OCR GCSE J560 Maths specification: every spec point and its video lesson
46of 143 spec points have a lesson out now
143have a lesson planned
Spec text is our short form of the board's statement. Always check the board's own specification.
| Spec | Statement | Lesson | YT search phrase |
|---|---|---|---|
| 1.01aOCR J560 | Use non-calculator methods to calculate the sum, difference, product and quotient of positive and negative whole numbers. | Adding, subtracting, multiplying and dividing positive and negative integers | ScholaFly MA01-03 |
| Adding, subtracting, multiplying and dividing decimals | ScholaFly MA01-04 | ||
| Adding and subtracting fractions and mixed numbers | ScholaFly MA04-04 | ||
| Multiplying and dividing fractions and mixed numbers | ScholaFly MA04-05 | ||
| 1.02aOCR J560 | Understand and use the terms odd, even, prime, factor (divisor), multiple, common factor (divisor), common multiple, square, cube, root. Understand and use place value. | Highest common factor (HCF) | ScholaFly MA02-02 |
| Lowest common multiple (LCM) | ScholaFly MA02-03 | ||
| 1.02bOCR J560 | Identify prime numbers less than 20. Express a whole number as a product of its prime factors. Understand that each number can be expressed as a product of prime factors in only one way. | Highest common factor (HCF) | ScholaFly MA02-02 |
| Lowest common multiple (LCM) | ScholaFly MA02-03 | ||
| 1.02cOCR J560 | Find the HCF and LCM of two whole numbers by listing. | Highest common factor (HCF) | ScholaFly MA02-02 |
| Lowest common multiple (LCM) | ScholaFly MA02-03 | ||
| 1.03aOCR J560 | Know the conventional order for performing calculations involving brackets, four rules and powers, roots and reciprocals. | Inverse operations | ScholaFly MA01-06 |
| 1.04aOCR J560 | Know that addition and subtraction, multiplication and division, and powers and roots, are inverse operations and use this to simplify and check calculations, for example, in reversing arithmetic in "I'm thinking of a number" or "missing digit" problems. | Inverse operations | ScholaFly MA01-06 |
| 2.01aOCR J560 | Recognise and use equivalence between simple fractions and mixed numbers. | Mixed numbers and improper (vulgar) fractions | ScholaFly MA04-02 |
| 2.01bOCR J560 | Add, subtract, multiply and divide simple fractions (proper and improper), including mixed numbers and negative fractions. | Adding, subtracting, multiplying and dividing positive and negative integers | ScholaFly MA01-03 |
| Adding, subtracting, multiplying and dividing decimals | ScholaFly MA01-04 | ||
| Adding and subtracting fractions and mixed numbers | ScholaFly MA04-04 | ||
| Multiplying and dividing fractions and mixed numbers | ScholaFly MA04-05 | ||
| 2.01cOCR J560 | Calculate a fraction of a quantity. Express one quantity as a fraction of another. | Fraction of a quantity; expressing a number as a fraction of another | ScholaFly MA04-06 |
| Find a percentage of a quantity | ScholaFly MA19-02 | ||
| 2.02aOCR J560 | Express a simple fraction as a terminating decimal or vice versa, without a calculator. Understand and use place value in decimals. | Converting recurring decimals into fractions (Higher) | ScholaFly MA04-08 |
| Convert between fractions and terminating decimals, and order them | ScholaFly MA19-01 | ||
| 2.02bOCR J560 | Add, subtract and multiply decimals including negative decimals, without a calculator. | Adding, subtracting, multiplying and dividing positive and negative integers | ScholaFly MA01-03 |
| Adding, subtracting, multiplying and dividing decimals | ScholaFly MA01-04 | ||
| Adding and subtracting fractions and mixed numbers | ScholaFly MA04-04 | ||
| Multiplying and dividing fractions and mixed numbers | ScholaFly MA04-05 | ||
| 2.02cOCR J560 | Divide a decimal by a whole number, including negative decimals, without a calculator. | Adding, subtracting, multiplying and dividing positive and negative integers | ScholaFly MA01-03 |
| Adding, subtracting, multiplying and dividing decimals | ScholaFly MA01-04 | ||
| Adding and subtracting fractions and mixed numbers | ScholaFly MA04-04 | ||
| Multiplying and dividing fractions and mixed numbers | ScholaFly MA04-05 | ||
| 2.03aOCR J560 | Convert between fractions, decimals and percentages. | Converting between fractions, decimals and percentages | ScholaFly MA04-07 |
| 2.03bOCR J560 | Understand percentage is `number of parts per hundred'. Calculate a percentage of a quantity, and express one quantity as a percentage of another, with or without a calculator. | Find a percentage of a quantity | ScholaFly MA19-02 |
