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 August 2022 to July 2023 season, focus is 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 |

For the August 2021 to July 2022 season, focus was 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 |

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 Championships will feature content at the same level and below.

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

1 | Arithmetic | Junior | Operations | Understand how rational exponents are short-hand for roots, and simplify number expressions accordingly |

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

11 | Arithmetic | Junior | Sequences and Series | Use conventional notation for geometric sequences in context |

12 | Arithmetic | Junior | Binomial expressions | Use the binomial expansion to solve a problem |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

33 | Arithmetic | Primary | Directions and Angles | Identify common factors within expressions |

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

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

36 | Arithmetic | Primary | Directions and Angles | Recognise appropriate units for quantities in context |

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

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

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

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

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

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

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

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

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

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

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

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

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

50 | Arithmetic | Secondary | Operations | Perform multi-step calculations, involving parentheses and indices, in the correct order |

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

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

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

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

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

56 | Arithmetic | Secondary | Vectors | Use vectors to translate images around a cartesian grid |

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

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

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

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

61 | Arithmetic | Secondary | Directions and Angles | Convert across common imperial and metric quantities |

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

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

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

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

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

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

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

69 | Arithmetic | Senior | Exponents | Manipulate numbers expressed in any form and within any common base |

70 | Arithmetic | Senior | Binomial expressions | Use the binomial expansion with simple rational values |

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

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

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

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

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

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

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

78 | Arithmetic | Senior | Rationality | Use the Ramanujan-Nagell exponential diophantine equation in context |

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

80 | Arithmetic | Senior | Manipulation | Identify values or quantity of digits within large numbers in any base |

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

82 | Arithmetic | Senior | Combinatorics | Calculate simple problems involving permutations |

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

84 | Arithmetic | Senior | Complex numbers | Use Pell's equation in context |

85 | Algebra & Geometry | Junior | Tessellations | Identify tilings that create monohedral tessellations |

86 | Algebra & Geometry | Junior | Relations Mappings and Equations | Graphically solve a small system of equations in context |

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

88 | Algebra & Geometry | Junior | Nets and Volume | Find Volume of composite Polyhedra from their net |

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

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

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

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

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

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

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

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

97 | Algebra & Geometry | Junior | Polygons and Polyhedra | Solve for measures of angles and segments relating to circles |

98 | Algebra & Geometry | Junior | Polygons and Polyhedra | Calculate perimeters and areas of sectors and segments relating to circles |

99 | Algebra & Geometry | Junior | Area and Surface Area | Calculate the area of any triangle |

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

101 | Algebra & Geometry | Junior | Area and Surface Area | Find the area of compound polygons |

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

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

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

105 | Algebra & Geometry | Junior | Nets and Volume | Find the dimensions of composite Polyhedra from the Volume |

106 | Algebra & Geometry | Junior | Vectors | Perform simple transformations within 3D space |

107 | Algebra & Geometry | Junior | Vectors | Identify multiple transformations in 2D |

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

109 | Algebra & Geometry | Junior | Combinatorics | Calculate binomial problems involving simple permutations |

110 | Algebra & Geometry | Junior | Area and Surface Area | Find the SA of compound polyhedra |

111 | Algebra & Geometry | Primary | Directions and Angles | Have an understanding of the estimation of magnitudes |

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

113 | Algebra & Geometry | Primary | Direction and Angles | Provide directions using a 4-point compass rose |

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

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

116 | Algebra & Geometry | Primary | Nets and Volume | Distinguish between and label common polygon shapes |

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

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

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

120 | Algebra & Geometry | Primary | Vectors | Recognise the spacial effect of a translation slide movement |

121 | Algebra & Geometry | Primary | Tessellations | Maintain a visual appreciation for shapes that create tiling patterns |

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

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

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

125 | Algebra & Geometry | Primary | Directions and Angles | Use appropriate metric units when representing quantities |

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

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

128 | Algebra & Geometry | Primary | Vectors | Recognise and describe the spacial effect of a spin rotation |

129 | Algebra & Geometry | Primary | Directions and Angles | Use appropriate imperial units when representing quantities |

130 | Algebra & Geometry | Primary | Polygons and Polyhedra | Identify the labels relating to circles |

131 | Algebra & Geometry | Primary | Area and Surface Area | Identify and name angles smaller or larger than multiples of quarter turns |

132 | Algebra & Geometry | Primary | Area and Surface Area | Distinguish triangles from the magnitude of their angles or lengths of sides |

133 | Algebra & Geometry | Primary | Vectors | Recognise the spacial effect of a mirror image reflection |

134 | Algebra & Geometry | Secondary | Direction and Angles | Provide directions using an 8-point compass rose |

135 | Algebra & Geometry | Secondary | Nets and Volume | Classify quadrilaterals by using interior and exterior angles |

