# 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
Arithmetic Junior Operations Understand how rational exponents are short-hand for roots, and simplify number expressions accordingly
Arithmetic Junior Operations Perform common binary operations on number values
Arithmetic Junior Quotients Manipulate any quotient raised to any exponent
Arithmetic Junior Exponents Communicate in base 2 and convert into base 10
Arithmetic Junior Ratio and Proportion Use indirect proportion as a constant rate of change for different quantities
Arithmetic Junior Matrices Use matrices to transform images around a cartesian grid
Arithmetic Junior Operations Use the factorial operation
Arithmetic Junior Operations Perform correct order of operation processes involving trigonometric ratios
Arithmetic Junior Rationality Interpret solutions involving any real-numbers in context
Arithmetic Junior Error Analyse innaccuracies of compounding rounded values
Arithmetic Junior Sequences and Series Use conventional notation for geometric sequences in context
Arithmetic Junior Binomial expressions Use the binomial expansion to solve a problem
Arithmetic Junior Cryptography Communicate in braille and morse code with precision
Arithmetic Junior Matrices Use matrices to visualise and draw transformed images of shapes on a cartesian grid
Arithmetic Junior Exponents Solve simple modular arithmetic problems
Arithmetic Junior Finance Create and interpret simple accounting documentation
Arithmetic Junior Divisibility Identify divisibilities of a number written in any base
Arithmetic Junior Relations Mappings and Equations Identify terms in a sequence pattern CODEBREAKERS
Arithmetic Junior Combinatorics Calculate simple binomial problems involving combinations
Arithmetic Junior Finance Solve problems involving amortization and annuity
Arithmetic Junior Exponents Communicate in base 10 and convert into base 2
Arithmetic Primary Time Read from an analog clock
Arithmetic Primary Operations Understand how multiplication is short-hand for repeated addition and use it accordingly
Arithmetic Primary Divisibility Identify the divisibility by 10, 5 and 2 of any number
Arithmetic Primary Quotients Understand how division is short-hand for repeated subtraction and find exact quotients without remainders
Arithmetic Primary Notation Articulate place value of number digits within words
Arithmetic Primary Exponents Appreciate the distinction between numbers arranged in a square compared to in an oblong
Arithmetic Primary Finance Appreciate and recognise 'value for money' involving decimals and percentages
Arithmetic Primary Error Identify approximations for sums and obvious mis-calculations
Arithmetic Primary Ratio and Proportion Calculate any percentage of an amount
Arithmetic Primary Sequences and Series Recite up to the 15 times tables as a fundamental axiom of number patterns
Arithmetic Primary Cryptography Communicate the phonetic alphabet, Atbash, handphone keypad and dancing men cipher with precision
Arithmetic Primary Directions and Angles Identify common factors within expressions
Arithmetic Primary Kinematics Calculate departure, arrival times or distance travelled in context
Arithmetic Primary Time Solve problems involving all convential formats of time
Arithmetic Primary Directions and Angles Recognise appropriate units for quantities in context
Arithmetic Primary Divisibility Identify and label numbers that have a maximum of 2 factors
Arithmetic Primary Rationality Distinguish between the different possible types of rational number
Arithmetic Primary Notation Communicate the value of items using words
Arithmetic Primary Exponents Calculate the value of integers raised to single-digit exponents
Arithmetic Primary Ratio and Proportion Create group representations for parts of a whole
Arithmetic Primary Exponents Use everyday contexts to perform exponent calculations with any base number
Arithmetic Primary Finance Consider costs and expenses when making value judgements within specified budgets
Arithmetic Primary Error Identify the magnitude of a rounding error
Arithmetic Primary Ratio and Proportion Use direct proportion as a constant rate of change for different quantities
Arithmetic Primary Divisibility Decompose any number into its prime factors and compare with others
Arithmetic Primary Sequences and Series Use conventional notation for common sequences in context
Arithmetic Primary Exponents Express values in exponent form
Arithmetic Primary Relations Mappings and Equations Identify terms in a sequence pattern CODEBREAKERS
Arithmetic Secondary Operations Perform multi-step calculations, involving parentheses and indices, in the correct order
Arithmetic Secondary Quotients Calculate quotients of values and interpret possible remainders in context
Arithmetic Secondary Divisibility Identify divisibilities by single-digit numbers