| 2.03cOCR J560 | Increase or decrease a quantity by a simple percentage, including simple decimal or fractional multipliers. Apply this to simple original value problems and simple interest. | Calculate a percentage increase or decrease | ScholaFly MA19-03 |
| Calculate a percentage change between two values | ScholaFly MA19-04 | ||
| Reverse percentages: find the original value | ScholaFly MA19-05 | ||
| Simple interest | ScholaFly MA19-06 | ||
| 2.04aOCR J560 | Order integers, fractions, decimals and percentages. | Converting between fractions, decimals and percentages | ScholaFly MA04-07 |
| 2.04bOCR J560 | Use <, >, ≤, ≥, =, ≠ | Converting between fractions, decimals and percentages | ScholaFly MA04-07 |
| 3.01aOCR J560 | Use positive integer indices to write, for example, 2 x 2 x 2 x 2 = 2^4 | Index laws: multiplying and dividing powers | ScholaFly MA03-03 |
| Power of a power, and zero and negative indices | ScholaFly MA03-04 | ||
| Fractional indices (Higher) | ScholaFly MA03-05 | ||
| 3.01bOCR J560 | Calculate positive integer powers and exact roots. Recognise simple powers of 2, 3, 4 and 5. | Square numbers, cube numbers and calculating them | ScholaFly MA03-01 |
| Square roots, cube roots and higher roots | ScholaFly MA03-02 | ||
| Index laws: multiplying and dividing powers | ScholaFly MA03-03 | ||
| Power of a power, and zero and negative indices | ScholaFly MA03-04 | ||
| Fractional indices (Higher) | ScholaFly MA03-05 | ||
| 3.01cOCR J560 | Know and apply: a^m x a^n = a^(m+n); a^m ÷ a^n = a^(m-n); (a^m)^n = a^(mn) | Index laws: multiplying and dividing powers | ScholaFly MA03-03 |
| Power of a power, and zero and negative indices | ScholaFly MA03-04 | ||
| 3.02aOCR J560 | Interpret and order numbers expressed in standard form. Convert numbers to and from standard form. | Converting to and from standard form | ScholaFly MA03-06 |
| Calculating with numbers in standard form | ScholaFly MA03-07 | ||
| 3.02bOCR J560 | Use a calculator to perform calculations with numbers in standard form. | Converting to and from standard form | ScholaFly MA03-06 |
| Calculating with numbers in standard form | ScholaFly MA03-07 | ||
| 3.03aOCR J560 | Use fractions in exact calculations without a calculator. | Calculating exactly with fractions | ScholaFly MA05-01 |
| Calculating exactly with multiples of pi | ScholaFly MA05-02 | ||
| Simplifying surds (Higher) | ScholaFly MA05-03 | ||
| Rationalising the denominator (Higher) | ScholaFly MA05-04 | ||
| 3.03bOCR J560 | Simplify expressions with surds, including rationalising denominators. | Simplifying surds (Higher) | ScholaFly MA05-03 |
| Rationalising the denominator (Higher) | ScholaFly MA05-04 | ||
| 4.01aOCR J560 | Round numbers to the nearest whole number, ten, hundred, etc. or to a given number of significant figures (sf) or decimal places (dp). | Rounding to significant figures and decimal places | ScholaFly MA07-01 |
| 4.01bOCR J560 | Estimate or check, without a calculator, the result of a calculation by using suitable approximations. | Estimating a calculation by rounding | ScholaFly MA07-02 |
| 4.01cOCR J560 | Use inequality notation to write down an error interval for a number or measurement rounded or truncated to a given degree of accuracy. Apply and interpret limits of accuracy. | Upper and lower bounds of a rounded value | ScholaFly MA07-03 |
| Bounds of a calculated result (Higher) | ScholaFly MA07-04 | ||
| Error intervals from rounding and truncation | ScholaFly MA07-05 | ||
| Limits of accuracy: upper and lower bounds | ScholaFly MA07-06 | ||
| 5.01aOCR J560 | Find the ratio of quantities in the form a : b and simplify. Find the ratio of quantities in the form 1 : n. | Ratio notation, simplifying and unitary form | ScholaFly MA20-01 |
| 5.01bOCR J560 | Split a quantity into two parts given the ratio of the parts. Express the division of a quantity into two parts as a ratio. Calculate one quantity from another, given the ratio of the two quantities. | Share an amount in a given ratio | ScholaFly MA20-02 |
| Share in a ratio when only a difference or one part is known | ScholaFly MA20-03 | ||
| 5.01cOCR J560 | Interpret a ratio of two parts as a fraction of a whole. | Ratio notation, simplifying and unitary form | ScholaFly MA20-01 |
| 5.01dOCR J560 | Solve simple ratio and proportion problems. Understand the relationship between ratio and linear functions. | Solve direct proportion problems | ScholaFly MA21-01 |
| 5.02aOCR J560 | Solve simple problems involving quantities in direct proportion including algebraic proportions. | Solve direct proportion problems | ScholaFly MA21-01 |
