The learning content of the OMC is organised into 6 themes across the Primary, Secondary, Junior and Senior levels:
*Note: Descriptors for the 'History' theme are comprised of 3 mathematicians. Every question in this theme will be about 1 of the 3 mathematicians in each descriptor.
All descriptors may be viewed in the table below, additionally with filters by theme and level:
| Theme | Level | Essential Understanding | Descriptor |
|---|---|---|---|
| Arithmetic | Primary | Complex numbers | Distinguish between the different possible types of numbers |
| Arithmetic | Primary | Divisibility | Identify the divisibility by 10 and 5 of any number |
| Arithmetic | Primary | Divisibility | Identify common factors within sets of numbers |
| Arithmetic | Primary | Divisibility | Use the LCM or GCF of 2 or more numbers to solve problems |
| Arithmetic | Primary | Error | Give measured values to the correct level of rounding |
| Arithmetic | Primary | Exponents | Express values in exponent form |
| Arithmetic | Primary | Exponents | Articulate place value of number digits within words |
| Arithmetic | Primary | Finance | Appreciate and recognise 'value for money' involving decimals and percentages |
| Arithmetic | Primary | Measures | Simplify quantities within imperial units of measurements |
| Arithmetic | Primary | Measures | Convert across time zones as well as between 12 and 24 hour formats |
| Arithmetic | Primary | Measures | Convert across different metric units of measurement |
| Arithmetic | Primary | Operations | Understand how multiplication is short-hand for repeated addition and use it accordingly |
| Arithmetic | Primary | Quotients | Calculate quotients of values and interpret possible remainders |
| Arithmetic | Primary | Ratio and Proportion | Calculate any percentage of an amount |
| Arithmetic | Primary | Ratio and Proportion | Use direct proportion as a constant rate of change to find different quantities |
| Arithmetic | Primary | Sequence and series | Find the value of the next term in a number pattern |
| Arithmetic | Secondary | Combinatorics | Recognise the pattern of Pascal's triangle as a tool for simple combination problems |
| Arithmetic | Secondary | Divisibility | Identify divisibilities by single-digit numbers |
| Arithmetic | Secondary | Divisibility | Use the LCM or GCF of 3 or more numbers to solve problems |
| Arithmetic | Secondary | Error | Write answers to appropriate decimal places or significant figures |
| Arithmetic | Secondary | Error | Identify the magnitude of a rounding error |
| Arithmetic | Secondary | Exponents | Solve simple exponential equations with a common base |
| Arithmetic | Secondary | Exponents | Understand appropriate representations for very small and very large numbers |
| Arithmetic | Secondary | Finance | Identify the difference that results from simple and compound interest |
| Arithmetic | Secondary | Finance | Identify the best valued product from 5 different shops |
| Arithmetic | Secondary | Measures | Given an approximate ratio, convert between metric and imperial units of measurement |
| Arithmetic | Secondary | Measures | Know and use units for expressing a measured quantity in standard index notation |
| Arithmetic | Secondary | Measures | Count ages to the nearest year and month |
| 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 |
| Arithmetic | Secondary | Quotients | Express any quotient in terms of the sum of unit fractions |
| Arithmetic | Secondary | Sequence and series | Find the value of a term in an arithmetic sequence |
| Arithmetic | Junior | Binomial expressions | Recognise binomial expansions to make number calculations more efficient |
| Arithmetic | Junior | Combinatorics | Calculate simple binomial problems involving combinations |
| Arithmetic | Junior | Divisibility | Identify divisibilities of a number written in any base |
| Arithmetic | Junior | Divisibility | Solve simple modular arithmetic problems |
| Arithmetic | Junior | Error | Calculate the inaccuracy between exact and rounded measurement values |
| Arithmetic | Junior | Exponents | Convert numbers between their binary and decimal forms |
| Arithmetic | Junior | Exponents | Calculate number sums involving roots and exponents |
| Arithmetic | Junior | Finance | Create and interpret simple accounting documentation |
| Arithmetic | Junior | Matrices | Use inverse 2 by 2 matrices to help transform data sets in solving problems |
| Arithmetic | Junior | Measures | Convert across different imperial units of measurement |
| Arithmetic | Junior | Operations | Calculate number sums involving the factorial operation |
| Arithmetic | Junior | Operations | Use BODMAS/BIDMAS/PEDMAS correctly on number values |
| Arithmetic | Junior | Operations | Calculate number sums involving trigonometric ratios |
| Arithmetic | Junior | Quotients | Manipulate any quotient raised to any exponent |
| Arithmetic | Junior | Ratio and Proportion | Use direct and indirect proportion as a constant rate of change for different quantities |