Arithmetic Secondary Rationality Appreciate there are infinitely many numbers between any two distinct numbers
Arithmetic Secondary Notation Understand appropriate representations for very small and very large numbers in context
Arithmetic Secondary Cryptography Communicate morse code, braille, Ceasar and PigPen cipher with precision
Arithmetic Secondary Vectors Use vectors to translate images around a cartesian grid
Arithmetic Secondary Rationality Perform calculations involving any real numbers
Arithmetic Secondary Notation Always communicate using conventional notation, including units of derived values
Arithmetic Secondary Finance Make financial value judgements within real contexts
Arithmetic Secondary Error Write answers to appropriate decimal places or significant figures
Arithmetic Secondary Directions and Angles Convert across common imperial and metric quantities
Arithmetic Secondary Quotients Express any quotient in terms of the sum of unit fractions
Arithmetic Secondary Finance Compare results using simple and compound interest
Arithmetic Secondary Divisibility Solve simple linear concruence problems
Arithmetic Secondary Relations Mappings and Equations Identify terms in a sequence pattern CODEBREAKERS
Arithmetic Secondary Exponential and Logarithmic Recognise and compare depreciation rates with absolute drops in value
Arithmetic Secondary Exponential and Logarithmic Identify and use the multiplier when calculating with increasing and decreasing percentages
Arithmetic Secondary Sequences and Series Use conventional notation for arithmetic sequences and find simple series in context
Arithmetic Senior Exponents Manipulate numbers expressed in any form and within any common base
Arithmetic Senior Binomial expressions Use the binomial expansion with simple rational values
Arithmetic Senior Matrices Use inverse 2 by 2 matrices to help transform (large) data sets in solving real-life problems
Arithmetic Senior Exponents Use modular arithmetic and linear congruences to solve number problems
Arithmetic Senior Finance Solve problems involving amortization
Arithmetic Senior Sequences and Series Distinguish between recursive and telescoping sequences and use conventional notation to sum their series where possible, in context
Arithmetic Senior Binomial expressions Use the binomial expansion with any exponent
Arithmetic Senior Complex numbers Use DeMoivre's Theorem as a tool within calculations
Arithmetic Senior Divisibility Use Fermat's Little Theorem
Arithmetic Senior Rationality Use the Ramanujan-Nagell exponential diophantine equation in context
Arithmetic Senior Finance Solve problems involving annuity
Arithmetic Senior Manipulation Identify values or quantity of digits within large numbers in any base
Arithmetic Senior Relations Mappings and Equations Identify terms in a sequence pattern CODEBREAKERS
Arithmetic Senior Combinatorics Calculate simple problems involving permutations
Arithmetic Senior Divisibility Identify divisibilities of a number written in any base
Arithmetic Senior Complex numbers Use Pell's equation in context
Algebra & Geometry Junior Tessellations Identify tilings that create monohedral tessellations
Algebra & Geometry Junior Relations Mappings and Equations Graphically solve a small system of equations in context
Algebra & Geometry Junior Perimeter and Area Use nets and coordinates to calculate perimeter and area
Algebra & Geometry Junior Nets and Volume Find Volume of composite Polyhedra from their net
Algebra & Geometry Junior Trigonometry Recognise common ratios between the sides of and angles within a right-angled triangle
Algebra & Geometry Junior Theorems identify and use the circle theorems in solving problems
Algebra & Geometry Junior Graph Theory Use the handshaking lemma and komplete graphs in simple cases
Algebra & Geometry Junior Direction and Angles Calculate and use amounts of turn in radians
Algebra & Geometry Junior Theorems Know and use Pick's Theorem as a tool within calculations
Algebra & Geometry Junior Tessellations Recognise the geometric properties of the Torus and Klein bottle are different in cartesian and spherical geometry
Algebra & Geometry Junior Vectors Represent a scalar product geometrically and use it in calculating intersections and angles of lines
Algebra & Geometry Junior Exponential and Logarithmic Recognise the effect of increasing interest rates over absolute interest
Algebra & Geometry Junior Polygons and Polyhedra Solve for measures of angles and segments relating to circles
Algebra & Geometry Junior Polygons and Polyhedra Calculate perimeters and areas of sectors and segments relating to circles
Algebra & Geometry Junior Area and Surface Area Calculate the area of any triangle
Algebra & Geometry Junior Proof Appreciate and follow the logic required in creating direct mathematical proofs, and proof by contradiction
Algebra & Geometry Junior Area and Surface Area Find the area of compound polygons
