BCS Written Mathematics study plan
BCS Written Mathematics · Give each week a clear focus.
8 weeks · About 7 hours per week
Algebra & Arithmetic
Solve linear and quadratic equations in one variable, including equations reducible to quadratics, with at least 90% accuracy on a timed set
Factorise polynomials and apply remainder and factor theorems to find unknown coefficients
Simplify algebraic fractions and solve simultaneous linear equations in two and three unknowns
Apply laws of indices, surds, and logarithms to simplify and evaluate expressions without a calculator
Your checkpoint
A 25-question self-made algebra and arithmetic test, completed in 50 minutes, with a written error log listing each mistake, its cause, and the corrected method
Algebra
Solve problems on arithmetic and geometric progressions, including sums to n terms and infinite GP where convergent
Apply the binomial theorem to expand expressions with positive integral indices and find a specified term
Solve inequalities in one variable and represent solution sets on the number line
Set up and solve word problems by forming equations from given conditions
Solve partial fractions decompositions for proper rational expressions with distinct and repeated linear factors
Your checkpoint
A one-page formula and method sheet for sequences, binomial expansion, and partial fractions, plus five fully worked word problems showing the equation-forming step explicitly
Calculus
Differentiate algebraic, trigonometric, exponential, and logarithmic functions using product, quotient, and chain rules
Compute higher-order derivatives and apply them to simple rate-of-change and maxima-minima problems
Integrate standard functions and apply substitution and integration by parts
Evaluate definite integrals and use them to compute areas under curves and between curves
Your checkpoint
A worked portfolio of 12 calculus problems (6 differentiation, 6 integration), each with a labelled sketch where geometry is involved, checked against a self-derived answer key
Calculus & Trigonometry
Solve trigonometric equations over a given interval and state all solutions in general form
Prove standard trigonometric identities involving sum, difference, and double-angle formulae
Apply the sine and cosine rules to solve triangles, including the ambiguous case
Relate derivatives of trigonometric functions to gradient and tangent problems
Your checkpoint
A closed-book 90-minute mock section covering calculus and trigonometry, scored and reviewed, with every lost mark traced to a named concept gap
Geometry & Trigonometry
Prove and apply circle theorems, including tangents, chords, and cyclic quadrilaterals
Compute areas and volumes of standard and composite solids, including frustums and spheres
Use coordinate geometry to find equations of lines and circles and to test for concurrency and collinearity
Convert between degrees and radians and compute arc length and sector area
Your checkpoint
A set of 10 fully reasoned geometry and trigonometry proofs written out line by line, each justified with a named theorem or formula
Matrices and Determinants & Algebra
Perform matrix addition, multiplication, and scalar multiplication and identify when operations are defined
Compute determinants of 2x2 and 3x3 matrices by expansion and by row reduction
Find inverses of 2x2 and 3x3 matrices and use them to solve linear systems
Apply Cramer's rule and interpret singular matrices in terms of solution existence
Your checkpoint
A solved set of three simultaneous-equation systems, each solved twice (inverse method and Cramer's rule), with a short note on which method was faster and why
Statistics and Probability & Arithmetic
Compute mean, median, mode, standard deviation, and quartiles for grouped and ungrouped data
Solve probability problems using addition and multiplication rules, conditional probability, and tree diagrams
Apply permutations and combinations to counting problems and distinguish when order matters
Solve percentage, ratio, profit-and-loss, and simple and compound interest problems under time pressure
Your checkpoint
A 20-question statistics and probability set plus a 10-question arithmetic speed drill, both timed, with scores and time-per-question recorded for comparison
Arithmetic & Algebra & Geometry & Trigonometry & Calculus & Statistics and Probability & Matrices and Determinants
Complete two full-length timed papers under exam conditions and mark them against a strict scheme
Rank all seven domains by mark loss and re-drill the two weakest with targeted questions
Consolidate a single condensed revision sheet of formulae for every domain
Rehearse time allocation per section so no question is left unattempted
Your checkpoint
Two completed mock papers with a final diagnostic table showing score per domain, and a one-page exam-day time-allocation plan
Milestones
Week 2: Score at least 80% on a self-set 20-question algebra paper covering equations, sequences, binomial expansion, and partial fractions, with no calculator for the simplification items
Week 4: Score at least 70% on the closed-book calculus and trigonometry mock and show a written correction for every missed question
Week 6: Correctly solve three 3x3 linear systems by both inverse and Cramer's rule with no arithmetic errors, and score at least 75% on a mixed geometry and matrices set
Week 8: Average at least 65% across two full-length mocks with no domain below 50%, and submit the completed revision sheet and time-allocation plan