Functions and equations

Here is a list of all of the skills that cover functions and equations! 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!

Here is a list of all of the skills that cover functions and equations! To start practising, just click on any link.

Year 9 skills

  1. F.18 Solve equations involving squares and square roots
  2. I.2 Write equations for proportional relationships from tables
  3. I.4 Find the constant of proportionality from a graph
  4. I.5 Write equations for proportional relationships from graphs
  5. I.6 Identify proportional relationships
  6. I.8 Interpret graphs of proportional relationships
  7. I.9 Write and solve equations for proportional relationships
  8. X.1 Which x satisfies an equation?
  9. X.2 Write an equation from words
  10. X.3 Model and solve equations using algebra tiles
  11. X.4 Write and solve equations that represent diagrams
  12. X.6 Solve one-step equations
  13. X.7 Solve two-step equations
  14. X.8 Solve multi-step equations
  15. X.9 Solve equations involving like terms
  16. X.10 Solve equations with variables on both sides
  17. X.11 Solve equations: mixed review
  18. X.12 Solve equations: complete the solution
  19. X.13 Solve equations: word problems
  20. Z.1 Find the gradient of a graph
  21. Z.2 Find the gradient from two points
  22. Z.4 Find the gradient of an equation
  23. Z.5 Graph a line using gradient
  24. Z.6 Graph a line from an equation
  25. Z.7 Write a linear equation from a gradient and y-intercept
  26. Z.8 Write a linear equation from a graph
  27. Z.9 Write a linear equation from a gradient and a point
  28. Z.10 Write a linear equation from two points
  29. Z.11 Gradients of parallel and perpendicular lines
  30. AA.1 Identify functions
  31. AA.2 Does (x, y) satisfy the linear function?
  32. AA.3 Identify independent and dependent variables
  33. AA.6 Complete a table for a linear function
  34. AA.7 Complete a table and graph a linear function
  35. AA.8 Interpret the graph of a linear function: word problems
  36. AA.9 Write a linear function from a table
  37. AA.10 Compare linear functions: graphs, tables and equations
  38. AA.11 Write linear functions: word problems
  39. AA.12 Interpret linear functions
  40. AA.13 Identify linear and nonlinear functions
  41. AA.14 Does (x, y) satisfy the nonlinear function?
  42. AA.15 Find values using function graphs
  43. AA.16 Complete a table for a function graph