| Arithmetic | Junior | Sequence and series | Find the value of a term in a geometric sequence |
| Arithmetic | Senior | Binomial expressions | Use the binomial expansion to find the coefficient of a term |
| Arithmetic | Senior | Combinatorics | Distinguish between and calculate simple problems involving permutations |
| Arithmetic | Senior | Complex numbers | Use DeMoivre's Theorem as a tool within calculations |
| Arithmetic | Senior | Divisibility | Identify the divisibility of 3- and 4-digit numbers |
| Arithmetic | Senior | Divisibility | Identify values or quantity of digits within large numbers |
| Arithmetic | Senior | Divisibility | Use Fermat's Little Theorem |
| Arithmetic | Senior | Error | Calculate the possible inaccuracy from rounded measurement values |
| Arithmetic | Senior | Exponents | Use modular arithmetic and linear congruences to solve number problems |
| Arithmetic | Senior | Exponents | Manipulate numbers expressed in any form and within any common base |
| Arithmetic | Senior | Finance | Solve problems involving annuity |
| Arithmetic | Senior | Finance | Solve problems involving amortization |
| Arithmetic | Senior | Matrices | Use inverse 3 by 3 matrices to help transform data sets in solving problems |
| Arithmetic | Senior | Operations | Calculate number sums involving exponents and logarithms |
| Arithmetic | Senior | Rationality | Solve linear diophantine equations |
| Arithmetic | Senior | Rationality | Use difference equations to solve problems in context |
| Arithmetic | Senior | Sequence and series | Find values within geometric and arithmetic sequences and series |
| Calculus | Junior | Rate of change | Distinguish between increasing and decreasing slope of graphs |
| Calculus | Junior | Rate of change | Use concavity of graphs to identify local behaviour |
| Calculus | Junior | Rate of change | Use average rate of change in context |
| Calculus | Junior | Rate of change | Use instantaneous rate of change in context |
| Calculus | Junior | Differentiation | Know and use the chain rule as a tool on simple functions |
| Calculus | Junior | Differentiation | Know and use the product rule as a tool on simple functions |
| Calculus | Junior | Differentiation | Know and use the quotient rule as a tool on simple functions in context |
| Calculus | Junior | Differentiation | Find minimums for optimised solutions |
| Calculus | Junior | Differentiation | Find maximums for optimised solutions |
| Calculus | Junior | Differentiation | Find inflections for optimised solutions |
| Calculus | Junior | Integration | Calculate areas between graphs, vertical bounds and horizontal axes |
| 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 | Kinematics | Use scalar equivalents of displacement and velocity vectors with time |
| Calculus | Junior | Kinematics | Use scalar equivalents of velocity and acceleration vectors with time |
| Calculus | Junior | Kinematics | Understand and calculate the linear movement of a particle |
| Calculus | Senior | Differentiation | Know and use the chain rule as a tool to differentiate a function |
| Calculus | Senior | Differentiation | Know and use the product and quotient rules as a tool to differentiate a function |
| Calculus | Senior | Differentiation | Use the Taylor Series to approximate a function at a given point |
| Calculus | Senior | Differentiation | Use implicit differentiation as a tool in related rates of change problems |
| Calculus | Senior | Differentiation | Use more than one tool to differentiate a function |
| Calculus | Senior | Integration | Know and use partial fractions as a tool to integrate a function |
| Calculus | Senior | Integration | Know and use integration by parts as a tool to integrate a function |
| Calculus | Senior | Integration | Know and use substitution as a tool to integrate a function |
| Calculus | Senior | Kinematics | Use and convert between displacement and acceleration functions that represent the motion of a particle |
| Calculus | Senior | Kinematics | Use and convert between velocity and acceleration functions that represent the motion of a particle |
| Calculus | Senior | Kinematics | Use and convert between displacement and velocity functions that represent the motion of a particle |
| Calculus | Senior | Limits | Use L'Hopitals rule to calculate limits to any point |
| Calculus | Senior | Limits | Use L'Hopitals rule to calculate limits to infinity |
| 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 |
| Pure Algebra | Primary | Expressions | Identify the highest common factor within the terms of an expression |
| Pure Algebra | Primary | Expressions | Identify the lowest common multiple of the terms within an expression |
| Pure Algebra | Primary | Expressions | Substitute into an expression |
| Pure Algebra | Primary | Expressions | Simplify expressions involving exponents |
| Pure Algebra | Primary | Expressions | Solve a multi-step linear equation with integer coefficients |
