GCSE Topics by grade
Grade A* skills are …

Calculating bounds in area and volume questions

Manipulating complex indices, including surds

Solving simultaneous equations – one linear and one quadratic

Using equation of a circle and finding points of intersection with a line

Transforming graphs of trigonometrical functions

Knowing graphs of exponential and more complex functions

Manipulating algebraic fractions

Rearranging complex equations

Transforming graphical functions, e.g. y = f(x+a); y = f(ax)

Solving 3D trigonometry problems

Using the sine and cosine rule

Mensuration in 3D solids and 2D shapes

Knowing proofs of circle theorems

Knowing proofs of construction theorems
Grade A skills are …

Rationlising surds

Calculating upper and lower bounds

Manipulating fractional indices

Rearranging formulae where the variable occurs twice

Manipulating simple algebraic fractions, e.g. + –

Solving algebraic problems, e.g. explain why (n+1)(n+20) is an even number

Solving quadratics by factorising, formula or completing the square

Solving equations graphically

Recognising the difference of two squares

Simplifying algebra involving powers

Calculating equation of line through a point and perpendicular to a given line

Finding trigonometrical solutions, e.g. cosx = 0∙5

Recognising graphs of trigonometrical functions

Using the sine and cosine rule in simple cases

Calculating surface area or volume of various solids

Solving problems involving arcs, sectors and segments

Using Pythagoras’ Theorem in 3D situations

Using similarity in length, area and volume

Calculating the distance between points using 3D coordinates

Proving that triangles are congruent

Using circle theorems

Carrying out an enlargement with a negative fractional scale factor

Using the fact that the area of triangle = ½absinC

Constructing and interpreting histograms

Understand stratified sampling

Find probability for combined events using multiplication and addition
Grade B skills are …

Calculating compound interest

Calculating reverse percentage problems

Calculating with fractions and mixed numbers

Calculating problems involving numbers in standard form

Understanding negative indices

Recognising the difference of 2 squares

Solving inequalities by algebraic or graphical methods

Solving simultaneous equations by graphical or algebraic methods

Matching equations to their graphs

Solving simple quadratics by factorising

Solving equations involving fractions

Expanding brackets

Using y=mx+c to find the gradient and equation of a line without drawing

Solving cubic equations graphically (when the graph is given)

Solving quadratic equations graphically

Recognising graphs of cubic and reciprocal functions

Simplifying fractions where the denominator is an algebraic expression

Factorising expressions, e.g. 6(ab)² – 3(ab)

Using circle theorems

Understanding similar shapes

Solving multistage trigonometrical problems

Describing transformations

Finding interior and exterior angles of polygons

Finding dimensions of a formulae

Using tree diagrams for probability

Analysing data to compare with theoretical results

Drawing box plots from a cumulative frequency table

Finding median and interquartile rangefrom cumulative frequency table or graph
Grade C skills are …

Estimation and division by a number less than 1

Calculating compound interest – no rounding necessary

Using a calculator in complex situations

Multiplication and division by a number between 0 and 1

Calculating with fractions

Calculating with ratios

Calculating percentage decrease and increase

Multiplication and division by powers of 10 and decimals

Finding the prime factor decomposition of a number

Using the rules of indices in numeric situations

Solving cubic equations by trial and improvement

Rearranging simple formulae

Solving equations

Solving inequalities

Expanding brackets and simplifying the result

Graphing quadratic functions in simple cases

Interpreting reallife graphs, e.g. travel graphs

Finding the n^{th} term for a linear sequence

Finding the length of a line given 2 points

Substitution into complex formulae

Constructing the perpendicular bisector of a given line

Constructing loci

Finding volumes of 3D shapes including prisms

Calculating area or circumference of a circle from diameter

Carry out transformations including translation with vectors

Use of Pythagoras’ Theorem and trigonometry

Carrying out constructions, e.g. triangles in all situations

Solving problems involving polygons, e.g. interior angles

Understanding, using and solving problems with bearings

Drawing box plots

Calculating moving averages

Finding mean and median from grouped data

Designing questionnaires

Explaining the use of different averages
Grade D skills are …

Estimation

Calculating profit and loss

Solving problems involving proportion in simple cases

Calculating an increase or decrease by a percentage

Calculating with fractions in simple cases

Calculating with ratios in recipes

Expanding brackets such as x(x+4)

