WMC learning content

for conceptual understanding

Challenging questions usually arise from the required problem-solving involved, rather than the level of content knowledge. An ideal question is one that nearly every participant would understand the solution of, even though they may not have seen how to solve it in the first instance.

The Confidence Round has 5 sections of 8 questions each. These 5 sections are:

  • Arithmetic
  • Algebra and Geometry
  • Calculus
  • Experimental Sciences
  • History (one century, prescribed for each WMC season)

The century for season 2020-21 is the twentieth. The work from any of the following mathematicians will form the questions in the History section:

A.N. Whitehead Alan Turing Alanzo Church Alexander Grothendiek Andre Weil
Andrey Kolmogorov Benoit Mandelbrot Bertrand Russell Claude Shannon David Hilbert
Emmy Noether G.H. Hardy Gerd Faltings J. E. Littlewood John Nash
John von Neumann Julia Robinson Yuri Matiyasevich Kurt Godel Nicolas Bourbaki
Paul Cohen Paul Erdos Srinivasa Ramanujan Thomas Hales Wolfgang Haken

These lists aim to offer all potential participants a feel for the level of mathematical knowledge expected, and hence help them make a reasoned decision on their suitability in becoming a participant.

LEVEL STAGE THEME ESSENTIAL UNDERSTADNING DESCRIPTOR
Primary Qualifier Arithmetic Time Read from an analog clock
Primary Qualifier Arithmetic Measures Have an understanding of the estimation of magnitudes
Primary Qualifier Arithmetic Operations
Primary Qualifier Arithmetic Oder of operations Understand how multiplication is short-hand for repeated addition and use it accordingly
Primary Qualifier Arithmetic Divisibility Identify the divisibility by 10, 5 and 2 of any number
Primary Qualifier Arithmetic Quotients Understand how division is short-hand for repeated subtraction and find exact quotients without remainders
Primary Qualifier Arithmetic Rationality
Primary Qualifier Arithmetic Notation Articulate place value of number digits within words
Primary Qualifier Arithmetic Exponents Appreciate the difference between numbers arranged in a square compared to in an oblong
Primary Qualifier Arithmetic Finance Appreciate and recognise 'value for money' involving decimals and percentages
Primary Qualifier Arithmetic Error Identify obvious mis-calculations
Primary Qualifier Arithmetic Ratio and proportion Calculate any percentage of an amount
Primary Qualifier Arithmetic Sequences and series Recite up to the 15 times tables as a fundamental axiom of number patterns
Primary Qualifier Arithmetic Binomial expressions
Primary Qualifier Arithmetic Complex numbers
Primary Qualifier Arithmetic Cryptography Communicate the phonetic alphabet with precision
Primary Qualifier Arithmetic Matrices
Primary Qualifier Algebra and Geometry Coordinates Know and use first quadrant cartesian coordinates in context
Primary Qualifier Algebra and Geometry Direction Provide directions with North, East, South and West
Primary Qualifier Algebra and Geometry Mappings and equations Visualise relations in simple bijective functions through a mapping and vice versa
Primary Qualifier Algebra and Geometry Graphs Appreciate the graphical representation of a constant input with independent output and vice versa
Primary Qualifier Algebra and Geometry Triangles Identify and name angles smaller or larger than multiples of quarter turns
Primary Qualifier Algebra and Geometry Polygons and polyhedra Recognise the properties of the platonic solids
Primary Qualifier Algebra and Geometry Perimeter and Area Understand perimeter as distances and rectangular areas as a 2D geometrical representation of a times table
Primary Qualifier Algebra and Geometry Surface area and volume
Primary Qualifier Algebra and Geometry Factorising Identify common factors within expressions
Primary Qualifier Algebra and Geometry Polynomials
Primary Qualifier Algebra and Geometry Exponentials and logarithmic
Primary Qualifier Algebra and Geometry Trigonometry
Primary Qualifier Algebra and Geometry Rates of change
Primary Qualifier Algebra and Geometry Theorems Recognise the fundamental axioms of geometry: Amount of turn round a point, vertically opposite and corresponding angles
Primary Qualifier Algebra and Geometry Transformations Recognise the spacial effect of a translation slide movement and a mirror image reflection
Primary Qualifier Algebra and Geometry Tesselations Maintain a visual appreciation for shapes that create tiling patterns
Primary Qualifier Algebra and Geometry Combinatorics