| Pure Algebra | Primary | Expressions | Combine simple algebraic fractions |
| Pure Algebra | Primary | Inequalities | Solve a simple linear inequality |
| Pure Algebra | Primary | Polynomials | Form linear equations from real-life situations |
| Pure Algebra | Primary | Polynomials | Represent and use a simple linear function algebraically |
| Pure Algebra | Primary | Polynomials | Identify the degree of a single variable polynomial |
| Pure Algebra | Primary | Polynomials | Solve simple square and cube root equations |
| Pure Algebra | Primary | Polynomials | Solve binomial quadratic equations |
| Pure Algebra | Primary | Polynomials | Solve binomial cubic equations |
| Pure Algebra | Primary | Recreational | Identify and complete simple magic squares |
| Pure Algebra | Primary | Recreational | Identify and complete logic puzzles involving objects |
| Pure Algebra | Primary | Sequences and Series | Give the nth term rule for shifted times table number patterns |
| Pure Algebra | Secondary | Expressions | Manipulate expressions involving parenthesis |
| Pure Algebra | Secondary | Expressions | Simplify an algebraic expression |
| Pure Algebra | Secondary | Expressions | Simplify an algebraic radical expression |
| Pure Algebra | Secondary | Expressions | Solve multi-step linear equations |
| Pure Algebra | Secondary | Expressions | Combine algebraic fractions into one expression |
| Pure Algebra | Secondary | Factorising | Fully factorise any algebraic expression |
| Pure Algebra | Secondary | Factorising | Factorise to solve a quadratic equation |
| Pure Algebra | Secondary | Inequalities | Solve a simple inequality |
| Pure Algebra | Secondary | Order of operations | Solve multi-step polynomial equations |
| Pure Algebra | Secondary | Order of operations | Perform binary operations on multi-variable algebraic expressions |
| Pure Algebra | Secondary | Order of operations | Change the subject of an equation, involving parentheses and indices |
| Pure Algebra | Secondary | Polynomials | Simplify a polynomial expression |
| Pure Algebra | Secondary | Polynomials | Identify the degree of a multi-variable polynomial |
| Pure Algebra | Secondary | Polynomials | Solve a system of linear equations |
| Pure Algebra | Secondary | Recreational | Identify and complete magic squares |
| Pure Algebra | Secondary | Sequences and Series | Find the nth term rule for simple polynomial sequences |
| Pure Algebra | Junior | Binomial expansion | Use the binomial expansion with integer values |
| Pure Algebra | Junior | Factorising | Use the Factor Theorem to factorise polynomials |
| Pure Algebra | Junior | Factorising | Use the Remainder Theorem to find coefficients of a term within polynomials |
| Pure Algebra | Junior | Order of operations | Manipulate algebra involving roots and exponents |
| Pure Algebra | Junior | Order of operations | Perform binary operations on algebraic values |
| Pure Algebra | Junior | Polynomials | Recognise the existence of solutions to linear Diophantine equations |
| Pure Algebra | Junior | Polynomials | Use BODMAS/BIDMAS/PEDMAS correctly on algebraic expressions |
| Pure Algebra | Junior | Polynomials | Use of two distinct real root 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 | Polynomials | Solve a system of equations algebraically |
| Pure Algebra | Junior | Quotients | Manipulate any algebraic quotient raised to any exponent |
| Pure Algebra | Junior | Sequences and Series | Find the nth term rule for common non-linear sequences |
| 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 | Senior | Binomial expansion | Use the binomial expansion to find algebraic coefficients of terms |
| Pure Algebra | Senior | Complex numbers | Recognise the existence of non-real solutions to some polynomial equations |
| Pure Algebra | Senior | Complex numbers | Use Euler's formula to express position in different forms |
| Pure Algebra | Senior | Factorising | Use the Factor Theorem with polynomial functions |
| Pure Algebra | Senior | Factorising | Use the Remainder Theorem with polynomial functions |
| Pure Algebra | Senior | Order of operations | Use matrices to solve a system of linear equations |
| Pure Algebra | Senior | Order of operations | Solve an equation involving exponent, logarithm and trigonometric functions |
| Pure Algebra | Senior | Polynomials | Use linear diophantine equations to find the quantity of possible solutions to a problem |
| Pure Algebra | Senior | Polynomials | Solve quadratic functions with complex roots |
| Pure Algebra | Senior | Polynomials | Use Vieta's Formula to help identify roots within polynomials |
| Pure Algebra | Senior | Quotients | Express an algebraic fraction into equivalent partial fractions |
| Pure Algebra | Senior | Sequences and Series | Find the nth term rule for recurrence relations |
| Pure Algebra | Senior | Sequences and Series | Distinguish between infinite, iterative and recurrence relation sequences |
