We believe **deep understanding** is enhanced with mental hooks onto **historical stories**, hence the Inspiration round and one section of the Confidence round is focused upon the work of twenty-five mathematicians from within a specified century.

For the **October 2021 to July 2022 season**, focus is on work from the **19th century**:

Adrian-Marie Legendre | Carl Fredrich Gauss | George Cantor | Jean-Robert Argard | Leonard Euler |

Arther Cayley | Charles Babbage | George Peacock | John Venn | Nikolai Lobachevsky |

Augustin-Ferdinand Mobius | Evariste Galois | Gottfried Wilhelm Leibniz | Joseph Fourier | Peter Dirichlet |

Augustin-Louis Cauchy | Felix Klein | Henri Poincare | Joseph-Louise LaGrange | Pierre-Simon LaPlace |

Bernard Riemann | George Boole | Janos Bolyai | Karl Weierstrass | William Hamilton |

For the October 2020 to July 2021 season, focus was on work from the 20th century:

A.N. Whitehead | Andrey Kolmogorov | Emmy Noether | John von Neumann | Paul Erdos |

Alan Turing | Benoit Mandelbrot | G.H. Hardy | Julia Robinson | Srinivasa Ramanujan |

Alanzo Church | Bertrand Russell | Gerd Faltings | Kurt Godel | Thomas Hales |

Alexander Grothendiek | Claude Shannon | J. E. Littlewood | Nicolas Bourbaki | Wolfgang Haken |

Andre Weil | David Hilbert | John Nash | Paul Cohen | Yuri Matiyasevich |

This learning content is comprised of conceptual understanding statements, which have been crafted by considering important generic knowledge, for a happier life, of:

- Numeracy
- Pattern spotting
- Logic
- Deductive reasoning

within real-life as well as abstract situations.

Each competition will feature content atÂ the same level and below.

# | THEME | LEVEL | EU | DESCRIPTOR |
---|---|---|---|---|

1 | Arithmetic | Junior | Order of operations | Understand how rational exponents are short-hand for roots, and simplify expressions accordingly |

2 | Arithmetic | Junior | Order of operations | Perform common binary operations on number values |

3 | Arithmetic | Junior | Quotients | Manipulate any quotient raised to any exponent |

4 | Arithmetic | Junior | Exponents | Communicate in base 2 and convert into base 10 |

5 | Arithmetic | Junior | Ratio and Proportion | Use indirect proportion as a constant rate of change for different quantities |

6 | Arithmetic | Junior | Matrices | Use matrices to transform images around a cartesian grid |

7 | Arithmetic | Junior | Operations | Use the factorial operation |

8 | Arithmetic | Junior | Order of operations | Perform correct order of operation processes involving trigonometric ratios |

9 | Arithmetic | Junior | Rationality | Interpret solutions involving any real-numbers in context |

10 | Arithmetic | Junior | Exponents | Manipulate numbers expressed in any form and within any common base |

11 | Arithmetic | Junior | Error | Analyse innaccuracies of compounding rounded values |

12 | Arithmetic | Junior | Sequences and Series | Use conventional notation for geometric sequences and find simple series in context |

13 | Arithmetic | Junior | Binomial expressions | Use the binomial expansion with integer values |

14 | Arithmetic | Junior | Cryptography | Communicate in braille and morse code with precision |

15 | Arithmetic | Junior | Matrices | Use matrices to visualise and draw transformed images of shapes on a cartesian grid |

16 | Arithmetic | Junior | Order of operations | Perform binary operations on algebraic values |

17 | Arithmetic | Junior | Exponents | Solve simple modular arithmetic problems |

18 | Arithmetic | Junior | Finance | Create and interpret simple accounting documentation |

19 | Arithmetic | Junior | Binomial expressions | Use the binomial expansion with simple rational values |

20 | Arithmetic | Junior | Matrices | Use inverse 2 by 2 matrices to help transform (large) data sets in solving real-life problems |

21 | Arithmetic | Junior | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

22 | Arithmetic | Junior | Combinatorics | Calculate simple binomial problems involving combinations |

23 | Arithmetic | Junior | Combinatorics | Distinguish between and calculate simple problems involving permutations |

24 | Arithmetic | Junior | Divisibility | Identify divisibilities of a number written in any base |

25 | Arithmetic | Junior | Finance | Solve problems involving amortization and annuity |

26 | Arithmetic | Junior | Rationality | Interpret solutions involving any real-numbers in context |

27 | Arithmetic | Primary | Time | Read from an analog clock |

28 | Arithmetic | Primary | Operations | Understand how multiplication is short-hand for repeated addition and use it accordingly |

29 | Arithmetic | Primary | Divisibility | Identify the divisibility by 10, 5 and 2 of any number |

30 | Arithmetic | Primary | Quotients | Understand how division is short-hand for repeated subtraction and find exact quotients without remainders |