Primary Qualifier Algebra and Geometry Topology and Graph Theory
Primary Qualifier Algebra and Geometry Vectors
Primary Qualifier Calculus Differentiation
Primary Qualifier Calculus Integration
Primary Qualifier Calculus Kinematics Calculate departure, arrival times or distance travelled in context
Primary Qualifier Calculus Limits and differential equations
Primary Qualifier Experimental Sciences Probability, random variables and distributions
Primary Qualifier Experimental Sciences Location and dispersion Identify the mode (most occuring object within a group)
Primary Qualifier Experimental Sciences Set theory Place objects into given overlapping groups
Primary Qualifier Experimental Sciences Regression
Primary Qualifier Experimental Sciences Representing data, tests and correlation Count frequencies through pictorial representations and interpret in context
Primary Qualifier Foundational Language Axioms and logic
Primary Qualifier Foundational Language Proof
Primary Qualifier Foundational Language Recreational
Primary Finals Arithmetic Time Solve problems involving all convential formats of time
Primary Finals Arithmetic Measures Recognise appropriate units for quantities in context
Primary Finals Arithmetic Operations Use everyday contexts to create calculations
Primary Finals Arithmetic Oder of operations Perform multi-step calculations, involving parentheses and indices, in the correct order
Primary Finals Arithmetic Divisibility Identify and label numbers that have a maximum of 2 factors
Primary Finals Arithmetic Quotients Calculate quotients of values and interpret possible remainders in context
Primary Finals Arithmetic Rationality
Primary Finals Arithmetic Notation Communicate the value of items using words
Primary Finals Arithmetic Exponents Calculate the value of integers raised to single-digit exponents
Primary Finals Arithmetic Finance
Primary Finals Arithmetic Error
Primary Finals Arithmetic Ratio and proportion Create group representations for parts of a whole
Primary Finals Arithmetic Sequences and series
Primary Finals Arithmetic Binomial expressions
Primary Finals Arithmetic Complex numbers
Primary Finals Arithmetic Cryptography Solve simple messages coded as Atbash ciphers, dancing men key or a handphone keypad
Primary Finals Arithmetic Matrices
Primary Finals Algebra and Geometry Coordinates
Primary Finals Algebra and Geometry Direction Provide directions using North-East, North-West, South-East and South-West
Primary Finals Algebra and Geometry Mappings and equations Identify times tables with an arithmetic translation
Primary Finals Algebra and Geometry Graphs Use convential notation when describing linear graphs
Primary Finals Algebra and Geometry Triangles Distinguish triangles from the magnitude of their angles or lengths of sides
Primary Finals Algebra and Geometry Polygons and polyhedra Distinguish between and label common polygon shapes
Primary Finals Algebra and Geometry Perimeter and Area Distinguish between and label any quadrilateral
Primary Finals Algebra and Geometry Surface area and volume Identify nets which form cuboids and use units for volume as a 3D space
Primary Finals Algebra and Geometry Factorising
Primary Finals Algebra and Geometry Polynomials
Primary Finals Algebra and Geometry Exponentials and logarithmic Recognise the effect of increasing interest rates over absolute interest
Primary Finals Algebra and Geometry Trigonometry Understand the relationship connecting the perpendicular sides and area of a right-angled triangle
Primary Finals Algebra and Geometry Rates of change
Primary Finals Algebra and Geometry Theorems
Primary Finals Algebra and Geometry Transformations
Primary Finals Algebra and Geometry Tesselations
Primary Finals Algebra and Geometry Combinatorics
Primary Finals Algebra and Geometry Topology and Graph Theory
Primary Finals Algebra and Geometry Vectors
Primary Finals Calculus Differentiation
Primary Finals Calculus Integration
Primary Finals Calculus Kinematics
Primary Finals Calculus Limits and differential equations
Primary Finals Experimental Sciences Probability, random variables and distributions
Primary Finals Experimental Sciences Location and dispersion Calculate the mode, median, mean and range from a list of quantative data
Primary Finals Experimental Sciences Set theory
Primary Finals Experimental Sciences Regression
Primary Finals Experimental Sciences Representing data, tests and correlation Count frequencies from bars and a number line scale, and interpret the results in context.