| Pure Algebra | Senior | Trigonometry | Identify all possible solutions to sine ratio equations within a given domain |
| Pure Algebra | Senior | Trigonometry | Identify all possible solutions to cosine ratio equations within a given domain |
| Pure Algebra | Senior | Trigonometry | Identify all possible solutions to tangent ratio equations within a given domain |
| Geometry & Algebra | Primary | Area and Surface Area | Recognise the differences between Euclidean and non-Euclidean geometry |
| Geometry & Algebra | Primary | Area and Surface Area | Find the area of a segment of a circle |
| Geometry & Algebra | Primary | Area and Surface Area | Find the area of any shape, using trigonometry to calculate angles where required |
| Geometry & Algebra | Primary | Nets and Volume | Find the volume of shapes described in terms of equations through integration |
| Geometry & Algebra | Primary | Polygons and Polyhedra | Find the SA of composite solid shapes |
| Geometry & Algebra | Primary | Polygons and Polyhedra | Identify and use bipyramids and uniform stars |
| Geometry & Algebra | Primary | Polygons and Polyhedra | Recognise Archimedean solids, duals and Kepler-Poinsot polyhedra |
| Geometry & Algebra | Primary | Polygons and Polyhedra | Use of Euler's characteristic and duality within simple contexts |
| Geometry & Algebra | Primary | Directions and Angles | Use the arctrigonometric identities as a tool to solve problems |
| Geometry & Algebra | Primary | Directions and Angles | Use the compound angle identities as a tool to solve problems |
| Geometry & Algebra | Primary | Directions and Angles | Know and use Menelaus' Theorem as a tool to solve problems |
| Geometry & Algebra | Primary | Tessellations | Navigate a board based on a hexagonal coordinate grid |
| Geometry & Algebra | Primary | Graph Theory | Recognise Hamiltonian cycles and circuits in context |
| Geometry & Algebra | Primary | Graph Theory | Use Kuratowski's and Wagner's theorems to identify planar graphs in context |
| Geometry & Algebra | Primary | Vectors | Represent a vector product geometrically and use it in calculating areas of plane segments |
| Geometry & Algebra | Primary | Transformations | Use shear and dilation transformations to manipulate shapes |
| Geometry & Algebra | Secondary | Area and Surface Area | Use length and area factors with mathematically similar shapes |
| Geometry & Algebra | Secondary | Area and Surface Area | Use the area and perimeter of a sector of a circle |
| Geometry & Algebra | Secondary | Area and Surface Area | Find the area of any triangle, maybe using Heron's Formula |
| Geometry & Algebra | Secondary | Nets and Volume | Find the volume of solid shapes with curved surfaces |
| Geometry & Algebra | Secondary | Nets and Volume | Use length, area and volume factors with mathematically similar solid shapes |
| Geometry & Algebra | Secondary | Polygons and Polyhedra | Find the SA of common solid shapes |
| Geometry & Algebra | Secondary | Polygons and Polyhedra | Use Euler's polyhedral formula with archimedean solids |
| Geometry & Algebra | Secondary | Directions and Angles | Recognise common ratios between the sides and angles of a right-angled triangle and their trigonometric equivalents |
| Geometry & Algebra | Secondary | Directions and Angles | Calculate and use amounts of turn in radians |
| Geometry & Algebra | Secondary | Directions and Angles | Know and use Ceva's Theorem as a tool to solve problems |
| Geometry & Algebra | Secondary | Directions and Angles | Use the circle theorems to solve problems |
| Geometry & Algebra | Secondary | Tessellations | Identify Hirschhorn, Periodic and Aperiodic tilings |
| Geometry & Algebra | Secondary | Graph Theory | Recognise Eulerian cycles and circuits in context |
| Geometry & Algebra | Secondary | Graph Theory | Use the handshaking lemma and Euler's Theorem in graph theory |
| Geometry & Algebra | Secondary | Vectors | Represent a scalar product geometrically and use it in calculating intersections and angles of lines |
| Geometry & Algebra | Secondary | Transformations | Use quarter turn rotations to manipulate shapes |
| Geometry & Algebra | Junior | Area and Surface Area | Calculate the lengths of mathematically similar shapes |
| Geometry & Algebra | Junior | Area and Surface Area | Use the area and circumference of a circle |
| Geometry & Algebra | Junior | Area and Surface Area | Know and use Pick's Theorem as a tool within calculations |
| Geometry & Algebra | Junior | Nets and Volume | Find the volume of regular polyhedra |
| Geometry & Algebra | Junior | Polygons and Polyhedra | Find the SA of regular polyhedra |
| Geometry & Algebra | Junior | Polygons and Polyhedra | Calculate interior and exterior angles of regular polygons |
| Geometry & Algebra | Junior | Polygons and Polyhedra | Find the area of regular polygons |
| Geometry & Algebra | Junior | Polygons and Polyhedra | Classify quadrilaterals by using interior and exterior angles |
