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 |