Primary Finals Foundational Language Axioms and logic
Primary Finals Foundational Language Proof
Primary Finals Foundational Language Recreational Identify and complete magic squares
Secondary Qualifier Arithmetic Time
Secondary Qualifier Arithmetic Measures Use approprite metric units when representing quantities
Secondary Qualifier Arithmetic Operations
Secondary Qualifier Arithmetic Oder of operations Understand how rational exponents are short-hand for roots, and simplify expressions accordingly
Secondary Qualifier Arithmetic Divisibility Identify divisibilities by single-digit numbers
Secondary Qualifier Arithmetic Quotients
Secondary Qualifier Arithmetic Rationality Appreciate there are infinitely many numbers between any two distinct numbers
Secondary Qualifier Arithmetic Notation Understand appropriate representations for very small and very large numbers in context
Secondary Qualifier Arithmetic Exponents Use everyday contexts to perform exponent calculations with any base number
Secondary Qualifier Arithmetic Finance Consider costs and expenses when making value judgements within specified budgets
Secondary Qualifier Arithmetic Error Identify the magnitude of a rounding error
Secondary Qualifier Arithmetic Ratio and proportion Use direct proportion as a constant rate of change for different quantities
Secondary Qualifier Arithmetic Sequences and series
Secondary Qualifier Arithmetic Binomial expressions
Secondary Qualifier Arithmetic Complex numbers
Secondary Qualifier Arithmetic Cryptography Communicate in morse code with precision
Secondary Qualifier Arithmetic Matrices Use vectors to translate images around a cartesian grid
Secondary Qualifier Algebra and Geometry Coordinates Know and use cartesian coordinates in context
Secondary Qualifier Algebra and Geometry Direction Estimate and describe amounts of turn in degrees
Secondary Qualifier Algebra and Geometry Mappings and equations Describe linear relationships from a mapping diagram and solve equivalent equations with rational coefficients
Secondary Qualifier Algebra and Geometry Graphs Describe key features of parabola graphs
Secondary Qualifier Algebra and Geometry Triangles Identify mathematically similar shapes
Secondary Qualifier Algebra and Geometry Polygons and polyhedra Classify quadrilaterals by using diagonals
Secondary Qualifier Algebra and Geometry Perimeter and Area
Secondary Qualifier Algebra and Geometry Surface area and volume Identify nets for prisms and common objects
Secondary Qualifier Algebra and Geometry Factorising Fully factorise any expression
Secondary Qualifier Algebra and Geometry Polynomials Simplify any expression
Secondary Qualifier Algebra and Geometry Exponentials and logarithmic Recognise and compare depreciation rates with absolute drops in value
Secondary Qualifier Algebra and Geometry Trigonometry
Secondary Qualifier Algebra and Geometry Rates of change
Secondary Qualifier Algebra and Geometry Theorems Understand the relationships of angles formed by a transversal over a pair of parallel lines
Secondary Qualifier Algebra and Geometry Transformations Recognise and describe the spacial effect of a spin rotation
Secondary Qualifier Algebra and Geometry Tesselations Identify tilings that create monohedral tessellations
Secondary Qualifier Algebra and Geometry Combinatorics
Secondary Qualifier Algebra and Geometry Topology and Graph Theory
Secondary Qualifier Algebra and Geometry Vectors
Secondary Qualifier Calculus Differentiation
Secondary Qualifier Calculus Integration
Secondary Qualifier Calculus Kinematics Calculate departure, arrival times or distance travelled in context
Secondary Qualifier Calculus Limits and differential equations
Secondary Qualifier Experimental Sciences Probability, random variables and distributions Appreciate and interpret theoretical probabilities of independent events, in context
Secondary Qualifier Experimental Sciences Location and dispersion Generate and interpret the arithmetic mean, median and modal values from frequency tables
Secondary Qualifier Experimental Sciences Set theory
Secondary Qualifier Experimental Sciences Regression
Secondary Qualifier Experimental Sciences Representing data, tests and correlation Identify proportions from pie charts and interpret in context
Secondary Qualifier Foundational Language Axioms and logic
Secondary Qualifier Foundational Language Proof
Secondary Qualifier Foundational Language Recreational
Secondary Finals Arithmetic Time
Secondary Finals Arithmetic Measures Use approprite imperial units when representing quantities
