Exponent Laws with Integer Exponents and Variables

Classify real numbers as rational or irrational and solve problems involving real numbers using digital tools.

Apply the exponent laws to numerical expressions with integer exponents and extend them to algebraic expressions with variables.

Expand algebraic expressions including binomial products, perfect squares, and the difference of two squares.

Factorise algebraic expressions by taking out common factors, factorising monic quadratics and special forms, and apply these skills to simplify algebraic fractions.

Find the gradient of a line segment, the midpoint of an interval and the distance between two points on the Cartesian plane.

Identify quadratic functions, graph parabolas from equations and tables, and recognise key features and the effects of coefficients.

Solve quadratic equations by factorising and numerical methods, including equations with rational, irrational, and no real roots, and apply quadratics to real-world problems.

Use mathematical modelling to solve applied problems involving change, including financial contexts, choosing linear or quadratic functions.

Experiment with the effects of varying parameters on graphs of related functions and make connections between graphical and algebraic representations.

Solve problems involving the volume and surface area of right prisms and cylinders using appropriate units.

Solve problems involving very small and very large measurements, time scales and intervals expressed in scientific notation.

Apply angle properties of parallel lines and polygons, and use similarity and scale to find unknown angles and side lengths in geometric problems.

Apply Pythagoras' theorem and trigonometric ratios in right-angled triangles to solve 2D and 3D spatial problems, including real-world applications.

Calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates.

Use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts.

Recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity.

Apply the enlargement transformation to shapes and objects, identifying what stays the same and what changes.

Design, test and refine algorithms involving sequences of steps and decisions based on geometric constructions and theorems.

Analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians.

Analyse how different sampling methods affect survey results and how choice of representation can support a particular point of view.

Represent and compare distributions of multiple data sets, considering centre, spread, shape and the effect of outliers.

Choose appropriate forms of display or visualisation for a given type of data, justify selections and interpret displays in context.

Plan and conduct statistical investigations involving the collection and analysis of different kinds of data, reporting findings and discussing the strength of evidence.

List all outcomes for compound events with and without replacement, using lists, tree diagrams, tables or arrays, and assign probabilities to outcomes.

Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and', inclusive 'or' and exclusive 'or'.

Design and conduct repeated chance experiments and simulations using digital tools to compare probabilities of simple events to related compound events.