| Construct direct and inverse proportion equations, including powers and roots | ScholaFly MA21-04 | ||
| 5.02bOCR J560 | Solve simple word problems involving quantities in inverse proportion or simple algebraic proportions. | Solve inverse proportion problems | ScholaFly MA21-03 |
| Inverse proportion to a power or root | ScholaFly MA21-05 | ||
| 5.03aOCR J560 | Calculate simple interest including in financial contexts. | Simple interest | ScholaFly MA19-06 |
| Growth and decay using repeated percentage multipliers | ScholaFly MA19-07 | ||
| 6.01aOCR J560 | Understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors. | Algebra Vocabulary: Expressions, Equations, Formulae, Identities and Inequalities | ScholaFly MA09-02 |
| Equations, Identities and Equivalent Expressions | ScholaFly MA10-09 | ||
| Constructing Algebraic Proofs | ScholaFly MA10-10 | ||
| 6.01bOCR J560 | Simplify algebraic expressions by collecting like terms. | Collecting Like Terms | ScholaFly MA09-04 |
| 6.01cOCR J560 | Simplify algebraic products and quotients. | Laws of Indices for Algebraic Terms | ScholaFly MA09-05 |
| 6.01dOCR J560 | Simplify algebraic expressions by multiplying a single term over a bracket. | Expanding a Single Bracket | ScholaFly MA10-01 |
| Expanding Double Brackets | ScholaFly MA10-02 | ||
| Expanding Three or More Brackets | ScholaFly MA10-03 | ||
| 6.01eOCR J560 | Take out common factors. | Factorising by Taking Out a Common Factor | ScholaFly MA10-04 |
| Factorising a Quadratic x^2+bx+c, Including Difference of Two Squares | ScholaFly MA10-05 | ||
| Factorising a General Quadratic ax^2+bx+c | ScholaFly MA10-06 | ||
| 6.01fOCR J560 | Complete the square on a quadratic expression. | Completing the Square | ScholaFly MA10-07 |
| 6.01gOCR J560 | Simplify and manipulate algebraic fractions. | Simplifying and Manipulating Algebraic Fractions | ScholaFly MA10-08 |
| 6.02aOCR J560 | Formulate simple formulae and expressions from real-world contexts. | Writing an Expression or Formula from a Context | ScholaFly MA11-05 |
| 6.02bOCR J560 | Substitute positive numbers into simple expressions and formulae to find the value of the subject. | Substituting Values into Expressions and Formulae | ScholaFly MA09-03 |
| 6.02cOCR J560 | Rearrange formulae to change the subject, where the subject appears once only. | Using and Rearranging a Formula (Subject Appears Once) | ScholaFly MA11-03 |
| Rearranging Harder Formulae (Subject Appears Twice, or Under a Power/Root) | ScholaFly MA11-04 | ||
| 6.02dOCR J560 | Recall and use: Circumference of a circle 2πr = πd; Area of a circle πr^2 | Recalling Circle, Pythagoras and Trig Formulae | ScholaFly MA11-07 |
| Choosing Between the Quadratic Formula, Sine Rule, Cosine Rule and Area Formula | ScholaFly MA11-08 | ||
| 6.02eOCR J560 | Use: v = u + at; s = ut + (1/2)at^2; v^2 = u^2 + 2as where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from position when t = 0 and t is time taken. | Using the Kinematics (SUVAT) Formulae | ScholaFly MA11-09 |
| 6.03aOCR J560 | Solve linear equations in one unknown algebraically. | Solving Linear Equations by Balancing | ScholaFly MA11-01 |
| Solving Linear Equations with Brackets | ScholaFly MA11-02 | ||
| Setting Up and Solving an Equation from a Context | ScholaFly MA11-06 | ||
| 6.03bOCR J560 | Solve quadratic equations with coefficient of x^2 equal to 1 by factorising. | Solving x^2+bx+c=0 by Factorising | ScholaFly MA12-01 |
| Rearranging and Factorising a General Quadratic Equation | ScholaFly MA12-02 | ||
| Solving a Quadratic with the Quadratic Formula | ScholaFly MA12-03 | ||
| 6.03cOCR J560 | Set up and solve two linear simultaneous equations in two variables algebraically. | Solving Simultaneous Linear Equations by Elimination | ScholaFly MA12-04 |
| Simultaneous Equations: One Linear, One Quadratic | ScholaFly MA12-05 | ||
| 6.03dOCR J560 | Use a graph to find the approximate solution of a linear equation. | Solving Linear Equations by Balancing | ScholaFly MA11-01 |
| Solving Linear Equations with Brackets | ScholaFly MA11-02 | ||
| Solving Simultaneous Linear Equations by Elimination | ScholaFly MA12-04 | ||
| Graph Intersections as Simultaneous Solutions | ScholaFly MA12-06 | ||
| 6.03eOCR J560 | Find approximate solutions to equations using systematic sign-change methods (for example, decimal search or interval bisection) when there is no simple analytical method of solving them. Specific methods will not be requested in the assessment. | Solving Equations by Iteration | ScholaFly MA12-07 |
| 6.04aOCR J560 | Understand and use the symbols <, ≤, > and ≥ | Inequality Symbols and Number-Line Conventions | ScholaFly MA18-01 |
