Cameroon GCE A-Level Pure Mathematics with Statistics study plan
Cameroon GCE A-Level Pure Mathematics with Statistics · Give each week a clear focus.
8 weeks · About 6 hours per week
Algebra and Functions & Calculus (Differentiation and Integration)
Sketch and classify rational, modulus, and piecewise functions, stating domain, range, asymptotes and intercepts for each
Apply the product, quotient and chain rules to differentiate composite expressions without referring to notes
Evaluate definite integrals using substitution and integration by parts on at least ten mixed exercises
Solve equations and inequalities involving modulus and rational expressions, verifying solutions graphically
Your checkpoint
A 20-question self-marked diagnostic paper covering Algebra and Functions plus Differentiation and Integration, with a written error log listing every mistake and its corrected method
Calculus (Differentiation and Integration)
Differentiate implicitly and find gradients of curves defined implicitly, including tangents and normals
Compute volumes of revolution about both axes and set up the correct integral for a stated region
Integrate rational functions using partial fractions and recognise when to use logarithmic results
Apply calculus to maxima and minima problems drawn from geometry and rates of change
Your checkpoint
A one-page formula-and-method sheet for calculus written from memory, then corrected, plus eight fully worked application problems on maxima, minima and volumes
Algebra and Functions & Sequences and Series
Decompose rational functions into partial fractions, including repeated and improper cases
Expand binomial expressions with rational or negative indices and state the range of validity
Use the binomial theorem to approximate a numerical value and bound the error
Sum arithmetic and geometric series and determine convergence conditions for infinite geometric series
Your checkpoint
A timed 45-minute test on partial fractions, binomial expansion and series summation, scored and reviewed against a marking scheme you write yourself
Probability and Probability Distributions & Descriptive Statistics and Data Representation
Compute probabilities using the addition and multiplication rules, including conditional probability and independence checks
Apply tree diagrams and two-way tables to multi-stage problems and state assumptions explicitly
Calculate and interpret mean, median, mode, variance and standard deviation for grouped and ungrouped data
Construct and read histograms with unequal class widths, cumulative frequency curves and box plots
Your checkpoint
A statistics portfolio of five solved past-paper-style probability and data-representation questions, each with a labelled diagram and a one-sentence justification of the chosen method
Coordinate Geometry & Trigonometry
Find equations of lines, circles and tangents, and solve intersection problems algebraically
Convert between Cartesian and parametric forms and eliminate the parameter
Prove and apply trigonometric identities involving double angles and the forms of sine and cosine
Solve trigonometric equations over a given interval and express general solutions correctly
Your checkpoint
A set of twelve coordinate geometry and trigonometry problems solved under exam timing, with all diagrams drawn accurately by hand and checked against the algebraic solution
Vectors and Matrices & Complex Numbers
Perform matrix addition, multiplication and inversion, and compute determinants of 2x2 and 3x3 matrices
Solve simultaneous linear equations using matrix methods and interpret singular cases
Resolve vectors into components and compute scalar and vector products with geometric interpretation
Express complex numbers in modulus-argument form and apply De Moivre's theorem to powers and roots
Your checkpoint
A worked solutions booklet covering matrix inversion, vector geometry and complex-number roots, including sketches of Argand diagrams and one explanation of why a matrix has no inverse
Probability and Probability Distributions & Statistical Inference (Estimation and Hypothesis Testing)
Compute binomial and normal probabilities, applying continuity corrections where required
Construct confidence intervals for a population mean and interpret the confidence level precisely
Carry out one- and two-tailed hypothesis tests for a mean, stating hypotheses and conclusion in context
Distinguish Type I and Type II errors and explain the effect of sample size on a test
Your checkpoint
Two complete hypothesis-test write-ups in exam format, each with hypotheses, test statistic, critical region, p-value and a contextual conclusion, plus a one-page comparison of binomial and normal approximations
Algebra and Functions & Calculus (Differentiation and Integration) & Probability and Probability Distributions
Complete two full timed mock papers under exam conditions and mark them strictly
Revisit the error logs from weeks 1 to 7 and re-solve every previously incorrect question
Consolidate a single revision sheet of formulae and standard results for all ten domains
Identify the three weakest sub-topics and drill them with targeted practice
Your checkpoint
Two marked mock papers with scores recorded, a final one-page formula sheet, and a prioritised list of three weak sub-topics with the practice completed for each
Milestones
Week 2: Score at least 70 percent on a self-set calculus mini-test of ten questions under 40 minutes, with no formula sheet available
Week 4: Correctly answer eight of ten mixed algebra, series and probability questions in a single sitting, and show a complete error log for the two missed
Week 6: Solve one matrix, one vector and one complex-number question in under 25 minutes total, with all working shown and no arithmetic slips
Week 8: Achieve at least 65 percent on both full mock papers, with no domain scoring below 50 percent, and confirm every week-1 error has been re-solved correctly