LC Higher Maths study plan

Factorise and simplify algebraic expressions, including cubic and quartic forms, by completing 12 mixed practice items without notes

Solve simultaneous equations, one linear and one quadratic, by substitution and verify each solution by back-substitution

Manipulate surds and indices, including rational and negative powers, by rewriting 10 expressions in simplified form

Solve quadratic inequalities and represent solution sets on the number line

Apply the factor and remainder theorems to find unknown coefficients in polynomials

Solve equations involving algebraic fractions by clearing denominators and identifying excluded values

Prove algebraic identities by transforming one side into the other without cross-multiplying

Construct and solve a system of equations from a word problem involving rates or mixtures

State and apply the sine rule, cosine rule and area formula to non-right triangles, choosing the correct rule from the given information

Solve 3D problems involving angles between a line and a plane by drawing a clear diagram and identifying the right triangle

Prove trigonometric identities using the Pythagorean identities and double-angle formulas

Solve trigonometric equations over a specified interval and list all solutions in the required range

Derive and use the equation of a circle and find points of intersection with a line by solving simultaneously

Apply coordinate geometry of the line, including slope, distance, midpoint and perpendicularity, to solve locus and triangle problems

Use the trapezoidal rule to approximate areas and compare the approximation with the exact integral

Convert between degrees and radians and compute arc length and sector area in applied contexts

Sketch graphs of quadratic, cubic, exponential and logarithmic functions showing intercepts, turning points and asymptotes

Determine domain and range from a graph and from a formula, including composite and inverse functions

Solve problems involving compound measures, currency conversion and significant-figure accuracy

Compute percentage error and express answers to an appropriate number of significant figures in measurement problems

Differentiate polynomial, trigonometric, exponential and logarithmic functions using the product, quotient and chain rules

Find maxima and minima in applied optimisation problems and justify each as a maximum or minimum using the second derivative

Integrate standard functions and evaluate definite integrals to find areas between curves and the x-axis

Apply the rules of differentiation and integration to rates of change and displacement-velocity-acceleration problems

Compute probabilities using the multiplication and addition rules and conditional probability, distinguishing independent from dependent events

Apply the binomial distribution to calculate probabilities and interpret the mean and standard deviation

Calculate and interpret the mean, median, mode and standard deviation of a data set, including grouped data

Interpret a histogram, cumulative frequency curve and scatter plot to draw justified conclusions about a data set

Solve multi-step unfamiliar problems by breaking them into known sub-problems and justifying each step in writing

Complete two full past-paper style mock exams under strict timing and self-mark using a marking scheme

Identify the three weakest topics from mock results and rework 5 questions on each until fully correct

Build a final one-page revision card linking key formulas across all nine domains