| Solving a Linear Inequality | ScholaFly MA18-02 | ||
| Solving a Quadratic Inequality | ScholaFly MA18-03 | ||
| 6.04bOCR J560 | Solve (several) linear inequalities in two variables, representing the solution set on a graph. | Regions Satisfying Linear Inequalities in Two Variables | ScholaFly MA18-04 |
| 6.05aOCR J560 | Interpret, where appropriate, simple expressions as functions with inputs and outputs. | Function Machines: Inputs, Outputs and Reversing | ScholaFly MA14-01 |
| Inverse and Composite Functions | ScholaFly MA14-02 | ||
| 6.06aOCR J560 | Generate a sequence by spotting a pattern or using a term-to-term rule given algebraically or in words. Find a position-to-term rule for simple arithmetic sequences, algebraically or in words. | Generating Terms of a Sequence | ScholaFly MA13-01 |
| Finding the nth Term of a Linear Sequence | ScholaFly MA13-04 | ||
| Finding the nth Term of a Quadratic Sequence | ScholaFly MA13-05 | ||
| 6.06bOCR J560 | Recognise sequences of triangular, square and cube numbers, and simple arithmetic progressions. | Recognising Special Sequences | ScholaFly MA13-02 |
| Sequences with a Surd Common Ratio | ScholaFly MA13-03 | ||
| 7.01aOCR J560 | Work with x- and y-coordinates in all four quadrants. | Coordinates in Four Quadrants | ScholaFly MA15-01 |
| 7.01bOCR J560 | Use a table of values to plot graphs of linear and quadratic functions. | Recognising Linear and Quadratic Graphs | ScholaFly MA16-01 |
| Cubic and Reciprocal Graphs | ScholaFly MA16-04 | ||
| 7.01cOCR J560 | Recognise and sketch the graphs of simple linear and quadratic functions. | Recognising Linear and Quadratic Graphs | ScholaFly MA16-01 |
| Roots, Y-Intercept and Turning Point of a Quadratic Graph | ScholaFly MA16-02 | ||
| Turning Point by Completing the Square | ScholaFly MA16-03 | ||
| 7.01dOCR J560 | Recognise and sketch graphs of exponential functions in the form y = k^x for positive k. | Exponential Graphs | ScholaFly MA16-05 |
| 7.01eOCR J560 | Recognise and sketch the graphs of y = sin x , y = cos x and y = tan x . | Trigonometric Graphs: sin, cos and tan | ScholaFly MA16-06 |
| 7.01fOCR J560 | Recognise and use the equation of a circle with centre at the origin. | Recognising the Equation of a Circle | ScholaFly MA16-11 |
| Finding the Equation of a Tangent to a Circle | ScholaFly MA16-12 | ||
| 7.02aOCR J560 | Find and interpret the gradient and intercept of straight lines, graphically and using y = mx + c . | Gradient and Y-Intercept via y=mx+c | ScholaFly MA15-05 |
| Finding the Equation of a Straight Line | ScholaFly MA15-06 | ||
| Regions Satisfying Linear Inequalities in Two Variables | ScholaFly MA18-04 | ||
| 7.02bOCR J560 | Identify and find equations of parallel lines. | Equations of Parallel Lines | ScholaFly MA15-07 |
| Equations of Perpendicular Lines | ScholaFly MA15-08 | ||
| Recognising the Equation of a Circle | ScholaFly MA16-11 | ||
| Finding the Equation of a Tangent to a Circle | ScholaFly MA16-12 | ||
| 7.03aOCR J560 | Identify and sketch translations and reflections of a given graph (or the graph of a given equation). | Translating a Graph: Vocabulary and y=f(x)+a, y=f(x+a) | ScholaFly MA16-08 |
| Stretching and Reflecting a Graph: y=af(x), y=f(ax) | ScholaFly MA16-09 | ||
| 7.04aOCR J560 | Construct and interpret graphs in real-world contexts. | Graphs of Direct and Inverse Proportion | ScholaFly MA16-10 |
| Plotting and Interpreting Real-World Graphs | ScholaFly MA17-01 | ||
| Gradient of a straight line as a rate of change | ScholaFly MA21-06 | ||
| 7.04bOCR J560 | Understand the relationship between gradient and ratio. | Estimating the Gradient of a Curve | ScholaFly MA17-03 |
| 7.04cOCR J560 | Calculate or estimate areas under graphs, and interpret in contexts such as distance-time graphs, velocity-time graphs and financial graphs. | Estimating the Area Under a Graph | ScholaFly MA17-04 |
| 8.01aOCR J560 | Use the terms points, lines, line segments, vertices, edges, planes, parallel lines, perpendicular lines. | Geometry notation and types of angle | ScholaFly MA25-01 |
| 8.01bOCR J560 | Know the terms acute, obtuse, right and reflex angles. Use the standard conventions for labelling and referring to the sides and angles of triangles. | Geometry notation and types of angle | ScholaFly MA25-01 |
| 8.01cOCR J560 | Know the terms: regular polygon; scalene, isosceles and equilateral triangle; quadrilateral, square, rectangle, kite, rhombus, parallelogram, trapezium; pentagon, hexagon, octagon. | Naming triangles, quadrilaterals and polygons | ScholaFly MA26-01 |
