QCE Maths Methods study plan
QCE Maths Methods · Give each week a clear focus.
8 weeks · About 6 hours per week
Algebra, functions and their graphs
Sketch and label the graphs of linear, quadratic, power and absolute-value functions, stating domain, range and key features
Solve quadratic equations and inequalities by factorising, completing the square and the quadratic formula
Apply transformations (dilations, reflections, translations) to basic graphs and write the resulting rule
Identify and interpret asymptotes and intercepts of rational functions of the form y = a/(x - h) + k
Your checkpoint
A one-page annotated summary sheet of function families with a worked example of each transformation type, plus 20 correctly solved practice items
Algebra, functions and their graphs
Solve simultaneous equations, including one linear and one non-linear equation, algebraically
Determine and interpret inverse functions, including domain restrictions and graphical symmetry in y = x
Compose functions and identify when a composite function is defined
Solve equations and inequalities involving absolute value and rational expressions
Your checkpoint
A timed 45-minute practice set of 15 mixed algebra and function questions, marked and corrected with error notes
Calculus
Differentiate polynomial, power and simple rational functions using the limit definition and the power rule
Apply the product, quotient and chain rules to composite expressions
Find equations of tangents and normals and interpret the derivative as a gradient and rate of change
Locate stationary points and classify them using the first derivative test
Your checkpoint
A worked solutions portfolio of 12 differentiation problems spanning all rules, with each step justified in writing
Calculus
Integrate power functions and find definite integrals using the fundamental theorem of calculus
Calculate areas under curves and between curves, including regions below the x-axis
Solve optimisation and kinematics problems using derivatives and integrals
Interpret displacement, velocity and acceleration relationships graphically and algebraically
Your checkpoint
A closed-book 60-minute calculus test (10 items) scored at 80% or better, with a written reflection on any lost marks
Statistical analysis
Classify data types and select appropriate graphical displays, describing shape, centre and spread
Calculate and interpret mean, median, standard deviation, quartiles and outliers
Apply the normal distribution to compute probabilities and inverse problems with z-scores
Interpret correlation, construct least-squares regression lines and assess the coefficient of determination
Your checkpoint
A statistics investigation write-up applying normal and bivariate techniques to a self-chosen dataset, with calculations shown
Trigonometry and circular functions
Convert fluently between degrees and radians and evaluate exact trigonometric ratios on the unit circle
Sketch sine, cosine and tangent graphs with amplitude, period, phase and vertical shifts
Solve trigonometric equations over specified intervals, including general solutions
Apply the sine and cosine rules and the area formula to non-right triangles
Your checkpoint
A set of 8 fully sketched circular-function graphs with matching equation, features and solution sets for associated equations
Exponential and logarithmic functions & Calculus
Sketch exponential and logarithmic functions and state domain, range and asymptotes
Apply index and logarithm laws to simplify expressions and solve exponential equations
Differentiate and integrate exponential and natural-log functions, including chain-rule cases
Model growth, decay and compound-interest situations and interpret parameters
Your checkpoint
A formula and technique card for exponentials and logarithms with 10 worked application problems, checked against a marking guide
Algebra, functions and their graphs & Calculus & Statistical analysis & Trigonometry and circular functions & Exponential and logarithmic functions
Synthesise all five domains by completing two full-length timed practice papers under exam conditions
Diagnose recurring error patterns and re-teach the two weakest sub-topics
Build a condensed revision sheet linking key formulas across domains
Rehearse time allocation and checking strategies per question type
Your checkpoint
Two completed timed practice papers with a score log, error analysis table and a final one-page formula sheet
Milestones
Week 2: Score at least 75% on the mixed algebra and function practice set, and correctly state domain and range for every function type without notes
Week 4: Score at least 80% on the closed-book calculus test, including at least one correct area-between-curves and one correct optimisation solution
Week 6: Correctly solve at least 9 of 10 trigonometric equations and accurately sketch all 8 circular-function graphs with correct features
Week 8: Average at least 80% across both full-length practice papers with no domain scoring below 70%