31 | Arithmetic | Primary | Notation | Articulate place value of number digits within words |

32 | Arithmetic | Primary | Exponents | Appreciate the distinction between numbers arranged in a square compared to in an oblong |

33 | Arithmetic | Primary | Finance | Appreciate and recognise 'value for money' involving decimals and percentages |

34 | Arithmetic | Primary | Error | Identify approximations for sums and obvious mis-calculations |

35 | Arithmetic | Primary | Ratio and Proportion | Calculate any percentage of an amount |

36 | Arithmetic | Primary | Sequences and Series | Recite up to the 15 times tables as a fundamental axiom of number patterns |

37 | Arithmetic | Primary | Cryptography | Communicate the phonetic alphabet, Atbash, handphone keypad and dancing men cipher with precision |

38 | Arithmetic | Primary | Expressions | Identify common factors within expressions |

39 | Arithmetic | Primary | Kinematics | Calculate departure, arrival times or distance travelled in context |

40 | Arithmetic | Primary | Time | Solve problems involving all convential formats of time |

41 | Arithmetic | Primary | Measures | Recognise appropriate units for quantities in context |

42 | Arithmetic | Primary | Divisibility | Identify and label numbers that have a maximum of 2 factors |

43 | Arithmetic | Primary | Rationality | Distinguish between the different possible types of rational number |

44 | Arithmetic | Primary | Notation | Communicate the value of items using words |

45 | Arithmetic | Primary | Exponents | Calculate the value of integers raised to single-digit exponents |

46 | Arithmetic | Primary | Ratio and Proportion | Create group representations for parts of a whole |

47 | Arithmetic | Primary | Exponents | Use everyday contexts to perform exponent calculations with any base number |

48 | Arithmetic | Primary | Finance | Consider costs and expenses when making value judgements within specified budgets |

49 | Arithmetic | Primary | Error | Identify the magnitude of a rounding error |

50 | Arithmetic | Primary | Ratio and Proportion | Use direct proportion as a constant rate of change for different quantities |

51 | Arithmetic | Primary | Divisibility | Decompose any number into its prime factors and compare with others |

52 | Arithmetic | Primary | Sequences and Series | Use conventional notation for common sequences in context |

53 | Arithmetic | Primary | Exponents | Express values in exponent form |

54 | Arithmetic | Primary | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

55 | Arithmetic | Secondary | Order of operations | Perform multi-step calculations, involving parentheses and indices, in the correct order |

56 | Arithmetic | Secondary | Quotients | Calculate quotients of values and interpret possible remainders in context |

57 | Arithmetic | Secondary | Divisibility | Identify divisibilities by single-digit numbers |

58 | Arithmetic | Secondary | Rationality | Appreciate there are infinitely many numbers between any two distinct numbers |

59 | Arithmetic | Secondary | Notation | Understand appropriate representations for very small and very large numbers in context |

60 | Arithmetic | Secondary | Cryptography | Communicate morse code, braille, Ceasar and PigPen cipher with precision |

61 | Arithmetic | Secondary | Transformations | Use vectors to translate images around a cartesian grid |

62 | Arithmetic | Secondary | Rationality | Perform calculations involving any real numbers |

63 | Arithmetic | Secondary | Notation | Always communicate using conventional notation, including units of derived values |

64 | Arithmetic | Secondary | Finance | Make financial value judgements within real contexts |

65 | Arithmetic | Secondary | Error | Write answers to appropriate decimal places or significant figures |

66 | Arithmetic | Secondary | Measures | Convert across common imperial and metric quantities |

67 | Arithmetic | Secondary | Quotients | Express any quotient in terms of the sum of unit fractions |

68 | Arithmetic | Secondary | Finance | Compare results using simple and compound interest |

69 | Arithmetic | Secondary | Divisibility | Solve simple linear concruence problems |

70 | Arithmetic | Secondary | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

71 | Arithmetic | Secondary | Exponential and Logarithmic | Recognise and compare depreciation rates with absolute drops in value |

72 | Arithmetic | Secondary | Exponential and Logarithmic | Identify and use the multiplier when calculating with increasing and decreasing percentages |

73 | Arithmetic | Secondary | Sequences and Series | Use conventional notation for arithmetic sequences and find simple series in context |

74 | Arithmetic | Senior | Divisibility | Identify divisibilities of a number written in any base |

75 | Arithmetic | Senior | Rationality | Solve linear diophantine equations |

76 | Arithmetic | Senior | Exponents | Use modular arithmetic and linear congruences to solve number problems |

77 | Arithmetic | Senior | Finance | Solve problems involving amortization |

78 | Arithmetic | Senior | Sequences and Series | Distinguish between recursive and telescoping sequences and use conventional notation to sum their series where possible, in context |

79 | Arithmetic | Senior | Binomial expressions | Use the binomial expansion with any exponent |