Factorising, e.g. x² – 5x and 12x – 8

Understanding unstructured linear graphs

Deriving and solving equations from diagrams

Substituting negative numbers into algebraic expressions

Expanding and simplifying brackets and expressions

Solving equations, including unknowns on both sides

Converting between units of area, e.g. m² to cm²

Calculating area or circumference of a circle given radius

Finding area of triangle, regular polygons, compound shapes

Drawing and measuring bearings

Finding midpoint of a line given the end coordinates

Carrying out simple transformations

Solving simple problems involving polygons

Solving problems involving similar triangles (+ve scale factor)

Constructing and interpreting plans and elevations

Solving problems involving parallel lines

Knowing triangle proofs (exterior angle & anglesum)

Constructing a stem and leaf diagram

Understanding and using relative frequency

Finding missing probability from a list or table of results

Constructing and interpreting scatter graphs

Drawing and using lines of best fit

Understanding correlation

Finding the modal class from grouped frequencies

Finding the mean from a discrete frequency distribution

Explaining deficiencies in questionnaires and sampling techniques
Grade E skills are …

Simplifying ratios

Using a calculator, e.g. ‘1∙5³’ and ‘square root of 23∙78’

Rounding to 1 significant figure

Calculating with fractions in simple cases

Long multiplication and division, including decimals

Finding percentages by mental methods

Ordering fractions, decimals and percentages

Calculating indices and roots, e.g. ‘4³’, ‘2³ x 3²’, ‘the cube of 4’

Using the four rules with negative numbers

Calculating VAT

Constructing simple linear graphs

Simplifying simple algebra

Using a formula inversely, e.g. find x if y=3 where y = 2x1

Using conversion graphs

Recognising complex number sequences

Solving simple equations, e.g. 3y + 2 = 8

Understanding the geometry of triangles and quadrilaterals

Measuring simple bearings

Carrying out enlargements in simple cases

Converting between metric and imperial units using known facts

Calculating volumes in simple cases

Completing tessellations

Finding area and perimeter of rectangles and kites

Identifying planes of symmetry

Working with nets of shapes

Constructing accurate drawings and angles

Carrying out simple transformations

Interpreting a stem and leaf diagram to find the median

Interpreting a time series graph

Using data collection sheets

Finding probabilities from a 2way table

Using the fact that the sum of probabilities is 1

Using ‘fx’ in a frequency table

Constructing a pie chart
Grade F skills are …

Carrying out long multiplication and division: 3digit by 2digit

Calculating simple percentages of quantities

Calculating simple fractions of quantities

Understanding the order of operations

Rounding to various decimal places

Understanding place value

Finding simple squares, cubes and roots

Finding factors of numbers

Converting between fractions, decimals and percentages

Using negative numbers in context

Finding terms in a linear sequence

Recognising nonlinear number sequences

Using coordinates in four quadrants

Using simple formulae

Solving simple equations, e.g. 5x = 25 and x2=6

Deriving simple expressions

Estimating lengths

Using simple scale drawings

Naming, measuring and drawing angles

Naming polygons

Identifying lines of symmetry

Identifying rotational symmetry

Using the angle sum on a straight line = 180º

Identifying faces, edges and vertices

Stating simple probability

Listing all outcomes for a single event

Estimating probability from diagrams, pie charts and tables

Finding range, and using to compare two distributions

Finding mean and mode

Interpreting pie charts

Using bar charts to compare two sets of data
Grade G skills are …

Rounding to the nearest integer

Interpreting bills and timetables

Rounding to the nearest 10,100, 1000

Identifying fractions from a shaded diagram

Identifying percentages from a shaded diagram

Calculating simple fractions of quantities (numerator of 1)

Ordering decimals

Ordering, reading and writing whole numbers

Converting fractions to a ratio, e.g. 1/3 of a whole is 1:2

Using coordinates in one quadrant

Reading from simple reallife graphs

Finding the next term in a simple linear sequence

Finding areas, perimeters and volumes by counting

Drawing 2D shapes

Measuring and drawing lines

Drawing circles

Naming shapes

Drawing lines of symmetry on a diagram

Using a given line of reflection

Completing accurate drawings of given shapes

Finding median and mode using single digits

Drawing and interpreting line graphs, bar charts and pictograms

Making tables, lists and tally charts from discrete data

Being able to choose the ‘most likely’ outcome from given information
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