Year 10 skills

  1. J.4 Write variable equations
  2. J.5 Does x satisfy the equation?
  3. J.6 Solve equations using order of operations
  4. K.1 Model and solve equations using algebra tiles
  5. K.2 Write and solve equations that represent diagrams
  6. K.3 Solve one-step linear equations
  7. K.4 Solve two-step linear equations
  8. K.5 Solve advanced linear equations
  9. K.6 Solve equations with variables on both sides
  10. K.7 Solve equations: complete the solution
  11. K.8 Find the number of solutions
  12. K.10 Solve linear equations: word problems
  13. K.11 Solve linear equations: mixed review
  14. M.7 Scatter plots: line of best fit
  15. N.1 Relations: convert between tables, graphs, mappings and lists of points
  16. N.2 Domain and range of relations
  17. N.3 Identify independent and dependent variables
  18. N.4 Identify functions
  19. N.5 Identify functions: vertical line test
  20. N.6 Identify types of functions from graphs
  21. N.7 Find values using function graphs
  22. N.8 Evaluate a function
  23. N.9 Evaluate a function: plug in an expression
  24. N.10 Complete a function table from a graph
  25. N.11 Complete a function table from an equation
  26. N.12 Interpret the graph of a function: word problems
  27. O.1 Identify proportional relationships
  28. O.2 Find the constant of variation
  29. O.3 Graph a proportional relationship
  30. O.4 Write direct variation equations
  31. O.5 Write and solve direct variation equations
  32. O.6 Identify direct variation and inverse variation
  33. O.7 Write inverse variation equations
  34. O.8 Write and solve inverse variation equations
  35. P.1 Identify linear functions
  36. P.2 Find the gradient of a graph
  37. P.3 Find the gradient from two points
  38. P.5 Find the gradient and y-intercept of a linear equation
  39. P.6 Graph an equation in y=mx+c form
  40. P.7 Write an equation in y=mx+c form from a graph
  41. P.8 Write an equation in y=mx+c form
  42. P.9 Write an equation in y=mx+c form from a table
  43. P.10 Write an equation in y=mx+c form from a word problem
  44. P.11 Linear equations: solve for y
  45. P.12 Write linear functions to solve word problems
  46. P.13 Complete a table and graph a linear function
  47. P.14 Compare linear functions: graphs, tables and equations
  48. P.15 Write equations in standard form
  49. P.16 Standard form: find x- and y-intercepts
  50. P.17 Standard form: graph an equation
  51. P.18 Equations of horizontal and vertical lines
  52. P.19 Graph a horizontal or vertical line
  53. P.20 Point-gradient form: graph an equation
  54. P.21 Point-gradient form: write an equation
  55. P.22 Point-gradient form: write an equation from a graph
  56. P.23 Gradients of parallel and perpendicular lines
  57. P.24 Write an equation for a parallel or perpendicular line
  58. P.25 Transformations of linear functions
  59. R.1 Is (x, y) a solution to the simultaneous equations?
  60. R.2 Solve simultaneous equations by graphing
  61. R.3 Solve simultaneous equations by graphing: word problems
  62. R.4 Find the number of solutions to simultaneous equations by graphing
  63. R.5 Find the number of solutions to simultaneous equations
  64. R.6 Solve simultaneous equations using substitution
  65. R.7 Solve simultaneous equations using substitution: word problems
  66. R.8 Solve simultaneous equations using elimination
  67. R.9 Solve simultaneous equations using elimination: word problems
  68. V.1 Evaluate an exponential function
  69. V.2 Match exponential functions and graphs
  70. V.3 Domain and range of exponential functions
  71. Z.1 Characteristics of quadratic functions
  72. Z.2 Complete a function table: quadratic functions
  73. Z.3 Solve a quadratic equation using square roots
  74. Z.4 Solve a quadratic equation using the zero product property
  75. Z.5 Solve a quadratic equation by factorising
  76. Z.7 Solve a quadratic equation by completing the square
  77. Z.8 Solve a quadratic equation using the quadratic formula
  78. BB.1 Rational functions: asymptotes and excluded values
  79. BB.7 Solve rational equations
  80. CC.4 Rate of travel: word problems
  81. CC.5 Weighted averages: word problems