Algebra & Geometry Junior Axioms and Logic Identify when a statement is logical or not (ie tautology)
Algebra & Geometry Junior Matrices Use matrices to transform images around a cartesian grid
Algebra & Geometry Junior Matrices Use matrices to visualise and draw transformed images of shapes on a cartesian grid
Algebra & Geometry Junior Nets and Volume Find the dimensions of composite Polyhedra from the Volume
Algebra & Geometry Junior Vectors Perform simple transformations within 3D space
Algebra & Geometry Junior Vectors Identify multiple transformations in 2D
Algebra & Geometry Junior Trigonometry Recognise common ratios between the sides of and angles within any triangle
Algebra & Geometry Junior Combinatorics Calculate binomial problems involving simple permutations
Algebra & Geometry Junior Area and Surface Area Find the SA of compound polyhedra
Algebra & Geometry Primary Directions and Angles Have an understanding of the estimation of magnitudes
Algebra & Geometry Primary Coordinates Know and use first quadrant cartesian coordinates in context
Algebra & Geometry Primary Direction and Angles Provide directions using a 4-point compass rose
Algebra & Geometry Primary Relations Mappings and Equations Visualise times tables with an arithmetic translation in a mapping
Algebra & Geometry Primary Graphs Appreciate the graphical representation of a constant input with independent output and vice versa
Algebra & Geometry Primary Nets and Volume Distinguish between and label common polygon shapes
Algebra & Geometry Primary Area and Surface Area Find area of right-angled polygons and surface area of right-angled polyhedra
Algebra & Geometry Primary Nets and Volume Find the volume of right-angled polyhedra
Algebra & Geometry Primary Theorems Recognise the fundamental axioms of geometry: Amount of turn round a point, vertically opposite and corresponding angles
Algebra & Geometry Primary Vectors Recognise the spacial effect of a translation slide movement
Algebra & Geometry Primary Tessellations Maintain a visual appreciation for shapes that create tiling patterns
Algebra & Geometry Primary Operations Use everyday contexts to create calculations
Algebra & Geometry Primary Polygons and Polyhedra Distinguish between and label common polyhedron objects
Algebra & Geometry Primary Nets and Volume Find the volume of right-angled polyhedra
Algebra & Geometry Primary Directions and Angles Use appropriate metric units when representing quantities
Algebra & Geometry Primary Polynomials Simplify any expression
Algebra & Geometry Primary Trigonometry Understand the relationship connecting the perpendicular sides and area of a right-angled triangle
Algebra & Geometry Primary Vectors Recognise and describe the spacial effect of a spin rotation
Algebra & Geometry Primary Directions and Angles Use appropriate imperial units when representing quantities
Algebra & Geometry Primary Polygons and Polyhedra Identify the labels relating to circles
Algebra & Geometry Primary Area and Surface Area Identify and name angles smaller or larger than multiples of quarter turns
Algebra & Geometry Primary Area and Surface Area Distinguish triangles from the magnitude of their angles or lengths of sides
Algebra & Geometry Primary Vectors Recognise the spacial effect of a mirror image reflection
Algebra & Geometry Secondary Direction and Angles Provide directions using an 8-point compass rose
Algebra & Geometry Secondary Nets and Volume Classify quadrilaterals by using interior and exterior angles
Algebra & Geometry Secondary Coordinates Know and use cartesian coordinates in context
Algebra & Geometry Secondary Direction and Angles Estimate and describe amounts of turn in degrees
Algebra & Geometry Secondary Relations Mappings and Equations Describe linear relationships from a mapping diagram and solve equivalent equations with rational coefficients
Algebra & Geometry Secondary Polygons and Polyhedra Recognise the properties of the platonic solids
Algebra & Geometry Secondary Perimeter and Area Use proportions to calculate area and perimeter
Algebra & Geometry Secondary Area and Surface Area Find area of common polygons and SA of common Polyhedra
Algebra & Geometry Secondary Factorising Fully factorise any expression
Algebra & Geometry Secondary Exponential and Logarithmic Recognise and compare depreciation rates with absolute drops in value
Algebra & Geometry Secondary Theorems Understand the relationships of angles formed by a transversal over a pair of parallel lines
Algebra & Geometry Secondary Graph Theory From given information about its faces, edges and vertices, recognise if a solid exists
Algebra & Geometry Secondary Direction and Angles Use three-figure bearings to describe the direction of an object compared to another
Algebra & Geometry Secondary Nets and Volume Find the volume of common Polyhedra from their net and vice versa