| 8.01dOCR J560 | Recognise the terms face, surface, edge, and vertex, cube, cuboid, prism, cylinder, pyramid, cone and sphere. | Naming 3D solids and their properties | ScholaFly MA29-01 |
| 8.01eOCR J560 | Draw diagrams from written descriptions as required by questions. | Geometry notation and types of angle | ScholaFly MA25-01 |
| 8.01fOCR J560 | Use a ruler to construct and measure straight lines. Use a protractor to construct and measure angles. Use compasses to construct circles. | Constructing triangles and shapes with a ruler, protractor and compasses | ScholaFly MA24-07 |
| 8.01gOCR J560 | Use x- and y-coordinates in plane geometry problems, including transformations of simple shapes. | Solving geometry problems on coordinate axes | ScholaFly MA28-09 |
| 8.02aOCR J560 | Construct the perpendicular bisector and midpoint of a line segment. | Constructing the perpendicular bisector of a line segment | ScholaFly MA24-01 |
| 8.02bOCR J560 | Construct the bisector of an angle formed from two lines. | Constructing the bisector of an angle | ScholaFly MA24-02 |
| 8.02cOCR J560 | Construct the perpendicular from a point to a line. Construct the perpendicular to a line at a point. Know that the perpendicular distance from a point to a line is the shortest distance to the line. | Constructing a perpendicular to a line from or at a point | ScholaFly MA24-03 |
| 8.02dOCR J560 | Apply ruler and compass constructions to construct figures and identify the loci of points, to include real-world problems. Understand the term `equidistant'. | Solving loci problems with a single condition | ScholaFly MA24-04 |
| Solving loci problems with combined conditions | ScholaFly MA24-05 | ||
| 8.03aOCR J560 | Know and use the sum of the angles at a point is 360°. | Angles at a point, on a line and vertically opposite angles | ScholaFly MA25-02 |
| Angles on parallel lines | ScholaFly MA25-03 | ||
| Chaining angle facts together with reasons | ScholaFly MA25-04 | ||
| Writing formal geometric proofs using angle facts (Higher) | ScholaFly MA25-08 | ||
| 8.03bOCR J560 | Know that the sum of the angles at a point on a line is 180°. | Angles at a point, on a line and vertically opposite angles | ScholaFly MA25-02 |
| Angles on parallel lines | ScholaFly MA25-03 | ||
| Chaining angle facts together with reasons | ScholaFly MA25-04 | ||
| Writing formal geometric proofs using angle facts (Higher) | ScholaFly MA25-08 | ||
| 8.03cOCR J560 | Know and use: vertically opposite angles are equal; alternate angles on parallel lines are equal; corresponding angles on parallel lines are equal. | Angles at a point, on a line and vertically opposite angles | ScholaFly MA25-02 |
| Angles on parallel lines | ScholaFly MA25-03 | ||
| Chaining angle facts together with reasons | ScholaFly MA25-04 | ||
| Writing formal geometric proofs using angle facts (Higher) | ScholaFly MA25-08 | ||
| 8.03dOCR J560 | Derive and use the sum of the interior angles of a triangle is 180°. Derive and use the sum of the exterior angles of a polygon is 360°. Find the sum of the interior angles of a polygon. Find the interior angle of a regular polygon. | Chaining angle facts together with reasons | ScholaFly MA25-04 |
| Angle sum of a triangle and the exterior angle rule | ScholaFly MA25-05 | ||
| Interior angles of polygons | ScholaFly MA25-06 | ||
| Exterior angles and regular polygons | ScholaFly MA25-07 | ||
| Writing formal geometric proofs using angle facts (Higher) | ScholaFly MA25-08 | ||
| 8.04aOCR J560 | Know the basic properties of isosceles, equilateral and right-angled triangles. Give geometrical reasons to justify these properties. | Properties of special quadrilaterals and triangles | ScholaFly MA26-02 |
| Formal proofs using triangle and quadrilateral properties (Higher) | ScholaFly MA26-09 | ||
| 8.04bOCR J560 | Know the basic properties of the square, rectangle, parallelogram, trapezium, kite and rhombus. Give geometrical reasons to justify these properties. | Properties of special quadrilaterals and triangles | ScholaFly MA26-02 |
| Formal proofs using triangle and quadrilateral properties (Higher) | ScholaFly MA26-09 | ||
| 8.04cOCR J560 | Identify reflection and rotation symmetries of triangles, quadrilaterals and other polygons. | Line and rotational symmetry of 2D shapes | ScholaFly MA26-10 |
| 8.05aOCR J560 | Understand and use the terms centre, radius, chord, diameter and circumference. | Circle vocabulary | ScholaFly MA27-01 |
| 8.05bOCR J560 | Apply and prove: the angle subtended by an arc at the centre is twice the angle at the circumference. | Circle theorem: angle at the centre | ScholaFly MA27-02 |