| Geometry & Algebra | Junior | Polygons and Polyhedra | Use Euler's polyhedral formula with the platonic solids |
| Geometry & Algebra | Junior | Directions and Angles | Understand a proof for the sum of angles in a triangle |
| Geometry & Algebra | Junior | Directions and Angles | Use an 8-point compass rose to describe the direction between two objects |
| Geometry & Algebra | Junior | Directions and Angles | Use three-figure bearings to describe the direction between two objects |
| Geometry & Algebra | Junior | Directions and Angles | Understand the relationships of angles formed by a transversal over a pair of parallel lines |
| Geometry & Algebra | Junior | Directions and Angles | Identify the loci of a situation given conditions |
| Geometry & Algebra | Junior | Tessellations | Identify tilings that create monohedral tilings |
| Geometry & Algebra | Junior | Transformations | Use reflections and enlargements along an axis to manipulate shapes |
| Geometry & Algebra | Senior | Area and Surface Area | Find the area of right-angled shapes |
| Geometry & Algebra | Senior | Area and Surface Area | Identify the parts of a circle |
| Geometry & Algebra | Senior | Area and Surface Area | Estimate area by counting the enclosed quantity of squares |
| Geometry & Algebra | Senior | Nets and Volume | Find the volume of right-angled polyhedra |
| Geometry & Algebra | Senior | Polygons and Polyhedra | Find the SA of right-angled polyhedra |
| Geometry & Algebra | Senior | Polygons and Polyhedra | Distinguish triangles from the magnitude of their angles or lengths of sides |
| Geometry & Algebra | Senior | Polygons and Polyhedra | Find the perimeter of a regular polygon |
| Geometry & Algebra | Senior | Polygons and Polyhedra | Distinguish between regular polygons from the quantity and angles of their edges |
| Geometry & Algebra | Senior | Polygons and Polyhedra | Distinguish between regular polyhedra from the quantity and shape of their faces |
| Geometry & Algebra | Senior | Directions and Angles | Identify and name angles smaller or larger than multiples of quarter turns |
| Geometry & Algebra | Senior | Directions and Angles | Use a 4-point compass rose to provide directions |
| Geometry & Algebra | Senior | Directions and Angles | Estimate and describe amounts of turn in degrees |
| Geometry & Algebra | Senior | Directions and Angles | Recognise a fundamental axiom of geometry: Vertically opposite angles |
| Geometry & Algebra | Senior | Directions and Angles | Recognise a fundamental axiom of geometry: Corresponding angles |
| Geometry & Algebra | Senior | Tessellations | Navigate a board based on a regular tessellation |
| Geometry & Algebra | Senior | Transformations | Identify the order of rotational symmetry within a shape |
| Graphs & Algebra | Primary | Coordinates | Know and use cartesian coordinates in the first quadrant |
| Graphs & Algebra | Primary | Coordinates | Identify the midpoint of a line segment in the first quadrant |
| Graphs & Algebra | Primary | Coordinates | Use coordinates to calculate perimeter of a shape |
| Graphs & Algebra | Primary | Inequality | Use convential notation to draw a 1D inequality |
| Graphs & Algebra | Primary | Mappings | Identify a linear function from a mapping |
| Graphs & Algebra | Primary | Relations | Identify if a relation expressed graphically is a function or not |
| Graphs & Algebra | Primary | Functions | Identify the roots of a graph |
| Graphs & Algebra | Primary | Functions | Identify the degree of a polynomial function from its graph |
| Graphs & Algebra | Primary | Functions | Deduce a quadratic function in factorised form from a parabola graph |
| Graphs & Algebra | Primary | Functions | Identify the graphical representation of a times table |
| Graphs & Algebra | Primary | Rate of change | Identify where a graph is increasing, stationary and decreasing |
| Graphs & Algebra | Primary | Transformations | Recognise the graphical transformation of an addition outside the function |
| Graphs & Algebra | Primary | Transformations | Draw the image of a shape on a coordinate grid from a given translation vector |
| Graphs & Algebra | Primary | Systems | Solve a small system of linear equations graphically |
| Graphs & Algebra | Primary | Vectors | Describe movement around a polygon using given vectors |
| Graphs & Algebra | Primary | Vectors | Identify vector addition and multiplication by a scalar from a coordinate grid |
| Graphs & Algebra | Secondary | Coordinates | Know and use cartesian coordinates |
| Graphs & Algebra | Secondary | Coordinates | Identify the midpoint and slope of a line segment plotted on a set of axes |
| Graphs & Algebra | Secondary | Coordinates | Use coordinates to calculate the area of a shape |
| Graphs & Algebra | Secondary | Inequality | Use conventional notation to identify a 2D linear region on a graph |
| Graphs & Algebra | Secondary | Mappings | Describe linear relationships from a mapping diagram |