80 | Arithmetic | Senior | Complex numbers | Use DeMoivre's Theorem as a tool within calculations |

81 | Arithmetic | Senior | Divisibility | Use Fermat's Little Theorem |

82 | Arithmetic | Senior | Rationality | Use the Ramanujan-Nagell exponential diophantine equation and Pell's equation in context |

83 | Arithmetic | Senior | Finance | Solve problems involving annuity |

84 | Arithmetic | Senior | Manipulation | Identify values or quantity of digits within large numbers |

85 | Arithmetic | Senior | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

86 | Algebra & Geometry | Junior | Polygons | Identify and use bipyramids and uniform stars |

87 | Algebra & Geometry | Junior | Relations Mappings and Equations | Solve a small system of equations in context and graph their relationship |

88 | Algebra & Geometry | Junior | Perimeter and Area | Use nets and coordinates to calculate perimeter and area |

89 | Algebra & Geometry | Junior | Nets and Volume | Find Volume of composite Polyhedra from their net and vice versa |

90 | Algebra & Geometry | Junior | Factorising | Appreciate the graphical representations of the 'difference of 2 squares' identity |

91 | Algebra & Geometry | Junior | Polynomials | Relate a quadratic equation to its parabola |

92 | Algebra & Geometry | Junior | Exponential and Logarithmic | Use and solve exponential and logarithmic equations considering their graphs |

93 | Algebra & Geometry | Junior | Trigonometry | Recognise common ratios between the sides of and angles within a right-angled triangle |

94 | Algebra & Geometry | Junior | Theorems | identify and use the circle theorems in solving problems |

95 | Algebra & Geometry | Junior | Tesselations | Recognise Hirschhorn, Periodic and Aperiodic tilings |

96 | Algebra & Geometry | Junior | Combinatorics | Calculate simple binomial problems involving combinations or permutations |

97 | Algebra & Geometry | Junior | Graph Theory | Use the handshaking lemma and komplete graphs in simple cases |

98 | Algebra & Geometry | Junior | Vectors | Use the magnitude of vectors in geometric problems |

99 | Algebra & Geometry | Junior | Coordinates | Convert between cartesian and simple polar coordinates |

100 | Algebra & Geometry | Junior | Direction | Calculate and use amounts of turn in radians |

101 | Algebra & Geometry | Junior | Relations Mappings and Equations | Manipulate quadratic, simple cubic and rational expressions and graph their relationship |

102 | Algebra & Geometry | Junior | Graphs | Use conventional notation to describe odd or even functions and key parts of graphs |

103 | Algebra & Geometry | Junior | Factorising | Know and use the Factor and Remainder Theorems as tools to help solve problems |

104 | Algebra & Geometry | Junior | Polynomials | Solve simple linear diophantine equations |

105 | Algebra & Geometry | Junior | Exponential and Logarithmic | Use exponential and/or logarithmic functions to linearize graphs of variable relationships |

106 | Algebra & Geometry | Junior | Trigonometry | Understand and graph the ratios for more than a full turn |

107 | Algebra & Geometry | Junior | Rate of change | Distinguish between increasing and decreasing slope and concavity of graphs in context |

108 | Algebra & Geometry | Junior | Theorems | Know and use Pick's Theorem as a tool within calculations |

109 | Algebra & Geometry | Junior | Combinatorics | Distinguish between and calculate simple problems involving permutations |

110 | Algebra & Geometry | Junior | Topology | Recognise the geometric properties of the Torus and Klein bottle are different in cartesian and spherical geometry |

111 | Algebra & Geometry | Junior | Vectors | Represent a scalar product geometrically and use it in calculating intersections and angles of lines and planes |

112 | Algebra & Geometry | Junior | Polygons | Use of Euler's characteristic and duality within simple contexts |

113 | Algebra & Geometry | Junior | Exponential and Logarithmic | Recognise the effect of increasing interest rates over absolute interest |

114 | Algebra & Geometry | Junior | Curved edge geometric shapes | Solve for measures of angles and segments relating to circles |

115 | Algebra & Geometry | Junior | Curved edge geometric shapes | Calculate perimeters and areas of sectors and segments relating to circles |

116 | Algebra & Geometry | Junior | Polyhedra | Recognise Archimedean solids, duals and Kepler-Poinsot polyhedra |

117 | Algebra & Geometry | Junior | Rate of change | Use average and instantaneous rate of change in context |

118 | Algebra & Geometry | Junior | Straight edge geometric shapes | Calculate the area of any triangle |

119 | Algebra & Geometry | Junior | Straight edge geometric shapes | Use Heron's Formula as a tool within calculations |

120 | Algebra & Geometry | Junior | Proof | Appreciate and follow the logic required in creating direct mathematical proofs, and proof by contradiction |

