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10 dot points across 10 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you manipulate expressions, solve equations and inequalities, and transform graphs?

Algebra and functions including indices and surds, quadratics, simultaneous equations, inequalities, polynomials, graphs, functions and transformations, the binomial expansion and partial fractions.
A focused answer to the Edexcel A-Level Mathematics algebra and functions content, covering indices and surds, quadratics, the discriminant, simultaneous equations, inequalities, polynomials, graphs, function notation, transformations, the binomial expansion and partial fractions.
12 min answer →

How do you describe lines, circles and curves with equations and use them?

Coordinate geometry in the x and y plane including straight lines, the equation of a circle, tangents, chords and parametric equations of curves.
A focused answer to the Edexcel A-Level Mathematics coordinate geometry content, covering the straight line, gradient and midpoint, parallel and perpendicular lines, the equation of a circle, tangents and chords, and parametric equations of curves.
11 min answer →

How do you find the rate at which a quantity changes, and how do you use that to analyse curves and solve optimisation problems?

Differentiation from first principles, the rules for powers, the chain, product and quotient rules, derivatives of standard functions, implicit and parametric differentiation, stationary points and connected rates of change.
A focused answer to the Edexcel A-Level Mathematics differentiation content, covering first principles, the chain, product and quotient rules, derivatives of standard functions, implicit and parametric differentiation, stationary points and their nature, and applications to optimisation.
11 min answer →

How do you work with exponential growth and decay, and how do logarithms undo exponentials?

The exponential function and the number e, the natural logarithm, the laws of logarithms, solving exponential equations, and using logarithms to linearise and model real data.
A focused answer to the Edexcel A-Level Mathematics exponentials and logarithms content, covering the exponential function and the number e, the natural logarithm, the laws of logarithms, solving exponential equations, and using logarithms to linearise data and model growth and decay.
9 min answer →

How do you reverse differentiation to find areas, volumes and total change?

Indefinite and definite integrals, areas under curves, integrals of standard functions, integration by substitution and by parts, integration using partial fractions, and differential equations.
A focused answer to the Edexcel A-Level Mathematics integration content, covering indefinite and definite integrals, areas under curves, standard integrals, integration by substitution and by parts, integration with partial fractions, and solving differential equations.
11 min answer →

How do you find roots and areas approximately when an exact answer is not available?

Locating roots by change of sign, iterative methods including the Newton-Raphson method, the trapezium rule for numerical integration, and the conditions under which these methods fail.
A focused answer to the Edexcel A-Level Mathematics numerical methods content, covering locating roots by change of sign, iterative methods, the Newton-Raphson method, the trapezium rule for numerical integration, and when these methods fail.
9 min answer →

How do you prove a statement is always true, and how do you show one is false?

Structure of mathematical proof including proof by deduction, proof by exhaustion, disproof by counter-example and proof by contradiction, applied to statements about numbers and inequalities.
A focused answer to the Edexcel A-Level Mathematics proof content, covering proof by deduction, proof by exhaustion, disproof by counter-example and proof by contradiction, including the irrationality of root 2 and the infinitude of primes.
9 min answer →

How do you describe and sum patterns of numbers, and expand binomials for any power?

Sequences and series including arithmetic and geometric sequences, sigma notation, sums to infinity, recurrence relations, and the binomial expansion for any rational power.
A focused answer to the Edexcel A-Level Mathematics sequences and series content, covering arithmetic and geometric sequences and their sums, sigma notation, the condition for convergence and sum to infinity, recurrence relations, and the binomial expansion for any rational power.
9 min answer →

How do you work with angles, trigonometric functions and identities to solve equations and model periodic behaviour?

Radian measure, arc length and sector area, exact values, the Pythagorean and addition identities, reciprocal and inverse functions, and solving trigonometric equations.
A focused answer to the Edexcel A-Level Mathematics trigonometry content, covering radian measure, arc length and sector area, exact values, the Pythagorean and addition identities, double angle formulae, reciprocal and inverse functions, and solving trigonometric equations over an interval.
11 min answer →

How do you represent quantities with both magnitude and direction, and use them in geometry and motion?

Vectors in two and three dimensions, magnitude and direction, addition and scalar multiplication, position vectors, unit vectors, and geometric applications.
A focused answer to the Edexcel A-Level Mathematics vectors content, covering vectors in two and three dimensions, magnitude and direction, addition and scalar multiplication, position vectors, unit vectors, and geometric applications such as collinearity and midpoints.
9 min answer →