| Graphs & Algebra | Secondary | Relations | Identify if a relation expressed graphically is a function that has an inverse or not |
| Graphs & Algebra | Secondary | Functions | Use conventional notation to describe the key features of a graph |
| Graphs & Algebra | Secondary | Functions | Identify simple rational functions from their graphs |
| Graphs & Algebra | Secondary | Functions | Deduce a quadratic function in vertex form from a parabola graph |
| Graphs & Algebra | Secondary | Functions | Deduce a cubic function from a graph |
| Graphs & Algebra | Secondary | Exponential and Logarithmic | Use and solve exponential equations graphically |
| Graphs & Algebra | Secondary | Rate of change | Distinguish between the graph of a function and its slope/gradient graph |
| Graphs & Algebra | Secondary | Transformations | Recognise the graphical transformation of a function multiplication outside the function |
| Graphs & Algebra | Secondary | Transformations | Use reflections and enlargements along an axis to manipulate shapes on a coordinate grid |
| Graphs & Algebra | Secondary | Systems | Graphically solve a system of equations |
| Graphs & Algebra | Secondary | Vectors | Find the magnitude of a vector from its component form |
| Graphs & Algebra | Junior | Coordinates | Convert between cartesian and simple polar coordinates |
| Graphs & Algebra | Junior | Coordinates | Find the perpendicular bisector of a line segment |
| Graphs & Algebra | Junior | Coordinates | Use matrix multiplication to transform a shape on a coordinate grid |
| Graphs & Algebra | Junior | Inequality | Use conventional notation to solve linear inequalities graphically |
| Graphs & Algebra | Junior | Relations | Know and use the relations that create circles |
| Graphs & Algebra | Junior | Functions | Identify odd or even functions from a graph |
| Graphs & Algebra | Junior | Functions | Deduce a rational function from a graph |
| Graphs & Algebra | Junior | Functions | Deduce a quadratic function from a parabola graph |
| Graphs & Algebra | Junior | Exponential and Logarithmic | Use and solve logarithmic equations graphically |
| Graphs & Algebra | Junior | Exponential and Logarithmic | Linearize a graph using the variable relationships |
| Graphs & Algebra | Junior | Trigonometry | Identify the solutions to trigonometric graphs within one full turn |
| Graphs & Algebra | Junior | Rate of change | Identify where a graph is concaving up and concaving down |
| Graphs & Algebra | Junior | Transformations | Recognise the graphical transformation of an addition inside the function |
| Graphs & Algebra | Junior | Transformations | Use quarter turn rotations to manipulate shapes on a coordinate grid |
| Graphs & Algebra | Junior | Systems | Use Voronoi diagrams to solve problems |
| Graphs & Algebra | Junior | Vectors | Use the magnitude of vectors to calculate areas and volumes |
| Graphs & Algebra | Senior | Coordinates | Use polar coordinates to solve problems |
| Graphs & Algebra | Senior | Coordinates | Use numbers expressed in Euler's form to solve problems |
| Graphs & Algebra | Senior | Coordinates | Use matrix multiplication to transform a shape twice on a coordinate grid |
| Graphs & Algebra | Senior | Inequality | Use conventional notation to solve any inequality graphically |
| Graphs & Algebra | Senior | Relations | Know and use the relations that create ellipses |
| Graphs & Algebra | Senior | Functions | Use conventional notation to describe piecewise functions and identify continuity across the domain |
| Graphs & Algebra | Senior | Functions | Calculate limits to any point of rational functions |
| Graphs & Algebra | Senior | Functions | Identify oblique asymptotes by taking limits of functions |
| Graphs & Algebra | Senior | Exponential and Logarithmic | Use and solve logistical functions through their graphs |
| Graphs & Algebra | Senior | Trigonometry | Identify all possible solutions from trigonometric graphs for any domain |
| Graphs & Algebra | Senior | Rate of change | Distinguish between the graphs of functions, their first and second differential graphs |
| Graphs & Algebra | Senior | Transformations | Recognise the graphical transformation of a function multiplication inside the function |
| Graphs & Algebra | Senior | Transformations | Use shear and dilation transformations to manipulate shapes on a coordinate grid |
| Graphs & Algebra | Senior | Systems | Use eigenvalues and eigenvectors as tools with phase portraits |
| Graphs & Algebra | Senior | Vectors | Represent a vector product geometrically and use it in calculating intersections and angles of lines and planes |
| Graphs & Algebra | Senior | Vectors | Use vectors to find the surface areas of polyhedra |
| Experimental Sciences | Primary | Set Theory | Place objects or numbers into given overlapping groups |
| Experimental Sciences | Primary | Probability | Interpret theoretical probabilities of simple independent events, in context |