121 | Algebra & Geometry | Junior | Area and Surface Area | Find area of compound polygons and SA of compound polyhedra |

122 | Algebra & Geometry | Junior | Axioms and Logic | Identify when a statement is logical or not (ie tautology) |

123 | Algebra & Geometry | Junior | Matrices | Use matrices to transform images around a cartesian grid |

124 | Algebra & Geometry | Junior | Matrices | Use matrices to visualise and draw transformed images of shapes on a cartesian grid |

125 | Algebra & Geometry | Junior | Matrices | Use inverse 2 by 2 matrices to help transform (large) data sets in solving real-life problems |

126 | Algebra & Geometry | Junior | Nets and Volume | Find the volume of composite Polyhedra from their net and vice versa |

127 | Algebra & Geometry | Junior | Transformations | Perform simple transformations within 3D space |

128 | Algebra & Geometry | Junior | Transformations | Identify multiple transformations in 2D |

129 | Algebra & Geometry | Junior | Trigonometry | Recognise common ratios between the sides of and angles within any triangle |

130 | Algebra & Geometry | Primary | Measures | Have an understanding of the estimation of magnitudes |

131 | Algebra & Geometry | Primary | Coordinates | Know and use first quadrant cartesian coordinates in context |

132 | Algebra & Geometry | Primary | Direction | Provide directions using a 4-point compass rose |

133 | Algebra & Geometry | Primary | Relations Mappings and Equations | Visualise times tables with an arithmetic translation in a mapping |

134 | Algebra & Geometry | Primary | Graphs | Appreciate the graphical representation of a constant input with independent output and vice versa |

135 | Algebra & Geometry | Primary | Polygons | Distinguish between and label common polygon shapes |

136 | Algebra & Geometry | Primary | Area and Surface Area | Find area of right-angled polygons and surface area of right-angled polyhedra |

137 | Algebra & Geometry | Primary | Nets and Volume | Find the volume of right-angled polyhedra |

138 | Algebra & Geometry | Primary | Theorems | Recognise the fundamental axioms of geometry: Amount of turn round a point, vertically opposite and corresponding angles |

139 | Algebra & Geometry | Primary | Transformations | Recognise the spacial effect of a translation slide movement |

140 | Algebra & Geometry | Primary | Tesselations | Maintain a visual appreciation for shapes that create tiling patterns |

141 | Algebra & Geometry | Primary | Operations | Use everyday contexts to create calculations |

142 | Algebra & Geometry | Primary | Polyhedra | Distinguish between and label common polyhedron objects |

143 | Algebra & Geometry | Primary | Nets and Volume | Find the volume of right-angled polyhedra |

144 | Algebra & Geometry | Primary | Measures | Use appropriate metric units when representing quantities |

145 | Algebra & Geometry | Primary | Polynomials | Simplify any expression |

146 | Algebra & Geometry | Primary | Trigonometry | Understand the relationship connecting the perpendicular sides and area of a right-angled triangle |

147 | Algebra & Geometry | Primary | Transformations | Recognise and describe the spacial effect of a spin rotation |

148 | Algebra & Geometry | Primary | Measures | Use appropriate imperial units when representing quantities |

149 | Algebra & Geometry | Primary | Curved edge geometric shapes | Identify the labels relating to circles |

150 | Algebra & Geometry | Primary | Straight edge geometric shapes | Identify and name angles smaller or larger than multiples of quarter turns |

151 | Algebra & Geometry | Primary | Straight edge geometric shapes | Distinguish triangles from the magnitude of their angles or lengths of sides |

152 | Algebra & Geometry | Primary | Transformations | Recognise the spacial effect of a mirror image reflection |

153 | Algebra & Geometry | Secondary | Direction | Provide directions using an 8-point compass rose |

154 | Algebra & Geometry | Secondary | Polygons | Classify quadrilaterals by using interior and exterior angles |

155 | Algebra & Geometry | Secondary | Coordinates | Know and use cartesian coordinates in context |

156 | Algebra & Geometry | Secondary | Direction | Estimate and describe amounts of turn in degrees |

157 | Algebra & Geometry | Secondary | Relations Mappings and Equations | Describe linear relationships from a mapping diagram and solve equivalent equations with rational coefficients |

158 | Algebra & Geometry | Secondary | Graphs | Describe key features of parabola graphs |

159 | Algebra & Geometry | Secondary | Polyhedra | Recognise the properties of the platonic solids |

160 | Algebra & Geometry | Secondary | Perimeter and Area | Use proportions to calculate area and perimeter |

161 | Algebra & Geometry | Secondary | Area and Surface Area | Find area of common polygons and SA of common Polyhedra |

162 | Algebra & Geometry | Secondary | Factorising | Fully factorise any expression |

163 | Algebra & Geometry | Secondary | Exponential and Logarithmic | Recognise and compare depreciation rates with absolute drops in value |

