LC Ordinary Maths study plan

Solve linear equations and simultaneous equations in two and three unknowns without a calculator, showing each algebraic step.

Manipulate expressions with brackets, fractions, and negative indices until simplification is automatic and error-free.

Factorise quadratics of the form ax² + bx + c by inspection and by the formula method, including cases with a ≠ 1.

Set up word problems as equations (age, speed, mixture, and consecutive-number types) and check answers against the original wording.

Solve quadratic equations by factorising, completing the square, and the quadratic formula, and state when each method is fastest.

Solve linear and quadratic inequalities and represent solution sets on the number line.

Apply the laws of indices and surds to simplify expressions and rationalise denominators.

Solve simultaneous equations where one is linear and one is quadratic, and interpret the two solutions geometrically.

Construct and interpret frequency tables, histograms, and cumulative frequency curves from raw data, and read quartiles and the interquartile range from a curve.

Calculate mean, median, mode, and standard deviation for grouped and ungrouped data, and explain how outliers affect each measure.

Apply the multiplication and addition rules of probability to independent and mutually exclusive events, including tree diagrams for two-stage experiments.

Use the binomial distribution to find probabilities of r successes in n trials and to compute expected value.

Interpret and construct scatter plots, draw a line of best fit by eye, and use it to estimate values while distinguishing interpolation from extrapolation.

Recognise and correct common exam errors in probability (adding when multiplication is required, forgetting without-replacement adjustments).

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

Solve 3D trigonometry problems involving a box or pyramid, including finding the angle between a line and a plane.

Differentiate polynomial, trigonometric, exponential, and logarithmic functions from first principles for simple cases and by rule for all others.

Apply the product, quotient, and chain rules to composite functions and simplify derivatives fully.

Find maxima, minima, and points of inflection using the first and second derivative tests, and solve applied optimisation problems.

Integrate standard functions, evaluate definite integrals, and find areas between a curve and the x-axis, handling regions below the axis correctly.

Sketch graphs of quadratic, cubic, exponential, and trigonometric functions, marking intercepts, turning points, and asymptotes.

Find the equation of a line and of a circle, and solve problems involving tangents to circles.

Apply the distance, midpoint, and slope formulas to coordinate geometry problems, including perpendicular and parallel lines.

Solve problems on the line segment division ratio and verify results by an independent method.

Identify arithmetic and geometric sequences, find the nth term and sum to n terms, and solve for n in context.

Apply compound interest, depreciation, and amortisation formulas, and compare a loan repayment schedule with the closed-form formula.

Perform the standard ruler-and-compass constructions (perpendicular bisector, angle bisector, perpendicular from a point) and justify each step.

Prove the standard synthetic geometry theorems on triangles and circles and apply them to multi-step angle-chasing problems.

Complete two full-length timed mock papers under exam conditions and record the time spent per section.

Classify every lost mark by domain and by error type (concept, algebra slip, misread, timing) and rank the top three fixes.

Re-solve the highest-frequency error types from the mock analysis until each is correct twice in a row.

Assemble a two-page final revision card covering formulas and method triggers for all seven domains.