# 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 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 at 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