2.02b Addition, subtraction and multiplication of decimals Add, subtract and multiply decimals including negative decimals, without a calculator. 2.02c Division of decimals Divide a decimal by a whole number, including negative decimals, without a calculator. e.g. Without a calculator, divide a decimal by a decimal. e.g. 2.03 Percentages 2.03a Percentage conversions Convert between fractions, decimals and percentages. e.g. 2.03b Percentage calculations 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.
5.02 Direct and inverse proportion 5.02a Direct proportion Solve simple problems involving quantities in direct proportion including algebraic proportions. e.g. Using equality of ratios, if , then or . Currency conversion problems. [see also Similar shapes, 9.04c] Solve more formal problems involving quantities in direct proportion (i.e. where). Recognise that if , where k is a constant, then y is proportional to x. Formulate equations and solve problems involving a quantity in direct proportion to a power or root of another quantity. 5.02b Inverse proportion Solve simple word problems involving quantities in inverse proportion or simple algebraic proportions. e.g. speed–time contexts (if speed is doubled, time is halved). Solve more formal problems involving quantities in inverse proportion (i.e. where). Recognise that if , where k is a constant, then y is inversely proportional to x. Formulate equations and solve problems involving a quantity in inverse proportion to a power or root of another quantity. 5.03 Discrete growth and decay 5.03a Growth and decay Calculate simple interest including in financial contexts. Solve problems step-by-step involving multipliers over a given interval, for example compound interest, depreciation, etc. e.g. A car worth £15 000 new depreciating by 30%, 20% and 15% respectively in three years. [see also Percentage change, 2.03c] Express exponential growth or decay as a formula. e.g. Amount £A subject to compound interest of 10% p.a. on £100 as . Solve and interpret answers in growth and decay problems. [see also Exponential functions, 7.01d, Formulate algebraic expressions, 6.02a] OCR 6 Algebra
6.01 Algebraic expressions 6.01a Algebraic terminology and proofs Understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors. Recognise the difference between an equation and an identity, and show algebraic expressions are equivalent. e.g. show that Use algebra to construct arguments. Use algebra to construct proofs and arguments. e.g. prove that the sum of three consecutive integers is a multiple of 3. 6.01b Collecting like terms in sums and differences of terms Simplify algebraic expressions by collecting like terms. e.g. 6.01c Simplifying products and quotients Simplify algebraic products and quotients. e.g. [see also Laws of indices, 3.01c] Simplify algebraic products and quotients using the laws of indices. e.g. 6.01d Multiplying out brackets Simplify algebraic expressions by multiplying a single term over a bracket. e.g. Expand products of two binomials. e.g. Expand products of more than two binomials. e.g. 6.01e Factorising Take out common factors. e.g. Factorise quadratic expressions of the form . e.g. Factorise quadratic expressions of the form (where a 0 or 1) e.g.
6.03 Algebraic equations 6.03a Linear equations in one unknown Solve linear equations in one unknown algebraically. e.g. Solve Set up and solve linear equations in mathematical and contexts, including those with the unknown on both sides of the equation. e.g. Solve Interpret solutions in context. [Examples may include manipulation of algebraic fractions, 6.01g] 6.03b Quadratic equations Solve quadratic equations with coefficient of x2 equal to 1 by factorising. e.g. Solve . Find x for an x cm by (x + 3) cm rectangle of area 40 cm2. Know the quadratic formula. Rearrange and solve quadratic equations by factorising, completing the square or using the quadratic formula. e.g. 6.03c Simultaneous equations Set up and solve two linear simultaneous equations in two variables algebraically. e.g. Solve simultaneously and Set up and solve two simultaneous equations (one linear and one quadratic) in two variables algebraically. e.g. Solve simultaneously and 6.03d Approximate solutions using a graph Use a graph to find the approximate solution of a linear equation. Use graphs to find approximate roots of quadratic equations and the approximate solution of two linear simultaneous equations. Know that the coordinates of the points of intersection of a curve and a straight line are the solutions to the simultaneous equations for the line and curve.
GCSE (9-1) content Ref. Subject content All GCSE maths learners should have confidence and competence to… Higher tier GCSE maths learners should also have confidence and competence to… Higher tier learners should also be able to… Revision notes Tick when achieved! OCR 7 Graphs of Equations and Functions 7.01 Graphs of equations and functions 7.01a x- and Work with x- and y- coordinates in all four quadrants. 7.01b Graphs of equations and functions Use a table of values to plot graphs of linear and quadratic functions. e.g. Use a table of values to plot other polynomial graphs and reciprocals. e.g. Use a table of values to plot exponential graphs. e.g. 7.01c Polynomial functions Recognise and sketch the graphs of simple linear and quadratic functions. e.g. Recognise and sketch graphs of: . Identify intercepts and, using symmetry, the turning point of graphs of quadratic functions. Find the roots of a quadratic equation algebraically. Sketch graphs of quadratic functions, identifying the turning point by completing the square. 7.01d Exponential functions Recognise and sketch graphs of exponential functions in the form y = kx for positive k. 7.01e Trigonometric functions Recognise and sketch the graphs of , and . 7.01f Equations of circles Recognise and use the equation of a circle with centre at the origin.
9.04b Enlargement Enlarge a simple shape from a given centre using a whole number scale factor, and identify the scale factor of an enlargement. Identify the centre and scale factor (including fractional scale factors) of an enlargement of a simple shape, and perform such an enlargement on a simple shape. Perform and recognise enlargements with negative scale factors. 9.04c Similar shapes Compare lengths, areas and volumes using ratio notation and scale factors. Apply similarity to calculate unknown lengths in similar figures. [see also Direct proportion, 5.02a] Understand the relationship between lengths, areas and volumes of similar shapes. [see also Direct proportion, 5.02a] OCR 10 Mensuration 10.01 Units and measurement 10.01a Units of measurement Use and convert standard units of measurement for length, area, volume/capacity, mass, time and money. Use and convert standard units in algebraic contexts. 10.01b Compound units Use and convert simple compound units (e.g. for speed, rates of pay, unit pricing). Know and apply in simple cases: speed = distance ÷ time Use and convert other compound units (e.g. density, pressure). Know and apply: density = mass ÷ volume Use and convert compound units in algebraic contexts. 10.01c Maps and scale drawings Use the scale of a map, and work with bearings. Construct and interpret scale drawings. 10.02 Perimeter calculations 10.02a Perimeter of rectilinear shapes Calculate the perimeter of rectilinear shapes.
11.01d Equally likely outcomes and probability 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. 11.02 Combined events and probability diagrams 11.02a Sample spaces Use tables and grids to list the outcomes of single events and simple combinations of events, and to calculate theoretical probabilities. e.g. Flipping two coins. Finding the number of orders in which the letters E, F and G can be written. Use sample spaces for more complex combinations of events e.g. Recording the outcomes for sum of two dice. Problems with two spinners. Recognise when a sample space is the most appropriate form to use when solving a complex probability problem. Use the most appropriate diagrams to solve unstructured questions where the route to the solution is less obvious. 11.02b Enumeration Use systematic listing strategies. Use the product rule for counting numbers of outcomes of combined events.