Algebra & Geometry Secondary Polynomials Represent and use a linear function graphically and algebraically
Algebra & Geometry Secondary Exponential and Logarithmic Identify and use the multiplier when calculating with increasing and decreasing percentages
Algebra & Geometry Secondary Trigonometry Understand and use the relationship connecting the 3 sides of a right-angled triangle and calculate its area
Algebra & Geometry Secondary Vectors Use the language of constant, increasing and decreasing for the visual rate of change of a graph
Algebra & Geometry Secondary Theorems Understand the relationship connecting areas around the sides of a right-angled triangle
Algebra & Geometry Secondary Vectors Perform stretch and sheer transformations on 2D shapes
Algebra & Geometry Secondary Combinatorics Recognise the pattern of Pascal's triangle as a tool for simple combination poblems
Algebra & Geometry Secondary Vectors Describe movement around a shape using given vectors
Algebra & Geometry Secondary Direction and Angles Identify the loci of a situation given conditions
Algebra & Geometry Secondary Vectors Rotate a 2D shape by any angle amount of turn
Algebra & Geometry Secondary Direction and Angles Construct and interpret scale drawings, using bearings
Algebra & Geometry Secondary Polygons and Polyhedra Calculate the perimeter and area relating to circles
Algebra & Geometry Secondary Tessellations Recognise the geometric properties of the mobius strip
Algebra & Geometry Secondary Vectors Describe or draw quarter-turn rotation images of shapes and integer scale factor enlargement on a cartesian grid
Algebra & Geometry Secondary Area and Surface Area Identify mathematically similar shapes
Algebra & Geometry Secondary Area and Surface Area Understand a proof for the sum of angles in a triangle
Algebra & Geometry Secondary Area and Surface Area Understand and use the side, angle and area relationships within any cartesian triangle
Algebra & Geometry Secondary Axioms and Logic Appreciate and recognise Euclid's postulates
Algebra & Geometry Secondary Direction and Angles Use different 2D planes within 3D spaces
Algebra & Geometry Secondary Nets and Volume Find the volume of common Polyhedra from their net and vice versa.
Algebra & Geometry Secondary Ratio and Proportion Construct angle bisectors and find the shortest distance between lines and a point
Algebra & Geometry Senior Nets and Volume Identify and use bipyramids
Algebra & Geometry Senior Tessellations Recognise Hirschhorn tilings
Algebra & Geometry Senior Nets and Volume Use of Euler's characteristic and duality within simple contexts
Algebra & Geometry Senior Trigonometry Use the compound angle identities as tools
Algebra & Geometry Senior Theorems Use Ceva's Theorem as a tool within calculations
Algebra & Geometry Senior Graph Theory Recognise Eulerian cycles in context
Algebra & Geometry Senior Trigonometry Use the arctrigonometric identities as tools
Algebra & Geometry Senior Theorems Know and use Carnot's Theorem as a tool within calculations
Algebra & Geometry Senior Polygons and Polyhedra Recognise Archimedean solids, duals and Kepler-Poinsot polyhedra
Algebra & Geometry Senior Area and Surface Area Use Heron's Formula as a tool within calculations
Algebra & Geometry Senior Directions and Angles Use completing the rectangle as a tool within calculations
Algebra & Geometry Senior Tessellations Recognise Periodic tilings
Algebra & Geometry Senior Tessellations Recognise Aperiodic tilings
Algebra & Geometry Senior Theorems Use Menelaus' Theorem as a tool within calculations
Algebra & Geometry Senior Graph Theory Recognise Eulerian circuits in context
Algebra & Geometry Senior Graph Theory Recognise Hamiltonian cycles in context
Algebra & Geometry Senior Graph Theory Recognise Hamiltonian circuits in context
Algebra & Geometry Senior Nets and Volume Identify and use uniform stars
Calculus Junior Kinematics Use scalar equivalents of displacement and velocity vectors with time
Calculus Junior Integration Calculate areas between graphs and axes, where common shapes and objects are generated
Calculus Junior Kinematics Understand and calculate the linear movement of a particle
Calculus Junior Differentiation Find minimums for optimsed solutions
Calculus Junior Vectors Distinguish between increasing and decreasing slope of graphs in context
Calculus Junior Vectors Use average rate of change in context
Calculus Junior Kinematics Use scalar equivalents of velocity and acceleration vectors with time
Calculus Junior Differentiation Know and use the chain rule as a tool to differentiate simple functions in context
Calculus Junior Differentiation Know and use the product rule as a tool to differentiate simple functions in context
Calculus Junior Differentiation Know and use the quotient rule as a tool to differentiate simple functions in context