Year 11 skills

  1. D.1 Solve one- and two-step linear equations
  2. D.2 Solve advanced linear equations
  3. D.3 Solve equations with variables on both sides
  4. D.4 Solve equations: complete the solution
  5. D.5 Find the number of solutions
  6. D.7 Solve linear equations: word problems
  7. D.8 Solve linear equations: mixed review
  8. F.1 Relations: convert between tables, graphs, mappings and lists of points
  9. F.2 Domain and range of relations
  10. F.3 Find values using function graphs
  11. F.4 Interpret the graph of a function: word problems
  12. F.5 Identify independent and dependent variables
  13. F.6 Identify functions
  14. F.7 Evaluate a function
  15. F.8 Complete a function table from a graph
  16. F.9 Complete a function table from an equation
  17. G.1 Identify proportional relationships
  18. G.2 Find the constant of variation
  19. G.3 Graph a proportional relationship
  20. G.4 Write direct variation equations
  21. G.5 Write and solve direct variation equations
  22. G.6 Write inverse variation equations
  23. G.7 Write and solve inverse variation equations
  24. G.8 Identify direct variation and inverse variation
  25. H.1 Identify linear functions
  26. H.2 Find the gradient of a graph
  27. H.3 Find the gradient from two points
  28. H.5 Find the gradient and y-intercept of a linear equation
  29. H.6 Graph an equation in y=mx+c form
  30. H.7 Write an equation in y=mx+c form from a graph
  31. H.8 Write an equation in y=mx+c form
  32. H.9 Write an equation in y=mx+c form from a table
  33. H.10 Write an equation in y=mx+c form from a word problem
  34. H.11 Write linear functions to solve word problems
  35. H.12 Complete a table and graph a linear function
  36. H.13 Compare linear functions: graphs, tables and equations
  37. H.14 Write equations in standard form
  38. H.15 Standard form: find x- and y-intercepts
  39. H.16 Standard form: graph an equation
  40. H.17 Equations of horizontal and vertical lines
  41. H.18 Graph a horizontal or vertical line
  42. H.19 Point-gradient form: graph an equation
  43. H.20 Point-gradient form: write an equation
  44. H.21 Point-gradient form: write an equation from a graph
  45. H.22 Gradients of parallel and perpendicular lines
  46. H.23 Write an equation for a parallel or perpendicular line
  47. H.26 Transformations of linear functions
  48. I.1 Is (x, y) a solution to the simultaneous equations?
  49. I.2 Solve simultaneous equations by graphing
  50. I.3 Solve simultaneous equations by graphing: word problems
  51. I.4 Find the number of solutions to simultaneous equations by graphing
  52. I.5 Find the number of solutions to simultaneous equations
  53. I.6 Solve simultaneous equations using substitution
  54. I.7 Solve simultaneous equations using substitution: word problems
  55. I.8 Solve simultaneous equations using elimination
  56. I.9 Solve simultaneous equations using elimination: word problems
  57. J.1 Evaluate an exponential function
  58. J.2 Match exponential functions and graphs
  59. J.3 Domain and range of exponential functions
  60. N.1 Characteristics of quadratic functions
  61. N.2 Complete a function table: quadratic functions
  62. N.3 Solve a quadratic equation using square roots
  63. N.4 Solve a quadratic equation using the zero product property
  64. N.5 Solve a quadratic equation by factorising
  65. N.7 Solve a quadratic equation by completing the square
  66. N.8 Solve a quadratic equation using the quadratic formula
  67. O.1 Identify linear, quadratic and exponential functions from graphs
  68. O.2 Identify linear, quadratic and exponential functions from tables
  69. O.3 Write linear, quadratic and exponential functions
  70. O.4 Linear functions over unit intervals
  71. O.5 Exponential functions over unit intervals
  72. O.6 Describe linear and exponential growth and decay
  73. O.8 Graph a quadratic function
  74. P.1 Function transformation rules
  75. P.2 Translations of functions
  76. P.3 Reflections of functions
  77. P.4 Dilations of functions
  78. P.5 Transformations of functions
  79. S.1 Rational functions: asymptotes and excluded values
  80. S.7 Solve rational equations
  81. HH.2 Rate of travel: word problems
  82. HH.3 Weighted averages: word problems
  83. LL.6 Scatter plots: line of best fit

