Mathematics

Expanding binomials and factorising trinomials, including the difference of two squares.

• Quadratic Factorisation and Expansion

  “Expanding binomials and factorising trinomials, including the difference of two squares.”

• Simultaneous Equations

  “Solving pairs of linear and non-linear equations using elimination and substitution.”

• Algebraic Fractions

  “Simplifying, adding, subtracting, and solving equations containing algebraic fractions.”

• Rearranging Complex Formulae

  “Changing the subject of a formula where the variable appears multiple times or within a root.”

• Linear and Quadratic Inequalities

  “Solving inequalities and representing solution sets on number lines and coordinate grids.”

• Completing the Square

  “Transforming quadratic expressions to find turning points and solve quadratic equations.”

Finding equations of lines and determining gradients of perpendiculars.

• Linear Graphs and Perpendicular Lines

  “Finding equations of lines and determining gradients of perpendiculars.”

• Quadratic and Cubic Functions

  “Plotting and interpreting the roots and intercepts of higher-order polynomials.”

• Transformation of Functions

  “Applying translations and reflections to the graphs of y = f(x).”

• Circle Equations and Tangents

  “Finding the equation of a circle and the line tangent to it at a specific point.”

• Kinematic Graphs

  “Analysing distance-time and velocity-time graphs to find acceleration and distance.”

Applying geometric properties of circles, tangents, and chords to find missing angles.

• Circle Theorems

  “Applying geometric properties of circles, tangents, and chords to find missing angles.”

• Sine and Cosine Rules

  “Calculating lengths and angles in non-right-angled triangles.”

• Pythagoras in Three Dimensions

  “Applying 2D geometric principles to 3D shapes like pyramids and cuboids.”

• Surface Area and Volume of Solids

  “Calculating metrics for spheres, cones, pyramids, and composite shapes.”

• Congruence and Similarity

  “Proving triangles are congruent and using scale factors for area and volume.”

Simplifying surds, rationalising denominators, and performing operations with radical expressions.

• Surds and Irrational Numbers

  “Simplifying surds, rationalising denominators, and performing operations with radical expressions.”

• Indices and Power Laws

  “Applying fractional and negative indices, and solving equations involving index laws.”

• Standard Form and Scientific Notation

  “Converting between standard and ordinary forms and performing calculations with very large or small numbers.”

• Upper and Lower Bounds

  “Calculating error intervals and determining the limits of accuracy in multi-step calculations.”

• Recurring Decimals and Fractions

  “Converting recurring decimals into exact fractions using algebraic proofs.”

Calculating the likelihood of events occurring given that another event has happened.

• Conditional Probability

  “Calculating the likelihood of events occurring given that another event has happened.”

• Tree Diagrams and Combined Events

  “Representing sequences of independent and dependent events visually.”

• Venn Diagrams and Set Notation

  “Using union, intersection, and complement notation to solve logical problems.”

• Product Rule for Counting

  “Determining the total number of possible outcomes in multi-stage scenarios.”

Setting up and solving equations using the constant of proportionality.

• Direct and Inverse Proportion

  “Setting up and solving equations using the constant of proportionality.”

• Compound Interest and Depreciation

  “Calculating exponential growth and decay over multiple time periods.”

• Compound Measures

  “Solving problems involving speed, density, and pressure with unit conversions.”

• Gradient and Rate of Change

  “Interpreting the slope of a graph as a physical rate in real-world contexts.”

• Percentage Change and Reverse Percentages

  “Finding original values and calculating percentage increases or decreases.”

Analysing data distributions, medians, and interquartile ranges.

• Cumulative Frequency and Box Plots

  “Analysing data distributions, medians, and interquartile ranges.”

• Histograms with Unequal Class Widths

  “Calculating frequency density and representing data with varying intervals.”

• Scatter Graphs and Correlation

  “Identifying relationships between variables and drawing lines of best fit.”

• Sampling and Bias

  “Evaluating different methods of data collection and their reliability.”

Performing operations on column vectors and resultant vector calculations.

• Vector Addition and Scaling

  “Performing operations on column vectors and resultant vector calculations.”

• Geometric Proof with Vectors

  “Using vector paths to prove lines are parallel or points are collinear.”

• Bearings and Navigation

  “Solving navigational problems using three-figure bearings and trigonometry.”

• Loci and Constructions

  “Using a compass and ruler to construct bisectors and regions satisfying conditions.”