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

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

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

139 | Algebra & Geometry | Secondary | Polygons and Polyhedra | Recognise the properties of the platonic solids |

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

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

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

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

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

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

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

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

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

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

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

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

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

153 | Algebra & Geometry | Secondary | Vectors | Perform stretch and sheer transformations on 2D shapes |

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

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

156 | Algebra & Geometry | Secondary | Direction and Angles | Identify the loci of a situation given conditions |

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

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

159 | Algebra & Geometry | Secondary | Polygons and Polyhedra | Calculate the perimeter and area relating to circles |

160 | Algebra & Geometry | Secondary | Tessellations | Recognise the geometric properties of the mobius strip |

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

162 | Algebra & Geometry | Secondary | Area and Surface Area | Identify mathematically similar shapes |

163 | Algebra & Geometry | Secondary | Area and Surface Area | Understand a proof for the sum of angles in a triangle |

164 | Algebra & Geometry | Secondary | Area and Surface Area | Understand and use the side, angle and area relationships within any cartesian triangle |

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

166 | Algebra & Geometry | Secondary | Direction and Angles | Use different 2D planes within 3D spaces |

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

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

169 | Algebra & Geometry | Senior | Nets and Volume | Identify and use bipyramids |

170 | Algebra & Geometry | Senior | Tessellations | Recognise Hirschhorn tilings |

171 | Algebra & Geometry | Senior | Nets and Volume | Use of Euler's characteristic and duality within simple contexts |

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

173 | Algebra & Geometry | Senior | Theorems | Use Ceva's Theorem as a tool within calculations |

174 | Algebra & Geometry | Senior | Graph Theory | Recognise Eulerian cycles in context |

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

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

177 | Algebra & Geometry | Senior | Polygons and Polyhedra | Recognise Archimedean solids, duals and Kepler-Poinsot polyhedra |

178 | Algebra & Geometry | Senior | Area and Surface Area | Use Heron's Formula as a tool within calculations |

179 | Algebra & Geometry | Senior | Directions and Angles | Use completing the rectangle as a tool within calculations |

180 | Algebra & Geometry | Senior | Tessellations | Recognise Periodic tilings |

181 | Algebra & Geometry | Senior | Tessellations | Recognise Aperiodic tilings |

182 | Algebra & Geometry | Senior | Theorems | Use Menelaus' Theorem as a tool within calculations |

183 | Algebra & Geometry | Senior | Graph Theory | Recognise Eulerian circuits in context |

184 | Algebra & Geometry | Senior | Graph Theory | Recognise Hamiltonian cycles in context |

185 | Algebra & Geometry | Senior | Graph Theory | Recognise Hamiltonian circuits in context |

186 | Algebra & Geometry | Senior | Nets and Volume | Identify and use uniform stars |

187 | Calculus | Junior | Kinematics | Use scalar equivalents of displacement and velocity vectors with time |

188 | Calculus | Junior | Integration | Calculate areas between graphs and axes, where common shapes and objects are generated |

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

190 | Calculus | Junior | Differentiation | Find minimums for optimsed solutions |

191 | Calculus | Junior | Vectors | Distinguish between increasing and decreasing slope of graphs in context |

192 | Calculus | Junior | Vectors | Use average rate of change in context |

193 | Calculus | Junior | Kinematics | Use scalar equivalents of velocity and acceleration vectors with time |

194 | Calculus | Junior | Differentiation | Know and use the chain rule as a tool to differentiate simple functions in context |

195 | Calculus | Junior | Differentiation | Know and use the product rule as a tool to differentiate simple functions in context |

196 | Calculus | Junior | Differentiation | Know and use the quotient rule as a tool to differentiate simple functions in context |

197 | Calculus | Junior | Integration | Calculate volumes of revolution of simple functions wrt x |

198 | Calculus | Junior | Integration | Calculate volumes of revolution of simple functions wrt y |

199 | Calculus | Junior | Differentiation | Find maximums for optimsed solutions |

200 | Calculus | Junior | Differentiation | Find inflections for optimsed solutions |

201 | Calculus | Junior | Vectors | Use concavity of graphs to identify local behaviour of a particle in context |

202 | Calculus | Junior | Vectors | Use instantaneous rate of change in context |

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

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

205 | Calculus | Senior | Differentiation | Know and use the chain rule and substitution as tools to differentiate simple functions in context |

206 | Calculus | Senior | Integration | Know and use the inverse chain rule and substitution as tools to integrate simple functions in context |

207 | Calculus | Senior | Kinematics | Use and convert between displacement and velocity functions in context |

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

209 | Calculus | Senior | Integration | Know and use integration by parts as tools within calculations |

210 | Calculus | Senior | Limits | Use Eulers Method and slope fields as tools in simple contexts |