164 | Algebra & Geometry | Secondary | Theorems | Understand the relationships of angles formed by a transversal over a pair of parallel lines |

165 | Algebra & Geometry | Secondary | Tesselations | Identify tilings that create monohedral tessellations |

166 | Algebra & Geometry | Secondary | Graph Theory | From given information about its faces, edges and vertices, recognise if a solid exists |

167 | Algebra & Geometry | Secondary | Direction | Use three-figure bearings to describe the direction of an object compared to another |

168 | Algebra & Geometry | Secondary | Perimeter and Area | Use nets and coordinates to calculate perimeter and area |

169 | Algebra & Geometry | Secondary | Nets and Volume | Find the volume of common Polyhedra from their net and vice versa |

170 | Algebra & Geometry | Secondary | Polynomials | Represent and use a linear function graphically and algebraically |

171 | Algebra & Geometry | Secondary | Exponential and Logarithmic | Identify and use the multiplier when calculating with increasing and decreasing percentages |

172 | Algebra & Geometry | Secondary | Trigonometry | Understand and use the relationship connecting the 3 sides of a right-angled triangle and calculate its area |

173 | Algebra & Geometry | Secondary | Rate of change | Use the language of constant, increasing and decreasing for the visual rate of change of a graph |

174 | Algebra & Geometry | Secondary | Theorems | Understand the relationship connecting areas around the sides of a right-angled triangle |

175 | Algebra & Geometry | Secondary | Transformations | Perform stretch and sheer transformations on 2D shapes |

176 | Algebra & Geometry | Secondary | Combinatorics | Recognise the pattern of Pascal's triangle as a tool for simple combination poblems |

177 | Algebra & Geometry | Secondary | Vectors | Describe movement around a shape using given vectors |

178 | Algebra & Geometry | Secondary | Direction | Identify the loci of a situation given conditions |

179 | Algebra & Geometry | Secondary | Transformations | Rotate a 2D shape by any angle amount of turn |

180 | Algebra & Geometry | Secondary | Direction | Construct and interpret scale drawings, using bearings |

181 | Algebra & Geometry | Secondary | Curved edge geometric shapes | Calculate the perimeter and area relating to circles |

182 | Algebra & Geometry | Secondary | Topology | Recognise the geometric properties of the mobius strip |

183 | Algebra & Geometry | Secondary | Transformations | Describe or draw quarter-turn rotation images of shapes and integer scale factor enlargement on a cartesian grid |

184 | Algebra & Geometry | Secondary | Straight edge geometric shapes | Identify mathematically similar shapes |

185 | Algebra & Geometry | Secondary | Straight edge geometric shapes | Understand a proof for the sum of angles in a triangle |

186 | Algebra & Geometry | Secondary | Straight edge geometric shapes | Understand and use the side, angle and area relationships within any cartesian triangle |

187 | Algebra & Geometry | Secondary | Axioms and Logic | Appreciate and recognise Euclid's postulates |

188 | Algebra & Geometry | Secondary | Direction | Use different 2D planes within 3D spaces |

189 | Algebra & Geometry | Secondary | Nets and Volume | Find the volume of common Polyhedra from their net and vice versa. |

190 | Algebra & Geometry | Secondary | Ratio and Proportion | Construct angle bisectors and find the shortest distance between lines and a point |

191 | Algebra & Geometry | Senior | Trigonometry | Use the compound angle identities as tools |

192 | Algebra & Geometry | Senior | Theorems | Use Ceva's and Menelaus' Theorems as tools within calculations |

193 | Algebra & Geometry | Senior | Graph Theory | Recognise Eulerian and Hamiltonian cycles and circuits in context |

194 | Algebra & Geometry | Senior | Factorising | Use completing the rectangle as a tool within calculations |

195 | Algebra & Geometry | Senior | Trigonometry | Use the arctrigonometric identities as tools |

196 | Algebra & Geometry | Senior | Theorems | Know and use Carnot's Theorem as a tool within calculations |

197 | Algebra & Geometry | Senior | Expressions | Use completing the rectangle as a tool within calculations |

198 | Calculus | Junior | Kinematics | Use scalar equivalents of displacement, velocity and acceleration vectors with time |

199 | Calculus | Junior | Differentiation | Know and use the chain, product and quotient rules as tools on simple functions in context |

200 | Calculus | Junior | Integration | Calculate areas between graphs and axes, and volumes of revolution where common shapes and objects are generated |

201 | Calculus | Junior | Kinematics | Understand and calculate the linear movement of a particle |

202 | Calculus | Junior | Differentiation | Find minimum, maximum and inflections for optimsed solutions |

203 | Calculus | Junior | Rate of change | Distinguish between increasing and decreasing slope and concavity of graphs in context |

204 | Calculus | Junior | Rate of change | Use average and instantaneous rate of change in context |