Secondary Finals Arithmetic Operations
Secondary Finals Arithmetic Oder of operations Perform common binary operations on number values
Secondary Finals Arithmetic Divisibility Decompose any number into its prime factors
Secondary Finals Arithmetic Quotients Manipulate any quotient raised to any exponent
Secondary Finals Arithmetic Rationality Perform calculations involving any real numbers
Secondary Finals Arithmetic Notation Always communicate using conventional notation, including units of derived values
Secondary Finals Arithmetic Exponents Communicate in base 2 and convert into base 10
Secondary Finals Arithmetic Finance Make financial value judgements within real contexts
Secondary Finals Arithmetic Error Write answers to appropriate decimal places or significant figures
Secondary Finals Arithmetic Ratio and proportion Use indirect proportion as a constant rate of change for different quantities
Secondary Finals Arithmetic Sequences and series Use conventional notation for arithmetic sequences and find simple series in context
Secondary Finals Arithmetic Binomial expressions
Secondary Finals Arithmetic Complex numbers
Secondary Finals Arithmetic Cryptography Solve simple messages coded as Caesar, ROT13 or PigPen ciphers
Secondary Finals Arithmetic Matrices Use matrices to transform images around a cartesian grid
Secondary Finals Algebra and Geometry Coordinates
Secondary Finals Algebra and Geometry Direction Use three-figure bearings to describe the direction of an object compared to another
Secondary Finals Algebra and Geometry Mappings and equations
Secondary Finals Algebra and Geometry Graphs Identify roots from graphs within context
Secondary Finals Algebra and Geometry Triangles Understand a proof for the sum of angles in a triangle
Secondary Finals Algebra and Geometry Polygons and polyhedra Recognise Archimedean solids, duals and Kepler-Poinsot polyhedra
Secondary Finals Algebra and Geometry Perimeter and Area Understand and use the relationship between the perimeter and radius of any circle, and calculate its area
Secondary Finals Algebra and Geometry Surface area and volume Create nets for objects and vice versa, and calculate simple surface areas and volumes
Secondary Finals Algebra and Geometry Factorising
Secondary Finals Algebra and Geometry Polynomials Represent and use a linear function graphically and algebraically
Secondary Finals Algebra and Geometry Exponentials and logarithmic Identify and use the multiplier when calculating with increasing and decreasing percentages
Secondary Finals Algebra and Geometry Trigonometry Understand and use the relationship connecting the 3 sides of a right-angled triangle and calculate its area
Secondary Finals Algebra and Geometry Rates of change
Secondary Finals Algebra and Geometry Theorems Understand the relationship connecting areas around the sides of a right-angled triangle
Secondary Finals Algebra and Geometry Transformations Describe or draw quarter-turn rotation images of shapes and integer scale factor enlargement on a cartesian grid
Secondary Finals Algebra and Geometry Tesselations
Secondary Finals Algebra and Geometry Combinatorics Recognise the pattern of Pascal's triangle as a tool for simple combination poblems
Secondary Finals Algebra and Geometry Topology and Graph Theory From given information about its faces, edges and vertices, recognise if a solid exists
Secondary Finals Algebra and Geometry Vectors Describe movement around a shape using given vectors
Secondary Finals Calculus Differentiation
Secondary Finals Calculus Integration
Secondary Finals Calculus Kinematics
Secondary Finals Calculus Limits and differential equations
Secondary Finals Experimental Sciences Probability, random variables and distributions Interpret experimental probabilities of independent events in context
Secondary Finals Experimental Sciences Location and dispersion Generate and interpret the arithmetic mean, median and modal values from grouped frequency tables
Secondary Finals Experimental Sciences Set theory Identify regions within Venn diagrams using conventianal notation and vice versa
Secondary Finals Experimental Sciences Regression Draw and use a line of best fit by hand, passing through the mean value
Secondary Finals Experimental Sciences Representing data, tests and correlation Distinguish between bar and pie charts and interpret in context
Secondary Finals Foundational Language Axioms and logic Appreciate and recognise Euclid's postulates
