GCSE Grade Descriptors
| grade | Number | Algebra |
| A* | Bounds in area/volume questions Complex indices, including surds |
Solve equations, one linear and one quadratic Equation of circle and intersection points with line Trig functions Exponential/complex functions Algebraic fractions Rearrange complex equations Graphical functions, y = f(x+a); y = f(ax) |
| A | Rationlising surds Upper/lower bounds Fractional indices |
Rearrange equations/formulae, variable twice Simple algebraic fractions, + - Algebraic problems, explain why (n+1)(n+20) is an even number Solve quadratics by, factorizing, formula or completing the square Solve equations graphically Difference of two squares Simplify algebra involving powers Equation of line through point and perpendicular to a given line |
| B | Compound Interest Reverse % Fractions, any form Standard form Negative Indices |
Difference of 2 squares Solve inequalities by algebra/graphical Simultaneous equations by graph/algebra Match equations to graphs Solve quadratics by factorizing, a =1 Solve equations, involving fractions Expand brackets and simplify Use y=mx+c to find the gradient and equation without drawing Solve cubic graphically (graph given) Solve quadratic graphically. Table and graphs, cubic and reciprocal Cancelling down where denominator is an algebraic expression Factorising various expressions, 6(a-b)² - 3(a-b) |
| C | Estimation, division by number less than 1 Compound interest, no rounding necessary Calculator use, complex Multiplication/division by number between 0 and 1 Fractions Ratios % decrease/increase Multiplication/division by powers of 10 and decimals Prime factors as indices Rules of indices, numeric but not ‘0’ |
Trial and improvement, cubic Simple rearrangement Solve equations Solve inequalities Expand brackets and simplify Quadratic tables and graphs Real life graphs, water filling, travel graphs Nth term linea rFind length of a line given 2 points Substitution into complex formulae |
| D | Estimation Profit/loss Simple proportion Increase/decrease by given % Fractions Ratios in recipes questions |
Expand x(x+4) Factorise x² - 5x, 12x – 8 Unstructured linear graphs Derive equations from diagrams and solve Substituting negative numbers into algebraic expressions Expand and simplify brackets and expressions Solve equations, variable on each side, brackets involved |
| E | Simplifying ratios Use of calculator, 1·5³; square root of 23·78 Rounding to 1 s.f. FractionsLong multiplication/division, involving decimals % without calculator Ordering fractions/decimals/percentages Indices/powers/roots, 4³, 2³ x 3², the cube of 4 Four rules of negative numbers Calculate VAT |
Linear table and graph Simplify simple algebra Use a formula inversely, find x if y=3 in the formula y = 2 -1 Conversion graphs Complex number sequences Solve equations 3y + 2 = 8 |
| F | Long multiplication/division, 3 digit by 2 digit Simple %/fraction of quantity BODMAS Rounding to d.p. Place value Simple squares/cubes/roots Number factors Convert %/fractions/decimals Negative numbers in context |
Finding terms in a linear sequence Non-linear number sequences Co-ordinates in 4 quadrants Use simple formula Solve equations 5x = 25, x-2=6 Derive simple expressions |
| G | Rounding to the nearest integer Bills/timetables Rounding to the nearest 10,100,etc Fraction/% shaded, from a diagram Simple number terms Simple fractions of quantities, numerator of 1 Ordering decimals Order/read/write whole numbers Convert to a ratio, 1/3 of a whole is 1:2 |
Co-ordinates in the 1st quadrant Reading from real life graphs Next term in a simple linear sequence |
| grade | Shape, space & measure | Handling Data |
| A* | Trig in 3-d Sine/cosine rule Mensuration in 3D solids and 2D shapes Proof of circle theorems Proof of construction theorems |
|
| A | Trig solutions, cosx = 0·5 Trig graphs Sine and cosine rule Surface area/volume of various solids Arcs/sectors/segments Trig/Pythagoras in 3D Similarity between length/area/volume Calculate distance between points using 3D co-ordinates Prove that triangles are congruent Circle theorems Enlargement, negative fractional scale factor Area of triangle = ½absinC |
Histograms Sampling, stratified sampling Combined events, using multiplication
|
| B | Use of circle theorems Similar shapes Trig – multistage Describing transformations Interior/Exterior angles of polygons – tessellations Dimensions of formulae |
Tree diagrams Use of 1-n Analysing data to compare with theoretical results Draw box plots from cumulative frequency table Median/IQR from cumulative frequency table/graph |
| C | Construct perpendicular bisector of a given line Loci Volumes Circles, area & circumference given diameter Transformations - Translation using vectors Trig/Pythagoras Formal constructions Polygons Bearings |
Draw box plot Moving averages Mean/median from grouped data Designing questionnaires Explain the use of mean, median, mode, etc |
| D | Area unit convert, m² to cm² Area/circumference of circles given radius Area of triangle/regular polygons/compound shapes Draw and measure bearings Midpoint of line given end co-ordinates Simple transformations Polygons Similar triangles, positive scale factor Plan and elevation Parallel lines and shapes linked with the same Triangle proofs, exterior angle property |
Construct a stem and leaf diagram Relative probability Find missing probability from list/table of results Scatter graph Draw and use lines of best fit Correlation Mode from grouped frequencies Mean from a discrete frequency distribution Explain defiencies in questionnaires/sampling techniques/practical techniques |
| E | Geometry of triangle/quadrilateral Measure simple bearings Enlargements Metric/Imperial conversions using known facts Simple volume calculations Complete tessellations Area/Perimeter of rectangles/kites Planes of symmetry Nets of shapes Accurate drawings/angles from given information Simple transformations |
Interpret a stem and leaf diagram to find the median Interpret a time series graph Data collection sheets Find probabilities from 2 way table Probability of not = 1-n Use fx in a frequency table Construct a pie chart |
| F | Estimate lengths Co-ordinates in all 4 quadrants Simple scale drawings Name/measure and draw angles Name polygons Lines of symmetry Rotational symmetry Angles on a straight line = 180 Faces/edges/vertices |
State simple probability List all outcomes Estimate probability from diagram/pie chart/table Find range, also comparing two distributions Find mean/mode Use pie chart Use Bar charts to compare 2 sets of data |
| G | Area/Perimeter/volume by counting Draw 2D shapes Measure/draw a line/circle Name shapes Draw line of symmetry Use given line of reflection Accurate drawings of given shapes |
Find median/mode using single digits Draw and interpret line graphs/bar charts/pictograms Make tables/lists/tally charts, discrete data Able to choose the ‘most likely’ from information given |
|