Year 11: AQA AS Mathematics 7356

Listed Mathematics content statements at AS, in the words of the AQA, with the practice on this site that covers it. Checked against the source on 7 September 2026.

Content statements from the AQA AS Mathematics specification (7356), version 1.3. AS content is a subset of the A-level: the statement numbering has gaps where a statement belongs to the full A-level only. Superscripts the PDF text layer does not carry have been restored.

52content statements
164skills mapped
88%have practice

Coverage is the percentage of listed content statements with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one content statement, so some appear more than once below.

A: Proof

A1Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion. Disproof by counter example.
- Geometric proofs - circle theorems
- Geometric proofs - Pythagoras theorem

B: Algebra and functions

B1Understand and use the laws of indices for all rational exponents.
B2Use and manipulate surds, including rationalising the denominator.
- Simplify nested surds
- Rationalise a binomial surd denominator
B3Work with quadratic functions and their graphs; the discriminant of a quadratic function, including the conditions for real and repeated roots; completing the square; solution of quadratic equations including solving quadratic equations in a function of the unknown.
B4Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation.
B5Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions. Express solutions through correct use of ‘and’ and ‘or’, or through set notation. Represent linear and quadratic inequalities such as y>x+1 and y>ax²+bx+c graphically.
B6Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the factor theorem.
B7Understand and use graphs of functions; sketch curves defined by simple equations including polynomials, y=a/x and y=a/x² (including their vertical and horizontal asymptotes); interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations. Understand and use proportional relationships and their graphs.
B9Understand the effect of simple transformations on the graph of y=f(x) including sketching associated graphs: y=af(x), y=f(x)+a, y=f(x+a), y=f(ax)

C: Coordinate geometry in the (x, y) plane

C1Understand and use the equation of a straight line, including the forms y-y_1=m(x-x_1) and ax+by+c=0; gradient conditions for two straight lines to be parallel or perpendicular. Be able to use straight line models in a variety of contexts.
C2Understand and use the coordinate geometry of the circle including using the equation of a circle in the form (x-a)²+(y-b)²=r²; completing the square to find the centre and radius of a circle; use of the following properties:the angle in a semicircle is a right anglethe perpendicular from the centre to a chord bisects the chordthe radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point.

D: Sequences and series

D1Understand and use the binomial expansion of (a+bx)ⁿ for positive integer n; the notations n!, nCr and (nr); link to binomial probabilities.
- Rationalise a binomial surd denominator
- Binomial theorem problem solving and identities

E: Trigonometry

E1Understand and use the definitions of sine, cosine and tangent for all arguments; the sine and cosine rules; the area of a triangle in the form 1/2absin C
E3Understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity.
E5Understand and use tanθ≡(sinθ)/(cosθ) Understand and use sin²θ+cos²θ≡1
- Co-function identities
- Angle sum and difference identities
E7Solve simple trigonometric equations in a given interval, including quadratic equations in sin, cos and tan and equations involving multiples of the unknown angle.

F: Exponentials and logarithms

F1Know and use the function a^x and its graph, where a is positive. Know and use the function e^x and its graph.
No practice for this one yet.
F2Know that the gradient of e^(kx) is equal to ke^(kx) and hence understand why the exponential model is suitable in many applications.
- Graph features of translated exponential functions
F3Know and use the definition of log_ax as the inverse of a^x, where a is positive and x≥0 Know and use the function lnx and its graph. Know and use lnx as the inverse function of e^x
F4Understand and use the laws of logarithms: log_ax+log_ay≡log_a(xy); log_ax-log_ay≡log_a(x/y); klog_ax≡log_ax^k (including, for example, k=-1 and k=-1/2)
F5Solve equations of the form a^x=b
No practice for this one yet.
F6Use logarithmic graphs to estimate parameters in relationships of the form y=axⁿ and y=kb^x, given data for x and y .
F7Understand and use exponential growth and decay; use in modelling (examples may include the use of e^ in continuous compound interest, radioactive decay, drug concentration decay, exponential growth as a model for population growth); consideration of limitations and refinements of exponential models.
- Graph features of translated exponential functions

G: Differentiation

G1Understand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; second derivatives; differentiation from first principles for small positive integer powers of x Understand and use the second derivative as the rate of change of gradient.
G2Differentiate xⁿ, for rational values of n, and related constant multiples, sums and differences.
G3Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points. Identify where functions are increasing or decreasing.

