SPM Add Maths study plan

State the first derivative from first principles and apply the chain, product and quotient rules to at least 20 composite expressions without referring to notes

Differentiate polynomial, trigonometric and exponential functions and evaluate gradients at given points, including negative and fractional indices

Distinguish and apply the concepts of relation, function, one-to-one function and composite function, and find the inverse of a given function

Sketch the graph of a function and its inverse on the same set of axes and state the domain and range of each

Solve 15 mixed differentiation and function problems under timed conditions (1.5 minutes per mark)

Apply differentiation to determine stationary points, classify them by the second derivative test, and sketch the curve with correct turning points

Solve rates of change and small-increment problems by setting up the relevant derivative relationship

Compute indefinite integrals of algebraic, trigonometric and exponential functions, including functions of a linear expression

Evaluate definite integrals and apply them to find the area under a curve and the area between a curve and a straight line

Set up and solve volumes of revolution about the x-axis for at least 5 rotated regions

Solve quadratic equations by completing the square, formula and factorisation, and form equations from given roots

Determine the nature of roots using the discriminant and solve inequalities involving quadratic expressions

Sketch quadratic function graphs and relate the discriminant, vertex form and axis of symmetry to the sketch

Solve simultaneous equations where one equation is linear and the other is non-linear, by substitution, and interpret the geometric meaning of the solutions

Complete 10 past-paper-style structured questions on quadratics and simultaneous equations within the time limit

Apply all laws of indices and logarithms, including change of base, to simplify and evaluate expressions without a calculator

Solve equations involving indices and logarithms, including those reducible to quadratic form

Find distance, midpoint, gradient and equations of straight lines, including parallel and perpendicular conditions

Solve locus problems involving constant distance from a point and constant distance from a line

Convert between Cartesian and parametric-style descriptions of loci and sketch the resulting locus

Express vectors in component and column form, and perform addition, subtraction and scalar multiplication

Use vector methods to prove collinearity and parallelism, and to find position vectors of points dividing a line in a given ratio

Convert between degrees and radians and compute arc length, sector area and segment area

Solve problems involving chords, tangents and the perimeter of composite circular regions

Apply vectors to solve at least 5 geometry problems from first principles without a diagram given

Apply the sine rule, cosine rule and area formula to solve triangles, including the ambiguous case of the sine rule

Solve three-dimensional problems involving angles between lines and planes using right-angled triangle reasoning

Compute and interpret price and quantity index numbers, including weighted indices

Calculate composite index numbers and solve problems involving index numbers and percentage changes over time

Complete 8 structured solution-of-triangles questions and 6 index-number questions under timed conditions

Use displacement, velocity and acceleration functions and their derivatives to describe motion along a straight line

Determine when a particle is instantaneously at rest, its maximum displacement and its direction of motion

Use definite integration of velocity to find displacement and total distance travelled over an interval

Solve maximum and minimum problems in kinematics by applying differentiation to velocity

Attempt 12 kinematics questions mixing differentiation and integration, marking each against the scheme

Sit two full-length timed papers under exam conditions and record raw marks per domain

Re-derive the key formulas for each domain from memory and check them against the syllabus list

Rework every error from the two papers and classify each as conceptual, procedural or careless

Target the two weakest domains with a focused drill of 20 questions each

Finalise an exam-day strategy covering question order, time per mark and checking routine