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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 co-ordinates

  • 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(a-b)² – 3(a-b)

  • Using circle theorems

  • Understanding similar shapes

  • Solving multi-stage 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 inter-quartile 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 real-life graphs, e.g. travel graphs

  • Finding the nth 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 co-ordinates

  • 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 & angle-sum)

  • 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 = 2x-1

  • 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 2-way 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:  3-digit by 2-digit

  • 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 non-linear number sequences

  • Using co-ordinates in four quadrants

  • Using simple formulae

  • Solving simple equations, e.g. 5x = 25 and x-2=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 co-ordinates in one quadrant

  • Reading from simple real-life 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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