| Experimental Sciences | Primary | Probability | Recognise the difference between dependent and independent events, in context |
| Experimental Sciences | Primary | Combinatorics | Count how many possible outcomes there are in context |
| Experimental Sciences | Primary | Location and Dispersion | Calculate the mode from a list of quantative data |
| Experimental Sciences | Primary | Location and Dispersion | Calculate the median from a list of quantative data |
| Experimental Sciences | Primary | Location and Dispersion | Calculate the mean average from a list of quantative data |
| Experimental Sciences | Primary | Location and Dispersion | Calculate the range from a list of quantative data |
| Experimental Sciences | Primary | Location and Dispersion | Count 'how many so far' from a frequenct table |
| Experimental Sciences | Primary | Collecting Data | Distinguish good survey questions for a given context |
| Experimental Sciences | Primary | Representing Data | Distinguish between qualitative and quantative data |
| Experimental Sciences | Primary | Representing Data | Interpret pictogram representations in context |
| Experimental Sciences | Primary | Representing Data | Interpret bar chart representations in context |
| Experimental Sciences | Primary | Representing Data | read proportions from a pie chart and interpret in context |
| Experimental Sciences | Primary | Representing Data | Use and graphically represent discrete data appropriately |
| Experimental Sciences | Primary | Regression | Calculate linear regression using technology |
| Experimental Sciences | Secondary | Set Theory | Identify regions within 2-set Venn diagrams from conventional notation |
| Experimental Sciences | Secondary | Probability | Interpret theoretical probabilities of dependent events, in context |
| Experimental Sciences | Secondary | Probability | Interpret experimental probabilities of independent events in context |
| Experimental Sciences | Secondary | Combinatorics | Identify conditional quantities from a 2-way table |
| Experimental Sciences | Secondary | Location and Dispersion | Calculate the modal value from a frequency table |
| Experimental Sciences | Secondary | Location and Dispersion | Calculate the median value from a frequency table |
| Experimental Sciences | Secondary | Location and Dispersion | Calculate the arithmetic mean value from a frequency table |
| Experimental Sciences | Secondary | Location and Dispersion | Calculate the interquartile range from a simple list of quantative data |
| Experimental Sciences | Secondary | Location and Dispersion | Interpret box-and-whisker plots |
| Experimental Sciences | Secondary | Collecting Data | Create survey questions appropriate for a given context |
| Experimental Sciences | Secondary | Representing Data | Distinguish between continuous and discrete data sets |
| Experimental Sciences | Secondary | Representing Data | Use and graphically represent discrete data appropriately |
| Experimental Sciences | Secondary | Representing Data | Distinguish between bar charts and histograms and interpret in context |
| Experimental Sciences | Secondary | Representing Data | Understand pie chart proportions and interpret in context |
| Experimental Sciences | Secondary | Representing Data | Use and graphically represent continuous data appropriately |
| Experimental Sciences | Secondary | Regression | Calculate polynomial regressions using technology |
| Experimental Sciences | Junior | Set Theory | Identify regions within 3-set Venn diagrams from conventional notation |
| Experimental Sciences | Junior | Probability | Know and use conditional probability in context |
| Experimental Sciences | Junior | Probability | Calculate and interpret expectation or variance in context of a fairground game |
| Experimental Sciences | Junior | Combinatorics | Calculate probabilities involving combinations |
| Experimental Sciences | Junior | Location and Dispersion | Calculate the modal and median group from a grouped frequency table |
| Experimental Sciences | Junior | Location and Dispersion | Calculate and interpret the arithmetic mean from a dataset |
| Experimental Sciences | Junior | Location and Dispersion | Calculate the interquartile range from a cumulative frequency table or graph |
| Experimental Sciences | Junior | Location and Dispersion | Use and interpret standard deviation or variance |
| Experimental Sciences | Junior | Collecting Data | Explain the difference between different sampling techniques |
| Experimental Sciences | Junior | Representing Data | Interpret histogram representations in context |
| Experimental Sciences | Junior | Data tests and correlation | Use PPMCC for bivariate data sets |
| Experimental Sciences | Junior | Data tests and correlation | Use Chi-squared test for independence |
| Experimental Sciences | Junior | Regression | Understand when it is suitable to perform regression analysis |
