As-level pure maths chapter checklist revision

Algebra

Review the laws of indices

Practice manipulating algebraic expressions

Solve linear equations and inequalities

Factorise quadratic expressions

Explore simultaneous equations (linear)

Understand and apply the quadratic formula

Simplify and perform operations with polynomials

Functions and Graphs

Define and identify types of functions (linear, quadratic, etc.)

Sketch graphs of basic functions

Understand transformations of graphs (translations, reflections, stretches)

Analyze the properties of functions (domain, range, asymptotes)

Solve equations graphically and interpret results

Coordinate Geometry

Review the distance formula

Understand the midpoint formula

Calculate the gradient of a line

Derive the equation of a straight line

Explore the equation of a circle

Solve problems involving tangents and normals

Trigonometry

Memorize key trigonometric identities

Solve right-angled triangles using sine, cosine, and tangent

Explore the unit circle and its applications

Understand the graphs of sine, cosine, and tangent functions

Solve trigonometric equations

Calculus

Understand the concept of limits

Differentiate polynomial functions

Apply differentiation to find gradients and tangents

Integrate basic functions

Apply integration to find areas under curves

Solve problems involving rates of change

Statistics

Review measures of central tendency (mean, median, mode)

Understand measures of dispersion (variance, standard deviation)

Explore probability concepts and rules

Analyze data using graphical representations (histograms, box plots)

Solve problems involving combinations and permutations

Vectors

Define and represent vectors in two dimensions

Perform operations with vectors (addition, subtraction, scalar multiplication)

Understand the concept of vector magnitude and direction

Solve problems using vector equations

Revision Techniques

Create summary notes for each topic

Practice past exam questions

Use spaced repetition for memorization

Form study groups for collaborative learning

Schedule regular revision sessions leading up to exams

Seek help on challenging topics from teachers or tutors