211 | Calculus | Senior | Differential Equations | Solve first order linear differential equations |

212 | Calculus | Senior | Differential Equations | Solve separable variable differential equations |

213 | Calculus | Senior | Differential Equations | Solve homogenous differential equations |

214 | Calculus | Senior | Differential Equations | Solve simple linear coupled simultaneous differential equations |

215 | Calculus | Senior | Integration | Know and use the product rule and substitution as tools to differentiate simple functions in context |

216 | Calculus | Senior | Integration | Know and use the inverse product rule and substitution as tools to integrate simple functions in context |

217 | Calculus | Senior | Kinematics | Use and convert between velocity and acceleration functions in context |

218 | Calculus | Senior | Kinematics | Use and convert between displacement and acceleration functions in context |

219 | Calculus | Senior | Limits | Calculate limits to infinity of rational functions |

220 | Calculus | Senior | Integration | Know and use partial fractions as tools within calculations |

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

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

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

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

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

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

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

228 | Experimental Sciences | Junior | Data tests and correlation | Use and interpret the correlation coefficient in context when analysing data |

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

230 | Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the arithmetic mean value from a grouped frequency table |

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

232 | Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the arithmetic median value from a grouped frequency table |

233 | Experimental Sciences | Junior | Probability | Know and use the complement of a set as a tool within calculations |

234 | Experimental Sciences | Junior | Combinatorics | Calculate probabilities involving combinations |

235 | Experimental Sciences | Junior | Location and Dispersion | Use and interpret standard deviation |

236 | Experimental Sciences | Junior | Location and Dispersion | Use and interpret variance |

237 | Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the arithmetic modal value from a grouped frequency table |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

252 | Experimental Sciences | Senior | Data tests and correlation | Use Chi-square test for independence |

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

254 | Experimental Sciences | Senior | Combinatorics | Calculate probabilities involving permutations |

255 | Experimental Sciences | Senior | Random variables and distributions | Use and interpret the test for the mean in a poisson distribution in context |

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

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

258 | Experimental Sciences | Senior | Location and Dispersion | Use and interpret transformations of standard deviation |

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

260 | Experimental Sciences | Senior | Data tests and correlation | Use PPMCC for bivariate data sets |

261 | Experimental Sciences | Senior | Data tests and correlation | Use Spearman's rank correlation coefficient for bivariate data sets |

262 | Experimental Sciences | Senior | Random variables and distributions | Use and interpret z-test for the mean of a normal probability distribution in context |

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

264 | Experimental Sciences | Senior | Data tests and correlation | Use Chi-square goodness of fit test |

265 | Experimental Sciences | Senior | Location and Dispersion | Use and interpret transformations of variance |

266 | Experimental Sciences | Senior | Data tests and correlation | Use 2-sample t-test in context |

267 | Experimental Sciences | Senior | Data tests and correlation | Use 1-sample t-test in context |

268 | Experimental Sciences | Senior | Data tests and correlation | Use and interpret the correlation coUse and interpret the coefficient of determination in context when analysing data |

269 | History | Junior | Recreational | Appreciate the patterns created from shuffling small packs of cards |

270 | History | Junior | Mathematicians | Know about some prominent 19th century mathematicians |

271 | History | Junior | Mathematicians | Know about some prominent 20th century mathematicians |

272 | History | Primary | Recreational | Identify and complete magic squares |

273 | History | Primary | Mathematicians | Know about some prominent 20th century mathematicians |

274 | History | Primary | Mathematicians | Know about some prominent 19th century mathematicians |

275 | History | Secondary | Axioms and Logic | Appreciate and recognise Euclid's postulates |

276 | History | Secondary | Proof | Create simple geometric proofs involving parallel lines |

277 | History | Secondary | Mathematicians | Know about some prominent 20th century mathematicians |

278 | History | Secondary | Mathematicians | Know about some prominent 19th century mathematicians |

279 | History | Senior | Proof | Follow the logic required in creating nonconstructive mathematical proofs and applications in Graph Theory |

280 | History | Senior | Proof | Think through a larger logic problem and create tests for efficiency and optimization |

281 | History | Senior | Mathematicians | Know about some prominent 20th century mathematicians |

282 | History | Senior | Mathematicians | Know about some prominent 19th century mathematicians |

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

284 | Algebra and Graphs | Junior | Vectors | Use the magnitude of vectors in geometric problems |

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

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

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

288 | Algebra and Graphs | Junior | Exponential and Logarithmic | Use exponential functions to linearize graphs of variable relationships |

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

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

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

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

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

294 | Algebra and Graphs | Junior | Relations Mappings and Equations | Manipulate quadratic expressions and graph their relationship |

295 | Algebra and Graphs | Junior | Trigonometry | Identify all possible solutions to trigonometric graphs |

