Mathematics Methods Level 4 study plan
Mathematics Methods Level 4 · Give each week a clear focus.
8 weeks · About 6 hours per week
Functions, Graphs, and Transformations
Sketch and label the parent graphs of linear, quadratic, cubic, absolute value, reciprocal, square root, exponential, and logarithmic functions from memory
Apply vertical and horizontal translations, dilations, and reflections to a given graph and state the resulting equation
Determine domain and range of transformed functions and justify each restriction in writing
Solve for unknown transformation parameters given two graphs or two sets of coordinates
Your checkpoint
A one-page transformation reference sheet plus 15 worked transformation problems with correct domain and range stated for each
Functions, Graphs, and Transformations & Polynomial, Rational, and Algebraic Functions
Classify functions as even, odd, or neither using both algebraic and graphical tests
Find inverse functions algebraically and verify graphically by reflection in the line y = x
Factor and divide polynomials using the factor theorem, remainder theorem, and long division
Sketch rational functions by locating intercepts, vertical asymptotes, and horizontal or oblique asymptotes
Your checkpoint
A 20-question mixed set covering inverses, polynomial division, and rational-function sketching, scored and corrected with written error notes
Polynomial, Rational, and Algebraic Functions & Exponential and Logarithmic Functions
Solve polynomial inequalities using sign charts built from factorised form
Simplify and solve rational equations, explicitly checking for extraneous solutions
Apply index laws to simplify and solve equations involving fractional and negative exponents
Convert fluently between exponential and logarithmic forms and apply the product, quotient, and power laws of logarithms
Your checkpoint
A corrected problem set of 12 algebraic and 12 exponential/logarithmic equations, each with a verification step shown
Exponential and Logarithmic Functions & Trigonometric Functions and Identities
Solve exponential equations by equating bases or by taking logarithms of both sides
Model growth and decay contexts by constructing and solving exponential equations
Convert angles between degrees and radians and evaluate exact trigonometric ratios on the unit circle
Sketch sine, cosine, and tangent graphs and identify amplitude, period, phase shift, and vertical shift
Your checkpoint
A timed 45-minute mid-course test covering Domains 1 to 3 plus trigonometric graph sketching, scored against a 75 percent benchmark
Trigonometric Functions and Identities
Prove and apply the Pythagorean, sum, difference, and double-angle identities
Solve trigonometric equations over a stated interval and list all solutions without omitting any
Simplify complex trigonometric expressions to a single term or ratio
Apply the sine and cosine rules to solve non-right triangles in context
Your checkpoint
A proof portfolio of 6 identities written out line by line with justifications, plus 10 trigonometric equations solved over a specified interval
Differential Calculus
Differentiate from first principles for polynomial and simple rational functions
Apply the product, quotient, and chain rules to composite expressions
Find equations of tangents and normals and locate stationary points using the derivative
Classify stationary points using first or second derivative tests and solve optimisation problems
Your checkpoint
A 15-question calculus set including two full optimisation word problems, with fully annotated solutions and a labelled stationary-point summary table
Integral Calculus and Applications & Mathematical Modeling and Problem Solving
Find antiderivatives of polynomial, exponential, and simple trigonometric functions
Evaluate definite integrals using the fundamental theorem and interpret them as signed area
Calculate areas between curves and volumes of revolution about the x-axis
Construct a mathematical model from a written scenario, state assumptions, and validate the model against given data
Your checkpoint
A modelling report of 400 to 600 words that builds a function model from data, uses calculus to optimise or measure it, and states the limitations of the assumptions
Probability and Statistics & Mathematical Modeling and Problem Solving
Compute probabilities using the addition and multiplication rules and conditional probability
Apply the binomial distribution to calculate probabilities and expected values
Interpret and calculate summary statistics including mean, median, standard deviation, and z-scores
Complete two full-length practice papers under timed conditions and categorise every error by domain
Your checkpoint
Two completed timed practice papers with an error log sorted by domain, plus a one-page revision sheet listing the three weakest topics and the corrective action for each
Milestones
Week 2: Score at least 70 percent on a self-marked 15-question quiz on transformations, inverses, and rational functions, with no more than one error on domain and range statements
Week 4: Complete the 45-minute mid-course test within time and score at least 75 percent, with at least 8 of 10 exponential and logarithmic items correct
Week 6: Differentiate 10 mixed functions with 90 percent accuracy in under 25 minutes, and correctly classify all stationary points in three optimisation problems
Week 8: Score at least 80 percent on both timed practice papers and show that every logged error has a written corrective note tied to a specific goal from weeks 1 to 7