Year 12 skills

  1. A.1 Solve linear equations
  2. A.2 Solve linear equations: word problems
  3. A.3 Solve absolute value equations
  4. A.4 Graph solutions to absolute value equations
  5. B.8 Graph solutions to absolute value inequalities
  6. C.1 Domain and range
  7. C.2 Identify functions
  8. C.3 Evaluate functions
  9. C.4 Find values using function graphs
  10. C.5 Complete a table for a function graph
  11. C.6 Find the gradient of a linear function
  12. C.7 Gradients of parallel and perpendicular lines
  13. C.8 Graph a linear function
  14. C.9 Write linear equations in standard form
  15. C.10 Write linear equations in point-gradient form
  16. C.11 Write an equation for a parallel or perpendicular line
  17. C.12 Linear functions over unit intervals
  18. C.13 Complete a function table: absolute value functions
  19. C.14 Graph an absolute value function
  20. D.1 Is (x, y) a solution to the simultaneous equations?
  21. D.2 Solve simultaneous equations by graphing
  22. D.3 Solve simultaneous equations by graphing: word problems
  23. D.6 Solve simultaneous equations using substitution: word problems
  24. D.7 Solve simultaneous equations using elimination
  25. D.8 Solve simultaneous equations using elimination: word problems
  26. D.9 Solve simultaneous equations using any method
  27. D.10 Solve simultaneous equations using any method: word problems
  28. D.11 Solve non-linear simultaneous equations
  29. F.1 Characteristics of quadratic functions
  30. F.2 Complete a function table: quadratic functions
  31. F.3 Find a quadratic function
  32. F.4 Graph a quadratic function
  33. F.5 Match quadratic functions and graphs
  34. F.6 Solve a quadratic equation using square roots
  35. F.7 Solve a quadratic equation using the zero product property
  36. F.8 Solve a quadratic equation by factorising
  37. F.9 Complete the square
  38. F.10 Solve a quadratic equation using the quadratic formula
  39. F.11 Using the discriminant
  40. H.5 Solve polynomial equations
  41. H.10 Match polynomials and graphs
  42. I.12 Domain and range of radical functions
  43. I.13 Solve radical equations
  44. K.1 Rational functions: asymptotes and excluded values
  45. K.7 Solve rational equations
  46. L.1 Add and subtract functions
  47. L.2 Multiply functions
  48. L.3 Divide functions
  49. L.4 Composition of linear functions: find a value
  50. L.5 Composition of linear functions: find an equation
  51. L.6 Composition of linear and quadratic functions: find a value
  52. L.7 Composition of linear and quadratic functions: find an equation
  53. L.8 Identify inverse functions
  54. L.9 Find values of inverse functions from tables
  55. L.10 Find values of inverse functions from graphs
  56. L.11 Find inverse functions and relations
  57. M.1 Translations of functions
  58. M.2 Reflections of functions
  59. M.3 Dilations of functions
  60. M.4 Transformations of functions
  61. M.5 Function transformation rules
  62. M.6 Describe function transformations
  63. O.9 Exponential functions over unit intervals
  64. O.10 Describe linear and exponential growth and decay
  65. S.1 Find properties of sine functions
  66. S.5 Find properties of cosine functions
  67. T.1 Complementary angle identities
  68. T.2 Symmetry and periodicity of trigonometric functions
  69. T.3 Trigonometric identities I
  70. T.4 Trigonometric identities II
  71. Z.6 Scatter plots: line of best fit
  72. AA.1 Find limits using graphs
  73. AA.2 Find one-sided limits using graphs
  74. AA.3 Determine if a limit exists
  75. BB.1 Find limits using addition, subtraction and multiplication laws
  76. BB.2 Find limits using the division law
  77. BB.3 Find limits using power and root laws
  78. BB.4 Find limits using limit laws
  79. BB.5 Find limits of polynomials and rational functions
  80. BB.6 Find limits involving factorisation and rationalisation
  81. BB.7 Find limits involving absolute value functions
  82. BB.8 Find limits involving trigonometric functions
  83. CC.1 Find limits at vertical asymptotes using graphs
  84. CC.2 Determine end behaviour using graphs
  85. CC.3 Determine end behaviour of polynomial and rational functions
  86. CC.4 Find the limit at a vertical asymptote of a rational function I
  87. CC.5 Find the limit at a vertical asymptote of a rational function II
  88. DD.1 Identify graphs of continuous functions
  89. DD.2 Determine continuity using graphs
  90. DD.3 Determine one-sided continuity using graphs
  91. DD.4 Find and analyse points of discontinuity using graphs
  92. DD.5 Determine continuity on an interval using graphs
  93. DD.6 Determine the continuity of a piecewise function at a point
  94. DD.7 Make a piecewise function continuous
  95. DD.8 Intermediate Value Theorem
  96. EE.8 Power rule I
  97. EE.9 Power rule II
  98. EE.10 Find derivatives of polynomials
  99. EE.11 Find second derivatives of polynomials

