# LEARNING CONTENT

## FOR CONCEPTUAL UNDERSTANDING

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