205 | Calculus | Secondary | Differentiation | Recognise and distinguish between graphs of functions and of their slope functions |

206 | Calculus | Secondary | Rate of change | Use the language of constant, increasing or decreasing for the visual rate of change of a graph |

207 | Calculus | Senior | Integration | Know and use the inverse chain and product rules and substitution as tools to integrate simple functions in context |

208 | Calculus | Senior | Kinematics | Use and convert between displacement, velocity and acceleration functions in context |

209 | Calculus | Senior | Limits and Differential Equations | Calculate limits to any point, and infinity, of rational functions |

210 | Calculus | Senior | Differentiation | Use implicit differentiation and related rates of change as tools on functions in context |

211 | Calculus | Senior | Integration | Know and use integration by parts and partial fractions as tools within calculations |

212 | Calculus | Senior | Limits and Differential Equations | Use Eulers Method and slope fields as tools in simple contexts |

213 | Calculus | Senior | Differential Equation | Solve first order linear differential equations |

214 | Calculus | Senior | Differential Equation | Solve separable variable differential equations |

215 | Calculus | Senior | Differential Equation | Solve homogenous differential equations |

216 | Calculus | Senior | Differential Equation | Solve simple linear coupled simultaneous differential equations |

217 | Experimental Sciences | Junior | Probability | Appreciate and interpret theoretical probabilities of independent events, in context |

218 | Experimental Sciences | Junior | Regression | Draw and use a line of best fit by hand, passing through the mean value |

219 | Experimental Sciences | Junior | Location and Dispersion | Make comparisons between data sets using cumulative frequency |

220 | Experimental Sciences | Junior | Probability | Know and use the rules for union, intersection, complement as tools within calculations |

221 | Experimental Sciences | Junior | Regression | Calculate simple least squares linear regression by hand |

222 | Experimental Sciences | Junior | Representing Data | Use and graphically represent discrete vs continuous data appropriately |

223 | Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the geometric mean from a dataset |

224 | Experimental Sciences | Junior | Data tests and correlation | Use and interpret the correlation coefficient and also coefficient of determination in context when analysing data |

225 | Experimental Sciences | Junior | Data tests and correlation | Understand the effect of sampling compared to population statistics |

226 | Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the arithmetic mean, median and modal values from grouped frequency tables |

227 | Experimental Sciences | Junior | Random variables and distributions | Use and interpret binomial probability distributions in context |

228 | Experimental Sciences | Primary | Location and Dispersion | Identify the mode (most occurring object) within a group |

229 | Experimental Sciences | Primary | Set Theory | Place objects into given overlapping groups |

230 | Experimental Sciences | Primary | Representing Data | Count frequencies through pictorial representations and interpret in context |

231 | Experimental Sciences | Primary | Location and Dispersion | Calculate the mode, median, mean and range from a list of quantative data |

232 | Experimental Sciences | Primary | Representing Data | Count frequencies from bars and a number line scale, and interpret the results in context. |

233 | Experimental Sciences | Primary | Representing Data | Identify proportions from pie charts and interpret in context |

234 | Experimental Sciences | Primary | Probability | Interpret theoretical probabilities of independent events, in context |

235 | Experimental Sciences | Secondary | Location and Dispersion | Generate and interpret the arithmetic mean, median and modal values from frequency tables |

236 | Experimental Sciences | Secondary | Probability | Interpret experimental probabilities of independent events in context |

237 | Experimental Sciences | Secondary | Set Theory | Identify regions within Venn diagrams using conventianal notation and vice versa |

238 | Experimental Sciences | Secondary | Representing Data | Distinguish between pie, bar charts and histograms and interpret in context |

239 | Experimental Sciences | Secondary | Probability | Interpret theoretical probabilities of dependent events, in context |

240 | Experimental Sciences | Senior | Probability | Know and use the rules for union, intersection, complement as tools within calculations |

241 | Experimental Sciences | Senior | Probability | Know and use Bayes' Theorem as a tool within calculations. |

242 | Experimental Sciences | Senior | Regression | Calculate function regressions using technology |

243 | Experimental Sciences | Senior | Data tests and correlation | Distinguish between when to use Chi-square test for independence, PMCC for bivariate data sets or Spearman's rank correlation coefficient |

244 | Experimental Sciences | Senior | Matrices | Find the steady state of a real-life Markov Chain system |

245 | Experimental Sciences | Senior | Combinatorics | Calculate problems involving combinations and permutations |

246 | Experimental Sciences | Senior | Random variables and distributions | Use and interpret poisson, normal, geometric and sampling probability distributions in context |

247 | Experimental Sciences | Senior | Probability | Use and interpret Expectation and Variance of combined independent events in context |

248 | Experimental Sciences | Senior | Representing Data | Use statistical hypothesis testing with real-life datasets |

