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

Year 10 skills

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

Year 11 skills

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

Year 12 skills

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