Secondary Finals Foundational Language Proof Create simple geometric proofs involving parallel lines
Secondary Finals Foundational Language Recreational
Junior Qualifier Arithmetic Time
Junior Qualifier Arithmetic Measures Convert across common imperial and metric quantities
Junior Qualifier Arithmetic Operations Use the factorial operation
Junior Qualifier Arithmetic Oder of operations Perform correct order of operation processes involving trigonometric ratios
Junior Qualifier Arithmetic Divisibility
Junior Qualifier Arithmetic Quotients Express any quotient in terms of the sum of unit fractions
Junior Qualifier Arithmetic Rationality Interpret solutions involving any real-numbers in context
Junior Qualifier Arithmetic Notation
Junior Qualifier Arithmetic Exponents Manipulate numbers expressed in any form and within any common base
Junior Qualifier Arithmetic Finance Compare results using simple and compund interest
Junior Qualifier Arithmetic Error Analyse innaccuracies of compounding rounded values
Junior Qualifier Arithmetic Ratio and proportion
Junior Qualifier Arithmetic Sequences and series Use conventional notation for geometic sequences and find simple series in context
Junior Qualifier Arithmetic Binomial expressions Use the binomial expansion with integer values
Junior Qualifier Arithmetic Complex numbers
Junior Qualifier Arithmetic Cryptography Solve simple messages coded as Permutation and Extended Polybius Square ciphers
Junior Qualifier Arithmetic Matrices Use matrices to visualise and draw transformed images of shapes on a cartesian grid
Junior Qualifier Algebra and Geometry Coordinates
Junior Qualifier Algebra and Geometry Direction
Junior Qualifier Algebra and Geometry Mappings and equations Solve a small system of equations in context and graph their relationship
Junior Qualifier Algebra and Geometry Graphs Use convential notation to describe and draw linear inequalities
Junior Qualifier Algebra and Geometry Triangles Understand and use the side, angle and area relationships within any cartesian triangle
Junior Qualifier Algebra and Geometry Polygons and polyhedra
Junior Qualifier Algebra and Geometry Perimeter and Area Calculate and use proportons of the perimeter and area of circles
Junior Qualifier Algebra and Geometry Surface area and volume Identify the net for any pyramid and calculate associated surface areas and volumes
Junior Qualifier Algebra and Geometry Factorising Appreciate the graphical representations of the 'difference of 2 squares' identity
Junior Qualifier Algebra and Geometry Polynomials Relate a quadratic equation to its parabola
Junior Qualifier Algebra and Geometry Exponentials and logarithmic Use and solve exponential and logarithmic equations considering their graphs
Junior Qualifier Algebra and Geometry Trigonometry Recognise common ratios between the sides of and angles within a right-angled triangle
Junior Qualifier Algebra and Geometry Rates of change Use the language of constant, increasing or decresing for the visual rate of change of a graph
Junior Qualifier Algebra and Geometry Theorems identify and use the circle theorems in solving problems
Junior Qualifier Algebra and Geometry Transformations Perform stretch and sheer transformations on 2D shapes
Junior Qualifier Algebra and Geometry Tesselations Recognise Hirschhorn, Periodic and Aperiodic tilings
Junior Qualifier Algebra and Geometry Combinatorics Calculate simple binomial problems involving combinations
Junior Qualifier Algebra and Geometry Topology and Graph Theory Recognise the geometric properties of the mobius strip
Junior Qualifier Algebra and Geometry Vectors Use the magnitude of vectors in geometric problems
Junior Qualifier Calculus Differentiation Recognise and distinguish between graphs of functions and of their slope functions
Junior Qualifier Calculus Integration
Junior Qualifier Calculus Kinematics Use scalar equivalents of displacement, velocity and acceleration vectors with time
Junior Qualifier Calculus Limits and differential equations Identify the equations of assymptotes on graphs
Junior Qualifier Experimental Sciences Probability, random variables and distributions Know and use the rules for union, intersection, complement, independence and mutually exclusive as tools within calculations
Junior Qualifier Experimental Sciences Location and dispersion Make comparisions between data sets using cumulative frequency
Junior Qualifier Experimental Sciences Set theory Use Venn Diagrams to solve problems involving 3 variables