Calculus Junior Integration Calculate volumes of revolution of simple functions wrt x
Calculus Junior Integration Calculate volumes of revolution of simple functions wrt y
Calculus Junior Differentiation Find maximums for optimsed solutions
Calculus Junior Differentiation Find inflections for optimsed solutions
Calculus Junior Vectors Use concavity of graphs to identify local behaviour of a particle in context
Calculus Junior Vectors Use instantaneous rate of change in context
Calculus Secondary Differentiation Recognise and distinguish between graphs of functions and of their slope functions
Calculus Secondary Vectors Use the language of constant, increasing or decreasing for the visual rate of change of a graph
Calculus Senior Differentiation Know and use the chain rule and substitution as tools to differentiate simple functions in context
Calculus Senior Integration Know and use the inverse chain rule and substitution as tools to integrate simple functions in context
Calculus Senior Kinematics Use and convert between displacement and velocity functions in context
Calculus Senior Differentiation Use implicit differentiation and related rates of change as tools on functions in context
Calculus Senior Integration Know and use integration by parts as tools within calculations
Calculus Senior Limits Use Eulers Method and slope fields as tools in simple contexts
Calculus Senior Differential Equations Solve first order linear differential equations
Calculus Senior Differential Equations Solve separable variable differential equations
Calculus Senior Differential Equations Solve homogenous differential equations
Calculus Senior Differential Equations Solve simple linear coupled simultaneous differential equations
Calculus Senior Integration Know and use the product rule and substitution as tools to differentiate simple functions in context
Calculus Senior Integration Know and use the inverse product rule and substitution as tools to integrate simple functions in context
Calculus Senior Kinematics Use and convert between velocity and acceleration functions in context
Calculus Senior Kinematics Use and convert between displacement and acceleration functions in context
Calculus Senior Limits Calculate limits to infinity of rational functions
Calculus Senior Integration Know and use partial fractions as tools within calculations
Experimental Sciences Junior Probability Appreciate and interpret theoretical probabilities of independent events, in context
Experimental Sciences Junior Regression Draw and use a line of best fit by hand, passing through the mean value
Experimental Sciences Junior Location and Dispersion Make comparisons between data sets using cumulative frequency
Experimental Sciences Junior Probability Know and use the rules for union, intersection as tools within calculations
Experimental Sciences Junior Regression Calculate simple least squares linear regression by hand
Experimental Sciences Junior Representing Data Use and graphically represent discrete vs continuous data appropriately
Experimental Sciences Junior Location and Dispersion Generate and interpret the geometric mean from a dataset
Experimental Sciences Junior Data tests and correlation Use and interpret the correlation coefficient in context when analysing data
Experimental Sciences Junior Data tests and correlation Understand the effect of sampling compared to population statistics
Experimental Sciences Junior Location and Dispersion Generate and interpret the arithmetic mean value from a grouped frequency table
Experimental Sciences Junior Random variables and distributions Use and interpret binomial probability distributions in context
Experimental Sciences Junior Location and Dispersion Generate and interpret the arithmetic median value from a grouped frequency table
Experimental Sciences Junior Probability Know and use the complement of a set as a tool within calculations
Experimental Sciences Junior Combinatorics Calculate probabilities involving combinations
Experimental Sciences Junior Location and Dispersion Use and interpret standard deviation
Experimental Sciences Junior Location and Dispersion Use and interpret variance
Experimental Sciences Junior Location and Dispersion Generate and interpret the arithmetic modal value from a grouped frequency table
Experimental Sciences Primary Location and Dispersion Identify the mode (most occurring object) within a group
Experimental Sciences Primary Set Theory Place objects into given overlapping groups
Experimental Sciences Primary Representing Data Count frequencies through pictorial representations and interpret in context
Experimental Sciences Primary Location and Dispersion Calculate the mode, median, mean and range from a list of quantative data
Experimental Sciences Primary Representing Data Count frequencies from bars and a number line scale, and interpret the results in context.