| 8.05cOCR J560 | Apply and prove: the angle on the circumference subtended by a diameter is a right angle. | Circle theorem: angle in a semicircle | ScholaFly MA27-03 |
| 8.05dOCR J560 | Apply and prove: two angles in the same segment are equal. | Circle theorem: angles in the same segment | ScholaFly MA27-04 |
| 8.05eOCR J560 | Apply and prove: a radius or diameter bisects a chord if and only if it is perpendicular to the chord. | Circle theorems: chords and the centre | ScholaFly MA27-09 |
| 8.05fOCR J560 | Apply and prove: for a point P on the circumference, the radius or diameter through P is perpendicular to the tangent at P. | Circle theorem: tangent and radius | ScholaFly MA27-06 |
| 8.05gOCR J560 | Apply and prove: for a point P on the circumference, the angle between the tangent and a chord through P equals the angle subtended by the chord in the opposite segment. | Circle theorem: alternate segment theorem | ScholaFly MA27-07 |
| 8.05hOCR J560 | Apply and prove: the opposite angles of a cyclic quadrilateral are supplementary. | Circle theorem: cyclic quadrilaterals | ScholaFly MA27-05 |
| 8.06aOCR J560 | Recognise and know the properties of the cube, cuboid, prism, cylinder, pyramid, cone and sphere. | Naming 3D solids and their properties | ScholaFly MA29-01 |
| 8.06bOCR J560 | Interpret plans and elevations of simple 3D solids. | Interpreting plans and elevations | ScholaFly MA29-02 |
| Constructing plans and elevations | ScholaFly MA29-03 | ||
| 9.01aOCR J560 | Reflect a simple shape in a given mirror line, and identify the mirror line from a shape and its image. | Reflecting a shape in a mirror line | ScholaFly MA28-01 |
| Finding the mirror line from a shape and its image | ScholaFly MA28-02 | ||
| 9.01bOCR J560 | Rotate a simple shape clockwise or anti-clockwise through a multiple of 90° about a given centre of rotation. | Rotating a shape and describing a rotation | ScholaFly MA28-03 |
| 9.01cOCR J560 | Use a column vector to describe a translation of a simple shape, and perform a specified translation. | Translating a shape using a column vector | ScholaFly MA28-04 |
| 9.01dOCR J560 | Perform a sequence of isometric transformations (reflections, rotations or translations), on a simple shape. Describe the resulting transformation and the changes and invariance achieved. | Describing combined transformations and invariance (Higher) | ScholaFly MA28-07 |
| 9.02aOCR J560 | Identify congruent triangles. | Congruent triangles: SSS, SAS, ASA and RHS | ScholaFly MA26-03 |
| 9.02bOCR J560 | Apply congruent triangles in calculations and simple proofs. | Proving results using congruent triangles and angle facts | ScholaFly MA26-07 |
| Proving results using similarity and Pythagoras | ScholaFly MA26-08 | ||
| 9.03aOCR J560 | Understand addition, subtraction and scalar multiplication of vectors. | Vector arithmetic: addition, subtraction and scalar multiplication | ScholaFly MA28-10 |
| Using vectors to prove geometric results (Higher) | ScholaFly MA28-12 | ||
| 9.03bOCR J560 | Represent a 2-dimensional vector as a column vector, and draw column vectors on a square or coordinate grid. | Vector arithmetic: addition, subtraction and scalar multiplication | ScholaFly MA28-10 |
| 9.04aOCR J560 | Identify similar triangles. | Congruent and similar shapes: finding unknown lengths | ScholaFly MA26-04 |
| 9.04bOCR J560 | Enlarge a simple shape from a given centre using a whole number scale factor, and identify the scale factor of an enlargement. | Enlarging a shape by a positive or fractional scale factor | ScholaFly MA28-05 |
| 9.04cOCR J560 | Compare lengths, areas and volumes using ratio notation and scale factors. | Congruent and similar shapes: finding unknown lengths | ScholaFly MA26-04 |
| Area ratio of similar shapes | ScholaFly MA26-05 | ||
| Volume ratio of similar shapes (Higher) | ScholaFly MA26-06 | ||
| 10.01aOCR J560 | Use and convert standard units of measurement for length, area, volume/capacity, mass, time and money. | Convert between standard and compound units | ScholaFly MA22-01 |
| 10.01bOCR J560 | Use and convert simple compound units (e.g. for speed, rates of pay, unit pricing). Know and apply in simple cases: speed = distance ÷ time | Compare rates: speed, pay and unit pricing | ScholaFly MA22-02 |
| Density: mass, volume and the direction of division | ScholaFly MA22-03 | ||
| Pressure: force, area and recognising when to use it | ScholaFly MA22-04 | ||
| 10.01cOCR J560 | Use the scale of a map, and work with bearings. Construct and interpret scale drawings. | Three-figure bearings | ScholaFly MA24-08 |
