Maths Grade Descriptors - Algebra
Year 7
Year 8
Year 9
Year 10
Year 11
Notation, vocabulary and manipulation
use and interpret algebraic notation, including: use and interpret algebraic notation, including:
ab in place of a × b, 3y in place of y + y + y and a²b in place of a × a × b, coefficients written as
3 × y, a² in place of a × a, a³ in place of a × a × a, fractions rather than as decimals
a/b in place of a ÷ b, brackets
substitute numerical values into formulae and
expressions
understand and use the concepts and
vocabulary of expressions, equations, formulae
and terms
substitute numerical values into scientific
formulae
understand and use the concepts and
vocabulary of inequalities and factors
simplify and manipulate algebraic expressions
by collecting like terms
simplify and manipulate algebraic expressions
by taking out common factors and simplifying
expressions involving sums, products and
powers, including the laws of indices
Colour code
understand and use the concepts and
vocabulary of identities
simplify and manipulate algebraic expressions
by expanding products of two binomials
including difference of 2 squares
simplify and manipulate algebraic expressions
by multiplying a single term over a bracket and
factorize linear expression
understand and use standard mathematical
formulae
simplify and manipulate algebraic expressions Simplify and manipulate algebraic fractions
by factorising quadratic expressions of the
including factorizing quadratic expressions
form x² + bx + c, including the difference of two
squares
simplify and manipulate algebraic expressions
by expanding products (including those
involving surds and algebraic fractions) of two
binomials including difference of 2 squares
rearrange formulae to change the subject of
simple linear equations
rearrange formulae to change the subject
involving powers and surds
simplify and manipulate algebraic expressions
by expanding products of more than two
binomials
know the difference between an equation and
an identity
argue mathematically to show algebraic
expressions are equivalent, and use algebra to
support and construct arguments
where appropriate, interpret simple
expressions as functions with inputs and
outputs
work with coordinates in all four quadrants
use the form y = mx + c to identify parallel
lines
use the form y = mx + c to identify
perpendicular lines
find the gradient of a drawn line and write its
equation
find the equation of the line through two given
points, or through one point with a given
gradient
identify and interpret roots, intercepts, turning
points of quadratic functions graphically
identify and interpret gradients and intercepts
of linear functions graphically and algebraically
Graphs
recognise , sketch and interpret graphs of
linear functions
recognise, sketch and interpret graphs of
quadratic functions
plot and interpret graphs of non-standard
functions in real contexts, to find approximate
solutions to problems such as distance - time
graphs
Grade 7 to
Grade 9
rearrange formulae to change the subject when
it appears more than once
write algebraic proofs
interpret the reverse process as the ‘inverse
function’
plot graphs of equations that correspond to
straight-line graphs in the coordinate plane
deduce roots of quadratic functions
algebraically
recognise, sketch and interpret graphs of
simple cubic functions and the reciprocal
function y = 1/x with x ≠ 0
plot and interpret graphs (including reciprocal
graphs) and graphs of non-standard functions
in real contexts, to find approximate solutions
to problems such as simple kinematic
problems involving distance, speed and
acceleration
interpret the succession of two functions as a
‘composite function’
deduce turning points of quadratic functions by
completing the square
recognise, sketch and interpret graphs of
exponential functions y = k^x for positive values
of k, and the trigonometric functions (with
arguments in degrees) y = sin x, y = cos x and y
= tan x for angles of any size
sketch translations and reflections of a given
function
plot and interpret graphs (including exponential
graphs) and graphs of non-standard functions
in real contexts, to find approximate solutions
to problems such as simple kinematic problems
involving distance, speed and acceleration
Sequences
Solving equations and inequalities
calculate or estimate gradients of graphs and
areas under graphs (including quadratic and
other non-linear graphs), and interpret results
in cases such as distance-time graphs, velocitytime graphs and graphs in financial contexts
solve linear equations in one unknown
algebraically
recognise and use the equation of a circle with
centre at the origin
find the equation of a tangent to a circle at a
given point
solve equations with algebraic fractions
solve linear equations with the unknown on
both sides of the equation
find approximate solutions to linear equations
using a graph
solve two linear simultaneous equations in two solve two linear simultaneous equations in two
variables algebraically
variables algebraically where both equations
need to be multiplied
find approximate solutions to simultaneous
equations using a graph
solve quadratic equations (including those that
require rearrangement) algebraically by
factorising
find approximate solutions to quadratic
equations using a graph
find approximate solutions to equations
numerically using iteration
translate simple situations or procedures into
algebraic expressions or formulae
derive an equation , solve the equation and
derive two simultaneous equations, solve the
interpret the solution
equations and interpret the solution
solve two simultaneous equations in two
variables where one is quadratic algebraically
solve linear inequalities in one variable
solve quadratic inequalities in one variable
solve linear inequalities in two variables
represent the solution set to an inequality on a represent the solution set to an inequality
number line
using set notation and on a graph
generate terms of a sequence from a term-toterm rule
generate terms of a sequence from either a
term-to-term or a position-to-term rule
deduce expressions to calculate the nth term
of linear sequences.
recognise and use sequences of triangular,
square and cube numbers, simple arithmetic
progressions
recognise and use Fibonacci type sequences,
quadratic sequences,
deduce expressions to calculate the nth term
of quadratic sequences
recognise and use simple geometric
progressions (r^n where n is an integer, and r is
a rational number > 0 )
Grade 1 to
Grade 3
Grade 4 to
Grade 6
solve quadratic equations by completing the
square and by using the quadratic formula
Old GCSE level
Grade G to
Grade D
Grade D+ to
Grade B+
Grade A-A*