Experimental Sciences Primary Representing Data Identify proportions from pie charts and interpret in context
Experimental Sciences Primary Probability Interpret theoretical probabilities of independent events, in context
Experimental Sciences Secondary Location and Dispersion Generate and interpret the arithmetic mean, median and modal values from frequency tables
Experimental Sciences Secondary Probability Interpret experimental probabilities of independent events in context
Experimental Sciences Secondary Set Theory Identify regions within Venn diagrams using conventianal notation and vice versa
Experimental Sciences Secondary Representing Data Distinguish between pie, bar charts and histograms and interpret in context
Experimental Sciences Secondary Probability Interpret theoretical probabilities of dependent events, in context
Experimental Sciences Senior Probability Know and use Bayes' Theorem as a tool within calculations.
Experimental Sciences Senior Regression Calculate function regressions using technology
Experimental Sciences Senior Data tests and correlation Use Chi-square test for independence
Experimental Sciences Senior Matrices Find the steady state of a real-life Markov Chain system
Experimental Sciences Senior Combinatorics Calculate probabilities involving permutations
Experimental Sciences Senior Random variables and distributions Use and interpret the test for the mean in a poisson distribution in context
Experimental Sciences Senior Probability Use and interpret Expectation of combined independent events in context
Experimental Sciences Senior Representing Data Use statistical hypothesis testing with real-life datasets
Experimental Sciences Senior Location and Dispersion Use and interpret transformations of standard deviation
Experimental Sciences Senior Regression Calculate least squares linear regression
Experimental Sciences Senior Data tests and correlation Use PPMCC for bivariate data sets
Experimental Sciences Senior Data tests and correlation Use Spearman's rank correlation coefficient for bivariate data sets
Experimental Sciences Senior Random variables and distributions Use and interpret z-test for the mean of a normal probability distribution in context
Experimental Sciences Senior Probability Use and interpret Variance of combined independent events in context
Experimental Sciences Senior Data tests and correlation Use Chi-square goodness of fit test
Experimental Sciences Senior Location and Dispersion Use and interpret transformations of variance
Experimental Sciences Senior Data tests and correlation Use 2-sample t-test in context
Experimental Sciences Senior Data tests and correlation Use 1-sample t-test in context
Experimental Sciences Senior Data tests and correlation Use and interpret the correlation coUse and interpret the coefficient of determination in context when analysing data
History Junior Recreational Appreciate the patterns created from shuffling small packs of cards
History Junior Mathematicians Know about some prominent 19th century mathematicians
History Junior Mathematicians Know about some prominent 20th century mathematicians
History Primary Recreational Identify and complete magic squares
History Primary Mathematicians Know about some prominent 20th century mathematicians
History Primary Mathematicians Know about some prominent 19th century mathematicians
History Secondary Axioms and Logic Appreciate and recognise Euclid's postulates
History Secondary Proof Create simple geometric proofs involving parallel lines
History Secondary Mathematicians Know about some prominent 20th century mathematicians
History Secondary Mathematicians Know about some prominent 19th century mathematicians
History Senior Proof Follow the logic required in creating nonconstructive mathematical proofs and applications in Graph Theory
History Senior Proof Think through a larger logic problem and create tests for efficiency and optimization
History Senior Mathematicians Know about some prominent 20th century mathematicians
History Senior Mathematicians Know about some prominent 19th century mathematicians
Algebra and Graphs Junior Exponential and Logarithmic Use and solve exponential equations considering their graphs
Algebra and Graphs Junior Vectors Use the magnitude of vectors in geometric problems
Algebra and Graphs Junior Polynomials Use the rational root and sum or product of zeros tools when manipulating polynomials
