# LEARNING CONTENT

## FOR CONCEPTUAL UNDERSTANDING

The learning content of the OMC is organised into 6 themes across the Primary, Secondary, Junior and Senior levels:

• Arithmetic
• Experimental Sciences
• Geometry & Algebra
• Graphs & Algebra
• Pure Algebra
• History (at the Primary/Secondary levels) or Calculus (at the Junior/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:

### Levels

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

### Crypto Bonus Game Hintsheet

If you would like help to initially learn the Braille, Pigpen or Morse Codes, then download and use this hintsheet when playing the bonus game.