Junior Qualifier Experimental Sciences Regression Calculate simple least squares linear regression by hand
Junior Qualifier Experimental Sciences Representing data, tests and correlation Use and graphically represent discrete vs continuous data appropriately
Junior Qualifier Foundational Language Axioms and logic Use truth tables to solve simple problems
Junior Qualifier Foundational Language Proof Appreciate and follow the logic required in creating direct mathematical proofs, and proof by contradiction
Junior Qualifier Foundational Language Recreational
Junior Finals Arithmetic Time
Junior Finals Arithmetic Measures
Junior Finals Arithmetic Operations
Junior Finals Arithmetic Oder of operations Perform binary operations on algebraic values
Junior Finals Arithmetic Divisibility Solve simple linear concruence problems
Junior Finals Arithmetic Quotients
Junior Finals Arithmetic Rationality
Junior Finals Arithmetic Notation
Junior Finals Arithmetic Exponents Solve simple modular arithmetic problems
Junior Finals Arithmetic Finance Create and interpret simple accounting documentation
Junior Finals Arithmetic Error
Junior Finals Arithmetic Ratio and proportion
Junior Finals Arithmetic Sequences and series Distinguish between infinite, iterative and recurrence relation sequences
Junior Finals Arithmetic Binomial expressions Use the binomial expansion with simple rational values
Junior Finals Arithmetic Complex numbers Recognise the existence of non-real solutions to mathematical problems
Junior Finals Arithmetic Cryptography Solve simple messages coded as Affine or Mixed Alphabet ciphers
Junior Finals Arithmetic Matrices Use inverse 2 by 2 matrices to help transform (large) data sets in solving real-life problems
Junior Finals Algebra and Geometry Coordinates Convert between cartesian and simple polar coordinates
Junior Finals Algebra and Geometry Direction Calculate and use amounts of turn in radians
Junior Finals Algebra and Geometry Mappings and equations Manipulate quadratic, simple cubic and rational expressions and graph their relationship
Junior Finals Algebra and Geometry Graphs Use convential notation to describe odd or even functions and key parts of graphs
Junior Finals Algebra and Geometry Triangles Calculate the area of any triangle
Junior Finals Algebra and Geometry Polygons and polyhedra Identify and use bipyramids and uniform stars
Junior Finals Algebra and Geometry Perimeter and Area
Junior Finals Algebra and Geometry Surface area and volume Calculate surface areas and volumes of truncated objects
Junior Finals Algebra and Geometry Factorising Know and use the Factor and Remainder Theorems as tools to help solve problems
Junior Finals Algebra and Geometry Polynomials Solve simple linear diophantine equtions
Junior Finals Algebra and Geometry Exponentials and logarithmic Use exponential and/or logarithmic functions to linearize graphs of variable relationships
Junior Finals Algebra and Geometry Trigonometry Understand and graph the ratios for more than a full turn
Junior Finals Algebra and Geometry Rates of change Distinguish between increasing and decreasing slope and concavity of graphs in context
Junior Finals Algebra and Geometry Theorems Know and use Pick's Theorem as a tool within calculations
Junior Finals Algebra and Geometry Transformations Rotate a 2D shape by any angle amount of turn
Junior Finals Algebra and Geometry Tesselations Create simple Voronoi tilings using midpoints
Junior Finals Algebra and Geometry Combinatorics Distinguish between and calculate simple problems involving permutations
Junior Finals Algebra and Geometry Topology and Graph Theory Recognise the geometric properties of the Torus and Klein bottle are different in cartesian and spherical geometry
Junior Finals Algebra and Geometry Vectors Represent a scalar product geometrically and use it in calculating intersections and angles of lines and planes
Junior Finals Calculus Differentiation Know and use the chain, product and quotient rules as tools on simple functions in context
Junior Finals Calculus Integration Calculate areas between graphs and axes, and volumes of revolution where common shapes and objects are generated
Junior Finals Calculus Kinematics Understand and calculate the linear movement of a particle
Junior Finals Calculus Limits and differential equations Identify vertical and horizontal asymptotes by taking limits of functions
Junior Finals Experimental Sciences Probability, random variables and distributions Know and use Bayes' Theorem as a tool within calculations. Use and interpret binomial probability distributions in context