Algebra and Graphs Junior Polynomials Represent and use a quadratic function graphically and algebraically
Algebra and Graphs Junior Coordinates Convert between cartesian and simple polar coordinates
Algebra and Graphs Junior Exponential and Logarithmic Use exponential functions to linearize graphs of variable relationships
Algebra and Graphs Junior Graphs Use conventional notation when describing curved graphs
Algebra and Graphs Junior Graphs Use conventional notation to describe odd functions and key parts of graphs
Algebra and Graphs Junior Graphs Describe piecewise functions and identify continuity across the domain
Algebra and Graphs Junior Graphs Know and use the relations that create circles
Algebra and Graphs Junior Limits Identify vertical asymptotes by taking limits of functions
Algebra and Graphs Junior Relations Mappings and Equations Manipulate quadratic expressions and graph their relationship
Algebra and Graphs Junior Trigonometry Identify all possible solutions to trigonometric graphs
Algebra and Graphs Junior Vectors Recognise the graphical movement of a function manipulation
Algebra and Graphs Junior Trigonometry Understand the sine graph for more than a full turn
Algebra and Graphs Junior Factorising Appreciate the graphical representations of the 'difference of 2 squares' identity
Algebra and Graphs Junior Polynomials Represent and use the 2 distinct roots of a quadratic function graphically
Algebra and Graphs Junior Polynomials Represent and use the repeated real root of a quadratic function graphically
Algebra and Graphs Junior Polynomials Understand and represent a quadratic function without any real roots graphically
Algebra and Graphs Junior Exponential and Logarithmic Use and solve logarithmic equations considering their graphs
Algebra and Graphs Junior Exponential and Logarithmic Use logarithmic functions to linearize graphs of variable relationships
Algebra and Graphs Junior Graphs Use conventional notation to describe even functions and key parts of graphs
Algebra and Graphs Junior Limits Identify horizontal asymptotes by taking limits of functions
Algebra and Graphs Junior Relations Mappings and Equations Manipulate simple cubic expressions and graph their relationship
Algebra and Graphs Junior Relations Mappings and Equations Manipulate simple rational expressions and graph their relationship
Algebra and Graphs Junior Trigonometry Understand the cosine graph for more than a full turn
Algebra and Graphs Junior Polynomials Relate a vertex-form quadratic equation to its parabola
Algebra and Graphs Junior Trigonometry Understand the tangent graph for more than a full turn
Algebra and Graphs Primary Relations Mappings and Equations Identify times tables with an arithmetic translation
Algebra and Graphs Primary Graphs Use convential notation to describe and draw linear inequalities
Algebra and Graphs Primary Graphs Identify roots from graphs within context
Algebra and Graphs Primary Graphs Use convential notation to describe and draw linear inequalities
Algebra and Graphs Primary Inequalities Solve one simple linear inequality
Algebra and Graphs Secondary Graphs Describe key features of parabola graphs
Algebra and Graphs Secondary Coordinates Know and use cartesian coordinates in context
Algebra and Graphs Secondary Graphs Use conventional notation when describing linear graphs
Algebra and Graphs Secondary Graphs Graphically solve a small system of equations in context
Algebra and Graphs Secondary Graphs Use conventional notation to solve 2D inequalities
Algebra and Graphs Secondary Limits Identify the equations of asymptotes on graphs
Algebra and Graphs Secondary Relations Mappings and Equations Describe linear relationships from a mapping diagram and solve equivalent equations with rational coefficients
Algebra and Graphs Secondary Relations Mappings and Equations Graphically solve a small system of equations in context
Algebra and Graphs Secondary Polynomials Represent and use a linear function graphically and algebraically
Algebra and Graphs Secondary Polynomials Relate a quadratic equation to its parabola
Algebra and Graphs Secondary Regression Draw and use a line of best fit by hand, passing through the mean value
Algebra and Graphs Senior Tessellations Create simple Voronoi tilings using midpoints