Year 13 skills

  1. A.1 Domain and range
  2. A.2 Identify functions
  3. A.3 Find the gradient of a linear function
  4. A.4 Graph a linear function
  5. A.5 Write the equation of a linear function
  6. A.6 Linear functions over unit intervals
  7. A.7 Evaluate functions
  8. A.8 Find values using function graphs
  9. A.9 Complete a table for a function graph
  10. A.10 Add, subtract, multiply and divide functions
  11. A.11 Composition of functions
  12. A.12 Identify inverse functions
  13. A.13 Find values of inverse functions from tables
  14. A.14 Find values of inverse functions from graphs
  15. A.15 Find inverse functions and relations
  16. B.1 Translations of functions
  17. B.2 Reflections of functions
  18. B.3 Dilations of functions
  19. B.4 Transformations of functions
  20. B.5 Function transformation rules
  21. B.6 Describe function transformations
  22. C.1 Characteristics of quadratic functions
  23. C.2 Find the maximum or minimum value of a quadratic function
  24. C.3 Graph a quadratic function
  25. C.4 Match quadratic functions and graphs
  26. C.5 Solve a quadratic equation using square roots
  27. C.6 Solve a quadratic equation by factorising
  28. C.7 Solve a quadratic equation by completing the square
  29. C.8 Solve a quadratic equation using the quadratic formula
  30. C.9 Using the discriminant
  31. D.9 Match polynomials and graphs
  32. D.11 Solve equations with sums and differences of cubes
  33. D.13 Solve equations using a quadratic pattern
  34. E.1 Rational functions: asymptotes and excluded values
  35. E.2 Solve rational equations
  36. E.3 Check whether two rational functions are inverses
  37. F.14 Exponential functions over unit intervals
  38. F.15 Describe linear and exponential growth and decay
  39. G.1 Domain and range of radical functions
  40. G.2 Solve radical equations
  41. I.1 Solve simultaneous equations by graphing
  42. I.2 Solve simultaneous equations by graphing: word problems
  43. I.3 Classify simultaneous equations
  44. I.4 Solve simultaneous equations using substitution
  45. I.5 Solve simultaneous equations using substitution: word problems
  46. I.6 Solve simultaneous equations using elimination
  47. I.7 Solve simultaneous equations using elimination: word problems
  48. I.8 Solve simultaneous equations in three variables using substitution
  49. I.9 Solve simultaneous equations in three variables using elimination
  50. I.10 Determine the number of solutions to simultaneous equations in three variables
  51. K.1 Find properties of sine functions
  52. K.5 Find properties of cosine functions
  53. L.1 Complementary angle identities
  54. L.2 Symmetry and periodicity of trigonometric functions
  55. L.3 Trigonometric identities I
  56. L.4 Trigonometric identities II
  57. S.8 Find the equation of a regression line
  58. U.1 Sum and difference rules
  59. U.2 Product rule
  60. U.3 Quotient rule
  61. U.4 Power rule I
  62. U.5 Power rule II
  63. U.6 Chain rule
  64. U.7 Inverse function rule
  65. V.1 Find derivatives of polynomials
  66. V.2 Find derivatives of rational functions
  67. V.3 Find derivatives of trigonometric functions I
  68. V.4 Find derivatives of trigonometric functions II
  69. V.5 Find derivatives of exponential functions
  70. V.6 Find derivatives of logarithmic functions
  71. V.7 Find derivatives of inverse trigonometric functions
  72. V.8 Find derivatives of radical functions
  73. V.9 Find derivatives using the product rule I
  74. V.10 Find derivatives using the product rule II
  75. V.11 Find derivatives using the quotient rule I
  76. V.12 Find derivatives using the quotient rule II
  77. V.13 Find derivatives using the chain rule I
  78. V.14 Find derivatives using the chain rule II
  79. W.1 Find derivatives using implicit differentiation
  80. W.2 Find tangent lines using implicit differentiation
  81. W.3 Find derivatives using logarithmic differentiation
  82. X.1 Find higher derivatives of polynomials
  83. X.2 Find higher derivatives of rational and radical functions
  84. X.3 Find second derivatives of trigonometric, exponential and logarithmic functions
  85. X.4 Find higher derivatives using patterns