296 | Algebra and Graphs | Junior | Vectors | Recognise the graphical movement of a function manipulation |

297 | Algebra and Graphs | Junior | Trigonometry | Understand the sine graph for more than a full turn |

298 | Algebra and Graphs | Junior | Factorising | Appreciate the graphical representations of the 'difference of 2 squares' identity |

299 | Algebra and Graphs | Junior | Polynomials | Represent and use the 2 distinct roots of a quadratic function graphically |

300 | Algebra and Graphs | Junior | Polynomials | Represent and use the repeated real root of a quadratic function graphically |

301 | Algebra and Graphs | Junior | Polynomials | Understand and represent a quadratic function without any real roots graphically |

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

303 | Algebra and Graphs | Junior | Exponential and Logarithmic | Use logarithmic functions to linearize graphs of variable relationships |

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

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

306 | Algebra and Graphs | Junior | Relations Mappings and Equations | Manipulate simple cubic expressions and graph their relationship |

307 | Algebra and Graphs | Junior | Relations Mappings and Equations | Manipulate simple rational expressions and graph their relationship |

308 | Algebra and Graphs | Junior | Trigonometry | Understand the cosine graph for more than a full turn |

309 | Algebra and Graphs | Junior | Polynomials | Relate a vertex-form quadratic equation to its parabola |

310 | Algebra and Graphs | Junior | Trigonometry | Understand the tangent graph for more than a full turn |

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

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

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

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

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

316 | Algebra and Graphs | Secondary | Graphs | Describe key features of parabola graphs |

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

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

319 | Algebra and Graphs | Secondary | Graphs | Graphically solve a small system of equations in context |

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

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

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

323 | Algebra and Graphs | Secondary | Relations Mappings and Equations | Graphically solve a small system of equations in context |

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

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

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

327 | Algebra and Graphs | Senior | Tessellations | Create simple Voronoi tilings using midpoints |

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

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

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

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

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

333 | Algebra and Graphs | Senior | Vectors | Recognise and distinguish between the graphs of functions, their first and second differential graphs |

334 | Algebra and Graphs | Senior | Vectors | Perform transformations within 3D space |

335 | Algebra and Graphs | Senior | Vectors | Represent a vector product geometrically and use it in calculating areas of plane segments |

336 | Algebra and Graphs | Senior | Limits | Calculate limits to any point of rational functions |

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

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

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

340 | Algebra and Graphs | Senior | Polygons and Polyhedra | Know and use the relations that create ellipses |

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

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

343 | Algebra and Graphs | Senior | Limits | Identify oblique asymptotes by taking limits of functions |

344 | Pure Algebra | Junior | Polynomials | Solve simple linear diophantine equations |

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

346 | Pure Algebra | Junior | Binomial expressions | Use the binomial expansion with integer values to work backwards to solve a problem |

347 | Pure Algebra | Junior | Inequalities | Solve a system of three linear inequalities |

348 | Pure Algebra | Junior | Operations | Understand how rational exponents are short-hand for roots, and simplify algebraic expressions accordingly |

349 | Pure Algebra | Junior | Quotients | Manipulate any algebraic quotient raised to any exponent |

350 | Pure Algebra | Junior | Operations | Perform multi-step algebraic calculations, involving parentheses and indices, in the correct order |

351 | Pure Algebra | Junior | Operations | Perform binary operations on algebraic values |

352 | Pure Algebra | Junior | Proof | Create simple constructive mathematical proofs |

353 | Pure Algebra | Junior | Factorising | Know and use the Factor Theorem |

354 | Pure Algebra | Junior | Factorising | Know and use Remainder Theorem |

355 | Pure Algebra | Junior | Polynomials | Use the 2 distinct roots of a quadratic function algebraically |

356 | Pure Algebra | Junior | Polynomials | Use the repeated real root of a quadratic function algebraically |

357 | Pure Algebra | Junior | Polynomials | Recognise quadratic functions without any real roots algebraically |

358 | Pure Algebra | Junior | Trigonometry | Identify all possible solutions to sine ratio equations |

359 | Pure Algebra | Junior | Trigonometry | Identify all possible solutions to cosine ratio equations |

360 | Pure Algebra | Junior | Trigonometry | Identify all possible solutions to tangent ratio equations |

361 | Pure Algebra | Secondary | Directions and Angles | Manipulate expressions involving parenthesis |

362 | Pure Algebra | Secondary | Directions and Angles | Solve a small system of equations in context |

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

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

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

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

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

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

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

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

371 | Pure Algebra | Senior | Polynomials | Solve linear diophantine equations |

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

373 | Pure Algebra | Senior | Factorising | Use the Factor Theorem as a tool to help solve problems |

374 | Pure Algebra | Senior | Factorising | Use the Remainder Theorem as a tool to help solve problems |