Junior Finals Experimental Sciences Location and dispersion Generate and interpret the geometric mean from a dataset
Junior Finals Experimental Sciences Set theory
Junior Finals Experimental Sciences Regression Calculate function regressions using technology
Junior Finals Experimental Sciences Representing 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
Junior Finals Foundational Language Axioms and logic Identify when a statement is logical or not (ie tautology)
Junior Finals Foundational Language Proof Appreciate and follow the logic required in creating constructive mathematical proofs and Fermat's infinite descent
Junior Finals Foundational Language Recreational Appreciate the patterns created from shuffling small packs of cards
Senior Qualifier Arithmetic Time
Senior Qualifier Arithmetic Measures
Senior Qualifier Arithmetic Operations
Senior Qualifier Arithmetic Oder of operations
Senior Qualifier Arithmetic Divisibility Identify divisibilities of a number written in any base
Senior Qualifier Arithmetic Quotients Understand the use for and manipulate partial fraction expressions
Senior Qualifier Arithmetic Rationality Solve linear diophantine equtions
Senior Qualifier Arithmetic Notation
Senior Qualifier Arithmetic Exponents Use modular arithmetic and linear congruences to solve number problems
Senior Qualifier Arithmetic Finance Solve problems involving amortization and annuity
Senior Qualifier Arithmetic Error
Senior Qualifier Arithmetic Ratio and proportion
Senior Qualifier Arithmetic Sequences and series Distinguish between recursive and telescoping sequences and use conventianal notation to sum their series where possible, in context
Senior Qualifier Arithmetic Binomial expressions Use the binomial expansion with any exponent
Senior Qualifier Arithmetic Complex numbers Use DeMoivre's Theorem as a tool within calculations
Senior Qualifier Arithmetic Cryptography Solve simple messages coded as Transposition or Rail-Fence ciphers
Senior Qualifier Arithmetic Matrices Find the steady state of a real-life Markov Chain system
Senior Qualifier Algebra and Geometry Coordinates Understand when polar coordinates are easier/more efficient than cartesian, and use them in simple contexts
Senior Qualifier Algebra and Geometry Direction
Senior Qualifier Algebra and Geometry Mappings and equations
Senior Qualifier Algebra and Geometry Graphs Use convential notation to describe piecewise functions and discuss continuity across the domain
Senior Qualifier Algebra and Geometry Triangles Use Heron's Formula as a tool within calculations
Senior Qualifier Algebra and Geometry Polygons and polyhedra Use of Euler's characteristic and duality within simple contexts
Senior Qualifier Algebra and Geometry Perimeter and Area
Senior Qualifier Algebra and Geometry Surface area and volume Calculate surface area and volumes of objects described using vectors
Senior Qualifier Algebra and Geometry Factorising Know and use Descartes Rule of Signs as a tool within calculations
Senior Qualifier Algebra and Geometry Polynomials Use the rational root and sum or product of zeros tools when manipulating polynomials
Senior Qualifier Algebra and Geometry Exponentials and logarithmic Use and solve logistical equations and their graphs
Senior Qualifier Algebra and Geometry Trigonometry Use the compound angle identities as tools
Senior Qualifier Algebra and Geometry Rates of change Recognise and distinguish between the graphs of functions, their first and second differential graphs
Senior Qualifier Algebra and Geometry Theorems Use Ceva's and Menelaus' Theorems as tools within calculations
Senior Qualifier Algebra and Geometry Transformations Perform simple transformations within 3D space
Senior Qualifier Algebra and Geometry Tesselations
Senior Qualifier Algebra and Geometry Combinatorics Calculate problems involving combinations and permutations
Senior Qualifier Algebra and Geometry Topology and Graph Theory Recognise Eulerian and Hamiltonian paths and circuits in context
Senior Qualifier Algebra and Geometry Vectors Represent a vector product geometrically and use it in calculating intersections and angles of lines and planes
Senior Qualifier Calculus Differentiation Find minimum or maximum optimsed solutions in a real-life problem
Senior Qualifier Calculus Integration Know and use the inverse chain and product rules and substitution as tools to integrate simple functions in context