| Scale drawings and maps | ScholaFly MA24-09 | ||
| 10.02aOCR J560 | Calculate the perimeter of rectilinear shapes. | Perimeter of 2D and composite shapes | ScholaFly MA23-01 |
| 10.02bOCR J560 | Know and apply the formula circumference = 2πr = πd to calculate the circumference of a circle. | Circle circumference and area | ScholaFly MA23-03 |
| Arc length and sector area, including major sectors | ScholaFly MA23-04 | ||
| 10.02cOCR J560 | Apply perimeter formulae in calculations involving the perimeter of composite 2D shapes. | Perimeter of 2D and composite shapes | ScholaFly MA23-01 |
| Composite solids: breaking a shape into parts | ScholaFly MA29-08 | ||
| 10.03aOCR J560 | Know and apply the formula: area = 1/2 base × height. | Area of triangles, parallelograms and trapezia | ScholaFly MA23-02 |
| The sine rule and the area of a triangle | ScholaFly MA30-05 | ||
| 10.03bOCR J560 | Know and apply the formula: area = base × height. | Area of triangles, parallelograms and trapezia | ScholaFly MA23-02 |
| 10.03cOCR J560 | Calculate the area of a trapezium. | Area of triangles, parallelograms and trapezia | ScholaFly MA23-02 |
| 10.03dOCR J560 | Know and apply the formula area = πr^2 to calculate the area of a circle. | Circle circumference and area | ScholaFly MA23-03 |
| Arc length and sector area, including major sectors | ScholaFly MA23-04 | ||
| 10.03eOCR J560 | Apply area formulae in calculations involving the area of composite 2D shapes. | Composite solids: breaking a shape into parts | ScholaFly MA29-08 |
| 10.04aOCR J560 | Calculate the surface area and volume of cuboids and other right prisms (including cylinders). | Volume of prisms, cuboids and cylinders | ScholaFly MA29-05 |
| 10.04bOCR J560 | Calculate the surface area and volume of spheres, cones and simple composite solids (formulae will be given). | Surface area and volume of a sphere and cone (Higher) | ScholaFly MA29-06 |
| Composite solids: breaking a shape into parts | ScholaFly MA29-08 | ||
| 10.04cOCR J560 | Calculate the surface area and volume of a pyramid (the formula 1/3 area of base × height will be given). | Surface area and volume of a sphere and cone (Higher) | ScholaFly MA29-06 |
| 10.05aOCR J560 | Know, derive and apply Pythagoras' theorem a^2 + b^2 = c^2 to find lengths in right-angled triangles in 2D figures. | Pythagoras' theorem in two dimensions | ScholaFly MA30-01 |
| Pythagoras' theorem in three dimensions | ScholaFly MA30-08 | ||
| 10.05bOCR J560 | Know and apply the trigonometric ratios, sin θ, cos θ and tan θ and apply them to find angles and lengths in right-angled triangles in 2D figures. | Trigonometric ratios: labelling sides and choosing sin, cos or tan | ScholaFly MA30-02 |
| Using trigonometry to find missing sides and angles | ScholaFly MA30-03 | ||
| Trigonometry in 3D and complex figures | ScholaFly MA30-11 | ||
| 10.05cOCR J560 | Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°. Know the exact value of tan θ for θ = 0°, 30°, 45° and 60°. | Trigonometric ratios: labelling sides and choosing sin, cos or tan | ScholaFly MA30-02 |
| 10.05dOCR J560 | Know and apply the sine rule, a/sin A = b/sin B = c/sin C , to find lengths and angles. | The sine rule and the area of a triangle | ScholaFly MA30-05 |
| The cosine rule | ScholaFly MA30-07 | ||
| 10.05eOCR J560 | Know and apply the cosine rule, a^2 = b^2 + c^2 - 2bc cos A, to find lengths and angles. | The sine rule and the area of a triangle | ScholaFly MA30-05 |
| The cosine rule | ScholaFly MA30-07 | ||
| 11.01aOCR J560 | Use the 0-1 probability scale as a measure of likelihood of random events, for example, `impossible' with 0, `evens' with 0.5, `certain' with 1. | Probability scale, vocabulary and simple probability | ScholaFly MA34-01 |
| 11.01bOCR J560 | Record, describe and analyse the relative frequency of outcomes of repeated experiments using tables and frequency trees. | Frequency tables and frequency trees | ScholaFly MA34-02 |
| 11.01cOCR J560 | Use relative frequency as an estimate of probability. | Relative frequency as an estimate of probability | ScholaFly MA34-03 |
| Sample size, reliability and theoretical probability language | ScholaFly MA34-04 | ||
| 11.01dOCR J560 | Calculate probabilities, expressed as fractions or decimals, in simple experiments with equally likely outcomes, for example flipping coins, rolling dice, etc. Apply ideas of randomness and fairness in simple experiments. Calculate probabilities of simple combined events, for example rolling two dice and looking at the totals. Use probabilities to calculate the number of expected outcomes in repeated experiments. | Probability scale, vocabulary and simple probability | ScholaFly MA34-01 |