H: Integration

H1Know and use the Fundamental Theorem of Calculus.
No practice for this one yet.
H2Integrate xⁿ (excluding n = -1), and related sums, differences and constant multiples.
H3Evaluate definite integrals; use a definite integral to find the area under a curve.
- Indefinite integration of polynomials
- Definite integration

J: Vectors

J1Use vectors in two dimensions.
J2Calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form.
J3Add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical interpretations.
J4Understand and use position vectors; calculate the distance between two points represented by position vectors.
J5Use vectors to solve problems in pure mathematics and in context, including forces.

K: Statistical sampling

K1Understand and use the terms ‘population’ and ‘sample’. Use samples to make informal inferences about the population. Understand and use sampling techniques, including simple random sampling and opportunity sampling. Select or critique sampling techniques in the context of solving a statistical problem, including understanding that different samples can lead to different conclusions about the population.
- Sample spaces, events and outcomes

L: Data presentation and interpretation

L1Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency. Connect to probability distributions.
L2Interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population (calculations involving regression lines are excluded). Understand informal interpretation of correlation. Understand that correlation does not imply causation.
- Summary and spread of data
- Understanding scatter plots
L3Interpret measures of central tendency and variation, extending to standard deviation. Be able to calculate standard deviation, including from summary statistics.
No practice for this one yet.
L4Recognise and interpret possible outliers in data sets and statistical diagrams. Select or critique data presentation techniques in the context of a statistical problem. Be able to clean data, including dealing with missing data, errors and outliers.
- Summary and spread of data
- Box plot outlier fences

M: Probability

M1Understand and use mutually exclusive and independent events when calculating probabilities. Link to discrete and continuous distributions.

N: Statistical distributions

N1Understand and use simple, discrete probability distributions (calculation of mean and variance of discrete random variables is excluded), including the binomial distribution, as a model; calculate probabilities using the binomial distribution.
- Discrete probability distributions
- Normal distribution probabilities and quantiles

O: Statistical hypothesis testing

O1Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p -value.
No practice for this one yet.
O2Conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context. Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis.
No practice for this one yet.

P: Quantities and units in mechanics

P1Understand and use fundamental quantities and units in the SI system: length, time, mass. Understand and use derived quantities and units: velocity, acceleration, force, weight.
- Quantities and units in mechanics

Q: Kinematics

Q1Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration.
- The language of kinematics
Q2Understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph.
- Motion graphs
- Interpreting a tanget to a graph
Q3Understand, use and derive the formulae for constant acceleration for motion in a straight line.
- Constant acceleration formulae
Q4Use calculus in kinematics for motion in a straight line: v=(dr)/(dt), a=(dv)/(dt)=(d²r)/(dt²), r=∫vdt, v=∫adt .
- Calculus in kinematics

R: Forces and Newton's laws

R1Understand the concept of a force; understand and use Newton’s first law.
- Forces and Newton's first law
R2Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2D vectors).
- Newton's second law
R3Understand and use weight and motion in a straight line under gravity; gravitational acceleration, g, and its value in SI units to varying degrees of accuracy.(The inverse square law for gravitation is not required and g may be assumed to be constant, but students should be aware that g is not a universal constant but depends on location).
- Weight and motion under gravity
R4Understand and use Newton’s third law; equilibrium of forces on a particle and motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2D vectors); application to problems involving smooth pulleys and connected particles.
- Newton's third law and connected bodies

Other Year 11 skills

Year 11 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.