Algebra and Graphs Senior Coordinates Understand when polar coordinates are easier/more efficient than cartesian, and use them in simple contexts
Algebra and Graphs Senior Graphs Use conventional notation to describe piecewise functions and discuss continuity across the domain
Algebra and Graphs Senior Vectors Find the volume of composite polyhedra using Vectors
Algebra and Graphs Senior Factorising Know and use Descartes Rule of Signs as a tool within calculations
Algebra and Graphs Senior Exponential and Logarithmic Use and solve logistical equations and their graphs
Algebra and Graphs Senior Vectors Recognise and distinguish between the graphs of functions, their first and second differential graphs
Algebra and Graphs Senior Vectors Perform transformations within 3D space
Algebra and Graphs Senior Vectors Represent a vector product geometrically and use it in calculating areas of plane segments
Algebra and Graphs Senior Limits Calculate limits to any point of rational functions
Algebra and Graphs Senior Matrices Use eigenvalues and eigenvectors as tools within simple calculations
Algebra and Graphs Senior Coordinates Use polar coordinates in context
Algebra and Graphs Senior Relations Mappings and Equations Use parametric equations as a tool within calculations
Algebra and Graphs Senior Polygons and Polyhedra Know and use the relations that create ellipses
Algebra and Graphs Senior Graphs Use conventional notation to solve any inequality
Algebra and Graphs Senior Vectors Find surface areas of composite polyhedra using Vectors
Algebra and Graphs Senior Limits Identify oblique asymptotes by taking limits of functions
Pure Algebra Junior Polynomials Solve simple linear diophantine equations
Pure Algebra Junior Axioms and Logic Use truth tables to solve simple problems
Pure Algebra Junior Binomial expressions Use the binomial expansion with integer values to work backwards to solve a problem
Pure Algebra Junior Inequalities Solve a system of three linear inequalities
Pure Algebra Junior Operations Understand how rational exponents are short-hand for roots, and simplify algebraic expressions accordingly
Pure Algebra Junior Quotients Manipulate any algebraic quotient raised to any exponent
Pure Algebra Junior Operations Perform multi-step algebraic calculations, involving parentheses and indices, in the correct order
Pure Algebra Junior Operations Perform binary operations on algebraic values
Pure Algebra Junior Proof Create simple constructive mathematical proofs
Pure Algebra Junior Factorising Know and use the Factor Theorem
Pure Algebra Junior Factorising Know and use Remainder Theorem
Pure Algebra Junior Polynomials Use the 2 distinct roots of a quadratic function algebraically
Pure Algebra Junior Polynomials Use the repeated real root of a quadratic function algebraically
Pure Algebra Junior Polynomials Recognise quadratic functions without any real roots algebraically
Pure Algebra Junior Trigonometry Identify all possible solutions to sine ratio equations
Pure Algebra Junior Trigonometry Identify all possible solutions to cosine ratio equations
Pure Algebra Junior Trigonometry Identify all possible solutions to tangent ratio equations
Pure Algebra Secondary Directions and Angles Manipulate expressions involving parenthesis
Pure Algebra Secondary Directions and Angles Solve a small system of equations in context
Pure Algebra Secondary Inequalities Solve a system of linear inequalities
Pure Algebra Senior Axioms and Logic Use truth tables to solve problems
Pure Algebra Senior Proof Appreciate and follow the logic required in Fermat's infinite descent proof
Pure Algebra Senior Quotients Understand the use for and manipulate partial fraction expressions
Pure Algebra Senior Sequences and Series Find the nth term rule for recurrence relations
Pure Algebra Senior Axioms and Logic Use digital logic gates to solve Boolean algebra problems
Pure Algebra Senior Axioms and Logic Use Venn diagrams to solve Boolean algebra logic problems
Pure Algebra Senior Complex numbers Recognise the existence of non-real solutions to mathematical problems
Pure Algebra Senior Polynomials Solve linear diophantine equations
Pure Algebra Senior Sequences and Series Distinguish between infinite, iterative and recurrence relation sequences
Pure Algebra Senior Factorising Use the Factor Theorem as a tool to help solve problems
Pure Algebra Senior Factorising Use the Remainder Theorem as a tool to help solve problems