| Expected frequency: probability times number of trials | ScholaFly MA34-05 | ||
| Constructing sample space diagrams | ScholaFly MA35-03 | ||
| 11.02aOCR J560 | Use tables and grids to list the outcomes of single events and simple combinations of events, and to calculate theoretical probabilities. | Constructing sample space diagrams | ScholaFly MA35-03 |
| 11.02bOCR J560 | Use systematic listing strategies. | The product rule for counting (Higher) | ScholaFly MA02-05 |
| 11.02cOCR J560 | Use a two-circle Venn diagram to enumerate sets, and use this to calculate related probabilities. Use simple set notation to describe simple sets of numbers or objects. | Sets: definitions and notation (union, intersection, element of) | ScholaFly MA06-01 |
| Venn diagrams: universal set, empty set and complement | ScholaFly MA06-02 | ||
| Reading Venn diagrams and n(...) notation | ScholaFly MA35-04 | ||
| Conditional probability using diagrams | ScholaFly MA36-04 | ||
| 11.02dOCR J560 | Use tree diagrams to enumerate sets and to record the probabilities of successive events (tree frames may be given and in some cases will be partly completed). | Constructing tree diagrams | ScholaFly MA36-01 |
| Combining probabilities on a tree diagram | ScholaFly MA36-02 | ||
| 11.02eOCR J560 | Use the addition law for mutually exclusive events. Use p(A) + p(not A) = 1 | The complement rule: P(not A) = 1 - P(A) | ScholaFly MA35-01 |
| Mutually exclusive events: the addition rule | ScholaFly MA35-02 | ||
| 11.02fOCR J560 | Use tree diagrams and other representations to calculate the probability of independent and dependent combined events. | Combined events: independent and dependent probabilities | ScholaFly MA36-03 |
| The formal conditional probability formula (OCR) | ScholaFly MA36-05 | ||
| 12.01aOCR J560 | Define the population in a study, and understand the difference between population and sample. Infer properties of populations or distributions from a sample. Understand what is meant by simple random sampling, and bias in sampling. | Sampling methods, bias and questionnaire design | ScholaFly MA31-01 |
| 12.02aOCR J560 | Interpret and construct charts appropriate to the data type; including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data. Interpret multiple and composite bar charts. | Tally charts and two-way tables | ScholaFly MA31-02 |
| Bar charts, pictograms and vertical line charts | ScholaFly MA31-04 | ||
| Pie charts: calculating angles and constructing | ScholaFly MA31-05 | ||
| Time series graphs and trends | ScholaFly MA31-06 | ||
| 12.02bOCR J560 | Interpret and construct diagrams for grouped data as appropriate, i.e. cumulative frequency graphs and histograms (with either equal or unequal class intervals). | Constructing histograms with frequency density | ScholaFly MA33-01 |
| Reading and calculating from histograms | ScholaFly MA33-02 | ||
| Constructing a cumulative frequency diagram | ScholaFly MA33-03 | ||
| Reading estimates from a cumulative frequency diagram | ScholaFly MA33-04 | ||
| 12.03aOCR J560 | Calculate the mean, mode, median and range for ungrouped data. Find the modal class, and calculate estimates of the range, mean and median for grouped data, and understand why they are estimates. Describe a population using statistics. Make simple comparisons. Compare data sets using `like for like' summary values. Understand the advantages and disadvantages of summary values. | Mean, median, mode and range | ScholaFly MA32-01 |
| Finding the modal class | ScholaFly MA32-02 | ||
| Estimating the mean from grouped data | ScholaFly MA32-03 | ||
| Quartiles and interquartile range | ScholaFly MA32-04 | ||
| Constructing and reading box plots | ScholaFly MA32-05 | ||
| Comparing distributions with box plots | ScholaFly MA32-06 | ||
| Constructing a cumulative frequency diagram | ScholaFly MA33-03 | ||
| Reading estimates from a cumulative frequency diagram | ScholaFly MA33-04 | ||
| 12.03bOCR J560 | Recognise graphical misrepresentation through incorrect scales, labels, etc. | Recognising misleading graphs | ScholaFly MA31-07 |
| 12.03cOCR J560 | Plot and interpret scatter diagrams for bivariate data. Recognise correlation. | Scatter graphs and types of correlation | ScholaFly MA32-09 |
| Line of best fit, correlation vs causation, and prediction | ScholaFly MA32-10 | ||
| 12.03dOCR J560 | Identify an outlier in simple cases. | Outliers | ScholaFly MA32-07 |