| Experimental Sciences | Junior | Regression | Use and interpret the correlation coefficient in context when analysing data |
| Experimental Sciences | Junior | Random variables and distributions | Use and interpret a probability from a binomial distribution |
| Experimental Sciences | Junior | Random variables and distributions | Use and interpret a probability from a normal distribution |
| Experimental Sciences | Senior | Set Theory | Know and use the rules for union, intersection and complement as tools within probability |
| Experimental Sciences | Senior | Probability | Know and use Bayes' Theorem as a tool within calculations. |
| Experimental Sciences | Senior | Probability | Use and interpret expectation or variance of combined independent events |
| Experimental Sciences | Senior | Combinatorics | Calculate probabilities involving permutations |
| Experimental Sciences | Senior | Location and Dispersion | Calculate and interpret the geometric mean from a dataset |
| Experimental Sciences | Senior | Location and Dispersion | Make comparisons between data sets using cumulative frequency |
| Experimental Sciences | Senior | Location and Dispersion | Use and interpret transformations of standard deviation or variance |
| Experimental Sciences | Senior | Collecting Data | Understand the effect of sampling compared to population statistics |
| Experimental Sciences | Senior | Representing Data | Find the steady state of a real-life Markov Chain system |
| Experimental Sciences | Senior | Data tests and correlation | Use Spearman's rank correlation coefficient for bivariate data sets |
| Experimental Sciences | Senior | Data tests and correlation | Use Chi-squared goodness of fit test |
| Experimental Sciences | Senior | Data tests and correlation | Use a 1- or a 2-sample t-test in context |
| Experimental Sciences | Senior | Regression | Calculate function regressions using technology |
| Experimental Sciences | Senior | Regression | Use and interpret the coefficient of determination in context when analysing data |
| Experimental Sciences | Senior | Random variables and distributions | Use and interpret a probability from a poisson distribution |
| Experimental Sciences | Senior | Random variables and distributions | Use and interpret z-test for the mean of a normal probability distribution in context |
| History | Primary | -- | Caucher Birkar, Peter Scholze and Akshay Venkatesh |
| History | Primary | -- | Artur Avila, Martin Hairer and Maryam Mirzakhani |
| History | Primary | -- | Ngo Bao Chau, Elon Lindenstrauss and Cedric Villani |
| History | Primary | -- | Grigori Perelman, Terence Tao and Wendelin Werner |
| History | Primary | -- | Richard Borcherds, W. Timothy Gowers and Curtis McMullen |
| History | Primary | -- | Jean Bourgain, Pierre-Louis Lions and Jean-Christopher Yoccoz |
| History | Primary | -- | Efim Zelmanov, Vladimir Drinfeld and Vaughan Jones |
| History | Primary | -- | Shigefumi Mori, Edward Witten and Simon Donaldson |
| History | Primary | -- | Gerd Faltings, Michael Freedman and Alain Connes |
| History | Primary | -- | William Thurston, Shing-Tung Yau and Pierre Rene Deligne |
| History | Primary | -- | Charles Louis Fefferman, Daniel Quillen and Enrico E Bombieri |
| History | Primary | -- | David Mumford, Alan Baker and Heisuke Hironaka |
| History | Primary | -- | John Thompson, Michael Atiyah and Paul Cohen |
| History | Primary | -- | Alexander Grothendieck, Stephen Smale and Lars Hormander |
| History | Primary | -- | John Milnor, Klaus Roth and Rene Thom |
| History | Primary | -- | Kunihiko Kodaira, Jean-Pierre Serre and Jesse Douglas |
| History | Secondary | -- | Fern Hunt, Katherine Okikiola and Bonita Saunders |
| History | Secondary | -- | Aissa Wade, Suzanne Weekes and Euphemia Loften Haynes |
| History | Secondary | -- | Evelyn Boyd Granville, Grace Alele-Williams and Katherine Johnson |
| History | Secondary | -- | Dorothy Vaughn, Marjorie Lee Browne and Mary Ross |
| History | Secondary | -- | Hypatia, Emilie du Chatelet and Maria Gaetana Agnesi |
| History | Secondary | -- | Marguerite Lehr, Florence Nightingale and Charlotte Angas Scott |
| History | Secondary | -- | Hilda Geiringer, Nina Karlovna Bari and Svetlana Jitomirskaya |
| History | Secondary | -- | Idun Reiter, Sophie Germain and Olga Taussky Todd |
| History | Secondary | -- | Mary Lucy Cartwright, Isabel Maddison and Alicia Book Stott |
| History | Secondary | -- | Emmy Noether, Johanna Weber and Grace Chisholm Young |
| History | Secondary | -- | Dorothy Maud Winch, Kathleen Ollerenshaw and Mina Rees |
| History | Secondary | -- | Virginia Ragsdale, Mary Frances Winston and Cora Sadosky |
| History | Secondary | -- | Cathleen Morawetz, Cecilia Krieger and Cheryl Draeger |
| History | Secondary | -- | Nancy Kopell, Joan Birman and Mayme Logsdon |
| History | Secondary | -- | Agnes Meyer Driscoll, Alice T. Schater and Gertrude Mary Cox |
| History | Secondary | -- | Mary Gray, Julia Bowman Robinson and Grace Murray Hopper |
