function
- D.1 Divide polynomials using long division
- D.2 Write a polynomial from its roots
- D.3 Find the roots of factorised polynomials
- D.4 Rational root theorem
- D.5 Complex conjugate theorem
- D.6 Conjugate root theorems
- D.7 Descartes' Rule of Signs
- D.8 Fundamental Theorem of Algebra
- D.10 Factorise sums and differences of cubes
- D.11 Solve equations with sums and differences of cubes
- D.12 Factorise using a quadratic pattern
- D.13 Solve equations using a quadratic pattern
- D.14 Pascal's triangle
- D.15 Pascal's triangle and the Binomial Theorem
- D.16 Binomial Theorem I
- D.17 Binomial Theorem II
- E.1 Rational functions: asymptotes and excluded values
- F.2 Solve simultaneous equations by graphing: word problems
- F.5 Solve simultaneous equations using substitution: word problems
- F.8 Solve simultaneous equations in three variables using substitution
- F.9 Solve simultaneous equations in three variables using elimination
- F.10 Determine the number of solutions to simultaneous equations in three variables
- G.1 Solve systems of linear inequalities by graphing
- G.2 Solve systems of linear and absolute value inequalities by graphing
- G.3 Find the vertices of a solution set
- G.4 Linear programming
- H.1 Graph solutions to quadratic inequalities
- H.2 Solve quadratic inequalities
- H.3 Graph solutions to higher-degree inequalities
- H.4 Solve higher-degree inequalities
- I.1 Matrix vocabulary
- I.2 Matrix operation rules
- I.3 Add and subtract matrices
- I.4 Multiply a matrix by a scalar
- I.5 Linear combinations of matrices
- I.6 Multiply two matrices
- I.7 Simplify matrix expressions
- I.8 Solve matrix equations
- I.9 Determinant of a matrix
- I.10 Is a matrix invertible?
- I.11 Inverse of a 2 x 2 matrix
- I.12 Inverse of a 3 x 3 matrix
- I.13 Identify inverse matrices
- I.14 Solve matrix equations using inverses
- K.1 Add and subtract complex numbers
- K.2 Complex conjugates
- K.3 Multiply and divide complex numbers
- K.4 Add, subtract, multiply and divide complex numbers
- K.5 Absolute values of complex numbers
- K.6 Powers of i
- L.1 Introduction to the Argand plane
- L.2 Graph complex numbers
- L.3 Addition in the Argand plane
- L.4 Subtraction in the Argand plane
- L.5 Graph complex conjugates
- L.6 Absolute value in the Argand plane
- L.7 Midpoints in the Argand plane
- L.8 Distance in the Argand plane
- M.1 Find the modulus and argument of a complex number
- M.2 Convert complex numbers from rectangular to polar form
- M.3 Convert complex numbers from polar to rectangular form
- M.4 Convert complex numbers between rectangular and polar form