249 | Experimental Sciences | Senior | Location and Dispersion | Use and interpret standard deviation and variance (including transformations of) |

250 | Experimental Sciences | Senior | Regression | Calculate least squares linear regression |

251 | Foundational Language | Junior | Axioms and Logic | Identify when a statement is logical or not (ie tautology) |

252 | Foundational Language | Junior | Recreational | Appreciate the patterns created from shuffling small packs of cards |

253 | Foundational Language | Junior | History | Know about some prominent 19th century mathematicians |

254 | Foundational Language | Junior | History | Know about some prominent 20th century mathematicians |

255 | Foundational Language | Primary | Recreational | Identify and complete magic squares |

256 | Foundational Language | Primary | History | Know about some prominent 20th century mathematicians |

257 | Foundational Language | Primary | History | Know about some prominent 19th century mathematicians |

258 | Foundational Language | Secondary | Axioms and Logic | Appreciate and recognise Euclid's postulates |

259 | Foundational Language | Secondary | Proof | Create simple geometric proofs involving parallel lines |

260 | Foundational Language | Secondary | History | Know about some prominent 20th century mathematicians |

261 | Foundational Language | Secondary | History | Know about some prominent 19th century mathematicians |

262 | Foundational Language | Senior | Proof | Follow the logic required in creating nonconstructive mathematical proofs and applications in Graph Theory |

263 | Foundational Language | Senior | Proof | Think through a larger logic problem and create tests for efficiency and optimization |

264 | Foundational Language | Senior | History | Know about some prominent 20th century mathematicians |

265 | Foundational Language | Senior | History | Know about some prominent 19th century mathematicians |

266 | Algebra and Graphs | Junior | Polynomials | Represent and use a quadratic function graphically and algebraically |

267 | Algebra and Graphs | Junior | Coordinates | Convert between cartesian and simple polar coordinates |

268 | Algebra and Graphs | Junior | Exponential and Logarithmic | Use and solve exponential and logarithmic equations considering their graphs |

269 | Algebra and Graphs | Junior | Exponential and Logarithmic | Use exponential and/or logarithmic functions to linearize graphs of variable relationships |

270 | Algebra and Graphs | Junior | Exponential and Logarithmic | Use and solve logistical equations and their graphs |

271 | Algebra and Graphs | Junior | Graph Theory | Use the handshaking lemma and komplete graphs in simple cases |

272 | Algebra and Graphs | Junior | Graphs | Use conventional notation when describing curved graphs |

273 | Algebra and Graphs | Junior | Graphs | Use conventional notation to describe odd or even functions and key parts of graphs |

274 | Algebra and Graphs | Junior | Graphs | Describe piecewise functions and identify continuity across the domain |

275 | Algebra and Graphs | Junior | Graphs | Know and use the relations that create circles |

276 | Algebra and Graphs | Junior | Kinematics | Understand and calculate the linear movement of a particle |

277 | Algebra and Graphs | Junior | Limits | Identify vertical and horizontal asymptotes by taking limits of functions |

278 | Algebra and Graphs | Junior | Limits | Calculate limits to any point, and infinity, of rational functions |

279 | Algebra and Graphs | Junior | Relations Mappings and Equations | Manipulate quadratic, simple cubic and rational expressions and graph their relationship |

280 | Algebra and Graphs | Junior | Order of operations | Perform correct order of operation processes involving trigonometric ratios |

281 | Algebra and Graphs | Junior | Polynomials | Use the rational root and sum or product of zeros tools when manipulating polynomials |

282 | Algebra and Graphs | Junior | Transformations | Recognise the graphical movement of a function manipulation |

283 | Algebra and Graphs | Junior | Trigonometry | Understand and graph the ratios for more than a full turn |

284 | Algebra and Graphs | Primary | Relations Mappings and Equations | Identify times tables with an arithmetic translation |

285 | Algebra and Graphs | Primary | Graphs | Use convential notation to describe and draw linear inequalities |

286 | Algebra and Graphs | Primary | Graphs | Identify roots from graphs within context |

287 | Algebra and Graphs | Primary | Graphs | Use convential notation to describe and draw linear inequalities |

288 | Algebra and Graphs | Primary | Inequalities | Solve one simple linear inequality |

289 | Algebra and Graphs | Secondary | Coordinates | Know and use cartesian coordinates in context |

290 | Algebra and Graphs | Secondary | Expressions | Appreciate the graphical representations of the 'difference of 2 squares' identity |

291 | Algebra and Graphs | Secondary | Graphs | Use conventional notation when describing linear graphs |

292 | Algebra and Graphs | Secondary | Graphs | Solve a small system of equations in context and graph their relationship |

293 | Algebra and Graphs | Secondary | Graphs | Use conventional notation to solve 2D inequalities |

294 | Algebra and Graphs | Secondary | Limits | Identify the equations of asymptotes on graphs |

