Specification checklist Every statement in the Pearson Edexcel 9MA0 specification. Tick what you're confident with; ticks are saved in this browser only. Each statement links to the past-paper questions that assess it.
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Pure P2 Algebra and functions P2.1 Indices AS and A level Understand and use the laws of indices for all rational exponents. Questions: Indices and surds P2.2 Surds AS and A level Use and manipulate surds, including rationalising the denominator. Questions: Indices and surds P2.3 Quadratics AS and A level Work 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. Questions: Quadratics and the discriminant P2.4 Simultaneous equations AS and A level Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation. Questions: Simultaneous equations P2.5 Inequalities AS and A level Solve 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. Questions: Inequalities P2.6 Polynomials & factor theorem Partly A level only Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the factor theorem. Simplify rational expressions, including by factorising and cancelling, and algebraic division (by linear expressions only). A-level-only part: simplifying rational expressions (factorising and cancelling, algebraic division by linear expressions) Questions: Algebraic methods: polynomials, factor theorem and division P2.7 Graphs of functions, modulus, proportion Partly A level only Understand and use graphs of functions; sketch curves defined by simple equations including polynomials, the modulus of a linear function, 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. A-level-only part: the modulus of a linear function, y = |ax + b| Questions: Graphs and transformations P2.8 Composite & inverse functions A level only Understand and use composite functions; inverse functions and their graphs. Questions: Functions, composite and inverse functions, modulus P2.9 Transformations of graphs Partly A level only Understand 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) and combinations of these transformations A-level-only part: graphs of y = |f(x)| and y = |f(−x)|; transformations of the A-level-only functions Questions: Graphs and transformations P2.10 Partial fractions A level only Decompose rational functions into partial fractions (denominators not more complicated than squared linear terms and with no more than 3 terms, numerators constant or linear). Questions: Partial fractions P2.11 Modelling with functions A level only Use of functions in modelling, including consideration of limitations and refinements of the models. Questions: Functions, composite and inverse functions, modulus P3 Coordinate geometry in the (x, y) plane P5 Trigonometry P5.1 Sine & cosine rules, radians, arcs & sectors Partly A level only Understand 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 ½ab sin C. Work with radian measure, including use for arc length and area of sector. A-level-only part: radian measure, arc length and sector area Questions: Trigonometric ratios, graphs, radians and the sine and cosine rules P5.2 Small angle approximations A level only Understand and use the standard small angle approximations of sine, cosine and tangent: sin θ ≈ θ, cos θ ≈ 1 − θ²/2, tan θ ≈ θ, where θ is in radians. Questions: Small-angle approximations P5.3 Trig graphs & exact values Partly A level only Understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. Know and use exact values of sin and cos for 0, π/6, π/4, π/3, π/2, π and multiples thereof, and exact values of tan for 0, π/6, π/4, π/3, π and multiples thereof. A-level-only part: exact values of sin, cos and tan (given in radians) Questions: Trigonometric ratios, graphs, radians and the sine and cosine rules P5.4 sec, cosec, cot; inverse trig A level only Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; their relationships to sine, cosine and tangent; understanding of their graphs; their ranges and domains. Questions: Reciprocal and inverse trigonometric functions P5.5 Trig identities (tan, Pythagorean) Partly A level only Understand and use tan θ = sin θ / cos θ. Understand and use sin²θ + cos²θ = 1; sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ. A-level-only part: sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ Questions: Trigonometric identities and proofs P5.6 Compound & double angles; R cos(θ ± α) A level only Understand and use double angle formulae; use of formulae for sin(A ± B), cos(A ± B) and tan(A ± B); understand geometrical proofs of these formulae. Understand and use expressions for a cos θ + b sin θ in the equivalent forms of r cos(θ ± α) or r sin(θ ± α). Questions: Addition and double-angle formulae, harmonic form P5.7 Solving trig equations AS and A level Solve simple trigonometric equations in a given interval, including quadratic equations in sin, cos and tan and equations involving multiples of the unknown angle. Questions: Solving trigonometric equations P5.8 Trig proofs A level only Construct proofs involving trigonometric functions and identities. Questions: Trigonometric identities and proofs P5.9 Trig in context A level only Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces. Questions: Trigonometric modelling P6 Exponentials and logarithms P6.1 Exponential functions Partly A level only Know and use the function aˣ and its graph, where a is positive. Know and use the function eˣ and its graph. A-level-only part: the graph of y = e^(ax + b) + c Questions: Exponentials and logarithms P6.2 Gradient of eᵏˣ AS and A level Know that the gradient of eᵏˣ is equal to keᵏˣ and hence understand why the exponential model is suitable in many applications. Questions: Exponentials and logarithms P6.3 Logarithms & ln x AS and A level Know and use the definition of logₐ x as the inverse of aˣ, where a is positive and x ⩾ 0 (as printed in the spec). Know and use the function ln x and its graph. Know and use ln x as the inverse function of eˣ. Questions: Exponentials and logarithms P6.4 Laws of logarithms AS and A level Understand and use the laws of logarithms: logₐ x + logₐ y = logₐ(xy); logₐ x − logₐ y = logₐ(x/y); k logₐ x = logₐ xᵏ (including, for example, k = −1 and k = −½). Questions: Exponentials and logarithms P6.5 Solving aˣ = b AS and A level Solve equations of the form aˣ = b. Questions: Exponentials and logarithms P6.6 Log graphs (y = axⁿ, y = kbˣ) AS and A level Use logarithmic graphs to estimate parameters in relationships of the form y = axⁿ and y = kbˣ, given data for x and y. Questions: Exponentials and logarithms P6.7 Exponential growth & decay models AS and A level Understand 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. Questions: Exponential growth, decay and modelling P7 Differentiation P7.1 Derivative, first principles, 2nd derivative, convexity Partly A level only Understand 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 and for sin x and cos x. Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection. A-level-only part: first principles for sin x and cos x; second derivative as rate of change of gradient, convex/concave sections and points of inflection Questions: Differentiation: first principles, gradients, stationary points P7.2 Differentiating standard functions Partly A level only Differentiate xⁿ, for rational values of n, and related constant multiples, sums and differences. Differentiate eᵏˣ and aᵏˣ, sin kx, cos kx, tan kx and related sums, differences and constant multiples. Understand and use the derivative of ln x. A-level-only part: differentiating eᵏˣ, aᵏˣ, sin kx, cos kx, tan kx and ln x Questions: Differentiation: first principles, gradients, stationary points P7.3 Tangents, normals, stationary points Partly A level only Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points, points of inflection. Identify where functions are increasing or decreasing. A-level-only part: points of inflection Questions: Differentiation: first principles, gradients, stationary points P7.4 Product, quotient & chain rules; connected rates A level only Differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions. Questions: Chain, product and quotient rules; connected rates of change P7.5 Implicit & parametric differentiation A level only Differentiate simple functions and relations defined implicitly or parametrically, for first derivative only. Questions: Implicit and parametric differentiation P7.6 Forming differential equations A level only Construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand). Questions: Differential equations P8 Integration P8.1 Fundamental theorem of calculus AS and A level Know and use the Fundamental Theorem of Calculus Questions: Integration: standard integrals, definite integrals and areas P8.2 Integrating standard functions Partly A level only Integrate xⁿ (excluding n = −1) and related sums, differences and constant multiples. Integrate eᵏˣ, 1/x, sin kx, cos kx and related sums, differences and constant multiples. A-level-only part: integrating eᵏˣ, 1/x, sin kx and cos kx Questions: Integration: standard integrals, definite integrals and areas P8.3 Definite integrals & areas Partly A level only Evaluate definite integrals; use a definite integral to find the area under a curve and the area between two curves. A-level-only part: the area between two curves; curves defined parametrically Questions: Integration: standard integrals, definite integrals and areas P8.4 Integration as limit of a sum A level only Understand and use integration as the limit of a sum. Questions: Integration: standard integrals, definite integrals and areas P8.5 Substitution & by parts A level only Carry out simple cases of integration by substitution and integration by parts; understand these methods as the inverse processes of the chain and product rules respectively (Integration by substitution includes finding a suitable substitution and is limited to cases where one substitution will lead to a function which can be integrated; integration by parts includes more than one application of the method but excludes reduction formulae.) Questions: Integration by parts and by substitution P8.6 Integration with partial fractions A level only Integrate using partial fractions that are linear in the denominator. Questions: Partial fractions P8.7 Solving separable differential equations A level only Evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions (Separation of variables may require factorisation involving a common factor.) Questions: Differential equations P8.8 Interpreting differential equations A level only Interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution; includes links to kinematics. Questions: Differential equations Statistics S2 Data presentation and interpretation S2.1 Single-variable data diagrams AS and A level Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency. Connect to probability distributions. Questions: Data presentation: histograms, box plots, measures and outliers S2.2 Scatter, regression & correlation Partly A level only Interpret 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. A-level-only part: predictions within the range of the explanatory variable; change of variable using logarithms Questions: Correlation and regression S2.3 Averages, spread, standard deviation AS and A level Interpret measures of central tendency and variation, extending to standard deviation. Be able to calculate standard deviation, including from summary statistics. Questions: Data presentation: histograms, box plots, measures and outliers S2.4 Outliers & cleaning data AS and A level Recognise 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. Questions: Data presentation: histograms, box plots, measures and outliers S4 Statistical distributions S5 Statistical hypothesis testing S5.1 Hypothesis-test language; correlation tests Partly A level only Understand 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; extend to correlation coefficients as measures of how close data points lie to a straight line and be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded). A-level-only part: correlation coefficients: interpreting r with a p-value or critical value, hypotheses on ρ Questions: Hypothesis testing S5.2 Binomial hypothesis test AS and A level Conduct 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. Questions: Hypothesis testing S5.3 Test for a Normal mean A level only Conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context. Questions: Hypothesis testing Mechanics M6 Quantities and units in mechanics M8 Forces and Newton’s laws M8.1 Forces; Newton’s first law AS and A level Understand the concept of a force; understand and use Newton’s first law. Questions: Forces, Newton's laws and connected particles M8.2 Newton’s second law Partly A level only Understand 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 2-D vectors); extend to situations where forces need to be resolved (restricted to 2 dimensions). A-level-only part: situations where forces need to be resolved (2 dimensions) Questions: Forces, Newton's laws and connected particles M8.3 Weight & gravity AS and A level Understand and use weight and motion in a straight line under gravity; gravitational acceleration, g, and its value in S.I. 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.) Questions: Forces, Newton's laws and connected particles M8.4 Newton’s third law, equilibrium, pulleys, connected particles Partly A level only Understand 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 2-D vectors); application to problems involving smooth pulleys and connected particles; resolving forces in 2 dimensions; equilibrium of a particle under coplanar forces. A-level-only part: resolving forces in 2 dimensions; equilibrium of a particle under coplanar forces Questions: Forces, Newton's laws and connected particles M8.5 Resultant forces; motion in a plane A level only Understand and use addition of forces; resultant forces; dynamics for motion in a plane. Questions: Friction, resultant forces and motion in a plane M8.6 Friction A level only Understand and use the F ≤ µR model for friction; coefficient of friction; motion of a body on a rough surface; limiting friction and statics. Questions: Friction, resultant forces and motion in a plane Find an Edexcel maths tutor Big gaps on the checklist? A tutor can plan the order to close them.
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