MATSEC AM Pure Mathematics study plan
MATSEC AM Pure Mathematics · Give each week a clear focus.
8 weeks · About 7 hours per week
Algebra and Functions & Differentiation and Applications
Factorise and simplify rational expressions and solve polynomial, modulus and inequality problems without notes
Differentiate sums, products, quotients and composite functions fluently
Sketch curves identifying stationary points, asymptotes and intercepts
Set up and solve optimisation problems from worded contexts
Your checkpoint
A timed 90-minute test of 12 mixed algebra-and-differentiation questions scored against a mark scheme, with errors logged
Integration and Applications & Algebra and Functions
Integrate standard functions, including by substitution and by parts
Evaluate definite integrals and find areas between curves
Apply partial fractions to integrate rational functions
Solve separable first-order differential equations arising from rate problems
Your checkpoint
A portfolio of 10 fully worked integration problems including two area and two differential-equation applications
Differentiation and Applications & Integration and Applications
Connect differentiation and integration techniques in combined problems
Find volumes of revolution and use integration to solve kinematics problems
Differentiate and integrate trigonometric and exponential functions confidently
Complete a full past-paper-style section under timed conditions
Your checkpoint
A closed-book 2-hour mock covering Domains 1, 6 and 7, self-marked with a topic-by-topic error analysis
Coordinate Geometry & Trigonometry
Derive and use equations of lines, circles and conics in coordinate form
Solve trigonometric equations over given intervals using identities
Apply the sine and cosine rules and radians to arc, sector and segment problems
Prove standard trigonometric identities step by step
Your checkpoint
A one-page formula-and-identity summary sheet written from memory plus 15 solved coordinate-geometry and trigonometry questions
Complex Numbers & Vectors and Three-Dimensional Geometry
Perform arithmetic on complex numbers in Cartesian, modulus-argument and exponential forms
Solve polynomial equations with complex roots and plot loci on the Argand diagram
Carry out vector addition, scalar products and vector equations of lines and planes
Calculate angles and distances between lines and planes in three dimensions
Your checkpoint
A worked solutions set of 12 complex-number and vector problems, including two Argand loci sketches and two 3D geometry problems
Sequences and Series & Exponentials and Logarithms
Identify and sum arithmetic and geometric series and apply convergence conditions
Use binomial expansion for positive and fractional indices with validity ranges
Apply laws of logarithms to solve exponential and logarithmic equations
Model growth and decay problems using exponentials
Your checkpoint
A timed 60-minute quiz on sequences, series, logarithms and exponentials scored at 75% or above
Numerical Methods & Probability and Statistics
Apply the trapezium rule and Newton-Raphson or fixed-point iteration to locate roots
Interpret and compute probabilities using conditional probability and independence
Calculate and interpret mean, variance and standard deviation of distributions
Use the binomial and normal distributions to solve contextual problems
Your checkpoint
A 10-question numerical-methods and statistics assignment with full working, including one iteration table and one normal-distribution calculation
Algebra and Functions & Differentiation and Applications & Integration and Applications & Probability and Statistics
Consolidate the heaviest domains through targeted revision of logged errors
Complete full past-paper-style papers under exam timing
Refine exam technique for showing method marks and checking answers
Review formula recall across all eleven domains
Your checkpoint
Two full timed mock papers completed and self-marked, with a final revision sheet listing remaining weak areas
Milestones
Week 4: Score at least 65% on the closed-book mock covering Domains 1, 6 and 7, with no domain below 55%
Week 6: Achieve 75% or above on the sequences, series, logarithms and exponentials quiz
Week 8: Average at least 70% across the two final full mock papers, with all eleven domains attempted