Senior Qualifier Calculus Kinematics Use and convert between displacement, velocity and acceleration functions in context
Senior Qualifier Calculus Limits and differential equations Calculate limits to any point, and infinity, of rational functions
Senior Qualifier Experimental Sciences Probability, random variables and distributions Use and interpret poisson and normal probability distributions in context
Senior Qualifier Experimental Sciences Location and dispersion Know and use the rules for standard deviation and variance as tools within calculations
Senior Qualifier Experimental Sciences Set theory
Senior Qualifier Experimental Sciences Regression
Senior Qualifier Experimental Sciences Representing data, tests and correlation Use and interpret the correlation coefficient and also coefficient of determination in context when analysing data
Senior Qualifier Foundational Language Axioms and logic Use Venn diagrams to solve Boolean algebra logic problems
Senior Qualifier Foundational Language Proof Follow the logic required in creating nonconstructive mathematical proofs and applications in Graph Theory
Senior Qualifier Foundational Language Recreational
Senior Finals Arithmetic Time
Senior Finals Arithmetic Measures
Senior Finals Arithmetic Operations
Senior Finals Arithmetic Oder of operations
Senior Finals Arithmetic Divisibility Use Fermat's Little Theorem
Senior Finals Arithmetic Quotients
Senior Finals Arithmetic Rationality Use the Ramanujan-Nagell exponential diophantine equation and Pell's equation in context
Senior Finals Arithmetic Notation
Senior Finals Arithmetic Exponents
Senior Finals Arithmetic Finance
Senior Finals Arithmetic Error
Senior Finals Arithmetic Ratio and proportion
Senior Finals Arithmetic Sequences and series Find the nth term rule for recurrence relations
Senior Finals Arithmetic Binomial expressions
Senior Finals Arithmetic Complex numbers
Senior Finals Arithmetic Cryptography Solve simple messages coded as Hill or Columnar Route ciphers
Senior Finals Arithmetic Matrices Use eigenvalues and eigenvectors as tools within simple calculations
Senior Finals Algebra and Geometry Coordinates Use polar coordinates in context
Senior Finals Algebra and Geometry Direction
Senior Finals Algebra and Geometry Mappings and equations Use parametric equations as a tool within calculations
Senior Finals Algebra and Geometry Graphs Know and use the relations that create circles and ellipses
Senior Finals Algebra and Geometry Triangles
Senior Finals Algebra and Geometry Polygons and polyhedra
Senior Finals Algebra and Geometry Perimeter and Area
Senior Finals Algebra and Geometry Surface area and volume
Senior Finals Algebra and Geometry Factorising Use completing the rectangle as a tool within calculations
Senior Finals Algebra and Geometry Polynomials
Senior Finals Algebra and Geometry Exponentials and logarithmic
Senior Finals Algebra and Geometry Trigonometry Use the arctrigonometric identities as tools
Senior Finals Algebra and Geometry Rates of change
Senior Finals Algebra and Geometry Theorems Know and use Carnot's Theorem as a tool within calculations
Senior Finals Algebra and Geometry Transformations
Senior Finals Algebra and Geometry Tesselations
Senior Finals Algebra and Geometry Combinatorics
Senior Finals Algebra and Geometry Topology and Graph Theory
Senior Finals Algebra and Geometry Vectors
Senior Finals Calculus Differentiation Use implicit differentiation and related rates of change as tools on functions in context
Senior Finals Calculus Integration Know and use integration by parts and partial fractions as tools within calculations
Senior Finals Calculus Kinematics
Senior Finals Calculus Limits and differential equations Use Eulers Method and slope fields as tools in simple contexts
Senior Finals Experimental Sciences Probability, random variables and distributions Use and interpret Expectation and Variance of combined independent events in context
Senior Finals Experimental Sciences Location and dispersion
Senior Finals Experimental Sciences Set theory
Senior Finals Experimental Sciences Regression
Senior Finals Experimental Sciences Representing data, tests and correlation Use statistical hypothesis testing with real-life datasets
Senior Finals Foundational Language Axioms and logic Use digital logic gates to solve Boolean algebra problems
Senior Finals Foundational Language Proof Think through a larger logic problem and create tests for efficiency and optimization
Senior Finals Foundational Language Recreational

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