Exam Preparation

Calculate the gradient of a straight line from two points or from a graph.

Form the equation of a straight line from its gradient and one point.

Form the equation of a straight line from two given points.

Convert a linear equation between standard form and gradient-intercept form.

Solve a pair of simultaneous linear equations using elimination.

Solve a pair of simultaneous linear equations using substitution.

Interpret and verify the intersection of two linear relationships in a mathematical context.

Expand and simplify products of two linear binomials.

Factorise a monic quadratic expression.

Factorise a non-monic quadratic expression.

Solve a factorable quadratic equation, including equations with rational solutions.

Form a quadratic equation from geometric or measurement information.

Determine the equation of a parabola from its intercepts and one additional point.

Identify intercepts, turning point, axis of symmetry, orientation, and range from a quadratic equation or graph.

Classify a sequence as linear, quadratic, or exponential using differences or ratios.

Derive an algebraic rule for a linear sequence.

Derive an algebraic rule for a quadratic sequence using first and second differences.

Derive an algebraic rule for an exponential sequence, including a sequence with a vertical offset.

Validate a proposed sequence rule against multiple terms and explain why it fits.

Determine intercepts, asymptotes, and growth behaviour from a transformed exponential equation.

Use an equation derived from a sequence to describe at least three features of its continuous graph.

Solve ratio and direct-proportion problems using a consistent set of units.

Calculate percentage increase, decrease, filled space, or empty space in a multi-step context.

Use rates such as density, mass per unit volume, speed, or cost per unit to solve a contextual problem.

Convert accurately between metric units of length, area, volume, capacity, mass, and tonnes.

Retain exact values or sufficient calculator precision through intermediate steps before rounding a final answer.

Compare two options by constructing and interpreting an appropriate percentage or rate.

Justify a whole-number decision caused by a practical constraint, such as the required number of trips or containers.

Use angle sums and angle relationships involving parallel lines, polygons, and intersecting lines.

Use properties of rectangles, rhombi, isosceles triangles, and other standard shapes to deduce missing information.

Apply Pythagoras’ theorem to find an unknown length in a two-dimensional figure.

Select and apply sine, cosine, or tangent to find an unknown side in a right-angled triangle.

Select and apply inverse trigonometric functions to find an unknown angle.

Combine geometric properties with Pythagoras or trigonometry in a multi-step problem.

Solve a three-dimensional problem by identifying and analysing appropriate right-angled triangles.

Construct a clear chain of geometric statements that justifies a calculated length or angle.

Form and solve an equation involving the perimeter of a shape with algebraic side lengths.

Calculate the area of a composite two-dimensional region by decomposing or rearranging it.

Calculate circumference, arc length, and perimeter involving sectors or partial circles.

Calculate the total surface area of a cuboid, prism, cylinder, or composite solid.

Calculate the volume of a prism, cylinder, sphere, or composite solid.

Work backwards from a given area, surface area, or volume to determine an unknown dimension.

Express a geometric length, area, or volume exactly in terms of a variable or π.

Compare packing arrangements by calculating the percentage of occupied or empty volume.

Select and order two or more mathematical methods needed to solve an unfamiliar problem.

Connect algebra, geometry, number, and measurement information within a single multi-step solution.

Develop a clear chain of logical reasoning without relying on unexplained calculator results.

Form a generalisation from a numerical, algebraic, or geometric pattern.

Provide a mathematical justification that establishes why a result is true.

Extend a familiar method to solve a problem with an unfamiliar arrangement or constraint.

Check a completed solution using units, substitution, estimation, or an alternative representation.

Produce a timed exam response that preserves essential working, mathematical statements, and a clearly communicated conclusion.