MSCE Mathematics study plan

MSCE Mathematics · Give each week a clear focus.

8 weeks · About 7 hours per week

Week 1

Number

Classify numbers into natural, integer, rational, irrational, real, and complex sets and justify each placement with a one-line reason
Convert fluently among fractions, decimals, percentages, and standard form without a calculator
Apply the order of operations and index laws to simplify expressions containing brackets, powers, and roots
Compute HCF, LCM, and prime factorisations and use them to solve divisibility and simplification problems

A 40-question self-marked number-sense quiz scoring at least 85%, with every error rewritten and corrected in a log

Week 2

Solve percentage problems covering increase, decrease, reverse percentage, and compound growth
Apply ratio and proportion to share quantities and scale recipes, maps, and mixtures
Complete a timed 25-minute set of number-domain past-paper-style items under exam conditions
Explain in writing how rounding and significant figures affect the accuracy of a final answer

A one-page formula and method sheet for the Number domain plus a timed 25-minute practice set scored and reviewed

Week 3

Expand and factorise algebraic expressions, including difference of two squares and quadratic trinomials
Rearrange formulas to make any given variable the subject, including cases with powers and roots
Simplify algebraic fractions and solve linear equations and inequalities, showing each step
Solve simultaneous linear equations by both substitution and elimination and verify the solution

A worked solutions portfolio of 30 algebra problems, each with full step-by-step reasoning and a check

Week 4

Solve quadratic equations by factorising, completing the square, and the quadratic formula
Interpret the discriminant to state the number and type of roots
Sketch quadratic and linear graphs from their equations, marking intercepts and turning points
Solve word problems that translate into linear or quadratic models and interpret the result in context

A closed-book 45-minute algebra mock test scoring at least 80%, with a written error analysis for each missed item

Week 5

Apply angle facts for parallel lines, triangles, and polygons to find unknown angles with stated reasons
Prove congruence and similarity and use similarity ratios to find lengths and areas
Apply Pythagoras' theorem and the sine, cosine, and tangent ratios to right-angled triangles
Calculate perimeter, area, surface area, and volume of standard 2D and 3D shapes, including composite figures
Convert between units of length, area, and volume correctly, including metric-imperial conversions

A formula card for geometry and mensuration plus 25 mixed shape problems solved and self-marked at 80% or higher

Week 6

Use the sine and cosine rules and the area formula for non-right-angled triangles
Convert between degrees and radians and evaluate trigonometric ratios for standard angles without a calculator
Sketch sine, cosine, and tangent graphs, stating amplitude, period, and key intercepts
Solve simple trigonometric equations within a given interval and state all solutions
Solve 3D problems involving bearings and angles of elevation and depression

A set of 20 trigonometry problems, including at least 5 bearing and 3D items, solved with diagrams and scored

Week 7

Construct and interpret frequency tables, histograms, and cumulative frequency curves to find median and quartiles
Calculate mean, median, mode, range, and interquartile range for raw and grouped data
Compute probabilities using the addition and multiplication rules and tree diagrams for independent and dependent events
Identify the domain, range, and transformations of a function and sketch linear, quadratic, and exponential graphs
Find and interpret the gradient and intercepts of a straight-line graph in context

A statistics and functions workbook of 30 problems, including two full data-interpretation questions, scored at 80% or above

Week 8

Complete two full-length timed mock papers under exam conditions and record the score for each domain
Revisit every logged error from weeks 1 to 7 and re-solve it correctly without notes
Memorise and recall all key formulas across the seven domains in a 15-minute self-test
Refine an exam-day strategy covering time allocation, question order, and checking procedures

Two completed mock papers with a domain-by-domain score breakdown and a final one-page revision sheet of weak areas

Week 2: Score at least 80% on the timed Number practice set and show a corrected error log for every missed question

Week 4: Score at least 80% on the closed-book algebra mock test, with no repeated error type from week 3

Week 6: Correctly solve at least 16 of 20 trigonometry problems, including all bearing and 3D items

Week 7: Score at least 80% on the statistics and functions workbook and interpret two full data sets accurately

Week 8: Achieve at least 75% on both full-length mock papers, with no domain below 60%