295 | Algebra and Graphs | Secondary | Relations Mappings and Equations | Describe linear relationships from a mapping diagram and solve equivalent equations with rational coefficients |

296 | Algebra and Graphs | Secondary | Relations Mappings and Equations | Solve a small system of equations in context and graph their relationship |

297 | Algebra and Graphs | Secondary | Polynomials | Represent and use a linear function graphically and algebraically |

298 | Algebra and Graphs | Secondary | Polynomials | Relate a quadratic equation to its parabola |

299 | Algebra and Graphs | Secondary | Regression | Draw and use a line of best fit by hand, passing through the mean value |

300 | Algebra and Graphs | Senior | Tesselations | Create simple Voronoi tilings using midpoints |

301 | Algebra and Graphs | Senior | Coordinates | Understand when polar coordinates are easier/more efficient than cartesian, and use them in simple contexts |

302 | Algebra and Graphs | Senior | Graphs | Use conventional notation to describe piecewise functions and discuss continuity across the domain |

303 | Algebra and Graphs | Senior | Vectors | Find the volume of composite polyhedra using Vectors |

304 | Algebra and Graphs | Senior | Factorising | Know and use Descartes Rule of Signs as a tool within calculations |

305 | Algebra and Graphs | Senior | Polynomials | Use the rational root and sum or product of zeros tools when manipulating polynomials |

306 | Algebra and Graphs | Senior | Exponential and Logarithmic | Use and solve logistical equations and their graphs |

307 | Algebra and Graphs | Senior | Rate of change | Recognise and distinguish between the graphs of functions, their first and second differential graphs |

308 | Algebra and Graphs | Senior | Transformations | Perform transformations within 3D space |

309 | Algebra and Graphs | Senior | Vectors | Represent a vector product geometrically and use it in calculating intersections and angles of lines and planes |

310 | Algebra and Graphs | Senior | Matrices | Use eigenvalues and eigenvectors as tools within simple calculations |

311 | Algebra and Graphs | Senior | Coordinates | Use polar coordinates in context |

312 | Algebra and Graphs | Senior | Relations Mappings and Equations | Use parametric equations as a tool within calculations |

313 | Algebra and Graphs | Senior | Curved edge geometric shapes | Know and use the relations that create ellipses |

314 | Algebra and Graphs | Senior | Graphs | Use conventional notation to solve any inequality |

315 | Algebra and Graphs | Senior | Vectors | Find surface areas of composite polyhedra using Vectors |

316 | Algebra and Graphs | Senior | Expressions | Know and use Descartes Rule of Signs as a tool within calculations |

317 | Pure Algebra | Junior | Axioms and Logic | Use truth tables to solve simple problems |

318 | Pure Algebra | Junior | Binomial expressions | Use the binomial expansion with integer values |

319 | Pure Algebra | Junior | Inequalities | Solve system of inequalities |

320 | Pure Algebra | Junior | Order of operations | Understand how rational exponents are short-hand for roots, and simplify expressions accordingly |

321 | Pure Algebra | Junior | Quotients | Manipulate any quotient raised to any exponent |

322 | Pure Algebra | Junior | Polynomials | Solve linear diophantine equations |

323 | Pure Algebra | Junior | Proof | Appreciate and follow the logic required in creating constructive mathematical proofs |

324 | Pure Algebra | Secondary | Expressions | Manipulate expressions involving parenthesis |

325 | Pure Algebra | Secondary | Expressions | Solve a small system of equations in context |

326 | Pure Algebra | Secondary | Inequalities | Solve a system of linear inequalities |

327 | Pure Algebra | Secondary | Order of operations | Perform multi-step calculations, involving parentheses and indices, in the correct order |

328 | Pure Algebra | Secondary | Order of operations | Perform binary operations on algebraic values |

329 | Pure Algebra | Secondary | Polynomials | Solve simple linear diophantine equations |

330 | Pure Algebra | Senior | Axioms and Logic | Use truth tables to solve problems |

331 | Pure Algebra | Senior | Proof | Appreciate and follow the logic required in Fermat's infinite descent proof |

332 | Pure Algebra | Senior | Quotients | Understand the use for and manipulate partial fraction expressions |

333 | Pure Algebra | Senior | Sequences and Series | Find the nth term rule for recurrence relations |

334 | Pure Algebra | Senior | Axioms and Logic | Use digital logic gates to solve Boolean algebra problems |

335 | Pure Algebra | Senior | Axioms and Logic | Use Venn diagrams to solve Boolean algebra logic problems |

336 | Pure Algebra | Senior | Complex numbers | Recognise the existence of non-real solutions to mathematical problems |

337 | Pure Algebra | Senior | Sequences and Series | Distinguish between infinite, iterative and recurrence relation sequences |

338 | Pure Algebra | Senior | Factorising | Use the Factor and Remainder Theorems |