MATSEC IM Applied Mathematics study plan

Build a one-page formula sheet covering differentiation rules (product, quotient, chain) and standard integrals, then use it to solve 20 mixed derivative and integral exercises without notes.

Sketch and interpret the graphs of the six basic trigonometric functions, marking amplitude, period, and asymptotes, and state domain and range for each.

Convert 15 expressions between exponential and logarithmic form and apply the laws of logarithms to simplify 10 composite expressions.

Solve 12 equations involving trigonometric identities, checking each solution against the required interval.

Differentiate composite, implicit, and parametric functions across 25 graded exercises, annotating which rule each step applies.

Compute definite integrals using substitution and integration by parts for 15 problems, verifying at least 5 by numerical approximation.

Apply calculus to 8 optimisation and rate-of-change word problems, stating the variable, constraint, and objective function before solving.

Identify and correct 5 common errors in a set of deliberately flawed worked solutions.

Resolve and compose vectors in two and three dimensions for 20 exercises, computing magnitudes, scalar and vector products, and angles between vectors.

Apply vector methods to 6 geometry problems (lines, planes, intersections) and interpret each result geometrically.

Construct and interpret displacement-time and velocity-time graphs for 8 kinematics scenarios, extracting acceleration and total distance travelled.

Solve 10 projectile and relative-motion problems using vector decomposition, keeping units consistent throughout.

Resolve forces on inclined planes and in equilibrium for 12 statics problems, drawing a complete free-body diagram for each.

Apply Newton's second law to 10 dynamics problems involving friction, tension, and connected particles.

Compute moments and torques for 8 rigid-body problems and verify equilibrium conditions.

Analyse 6 circular-motion and simple-harmonic-motion scenarios, deriving the governing relations from first principles.

Model 10 real-world situations as differential equations, classifying order, degree, and linearity for each.

Solve first-order separable and linear differential equations for 12 problems, applying an initial condition in each case.

Interpret the solution of a differential equation in context, describing long-term behaviour and any equilibrium states.

Set up and solve 5 applied modelling problems (growth, decay, cooling, mixing) and state the assumptions made.

Compute probabilities using the addition and multiplication rules, conditional probability, and independence for 20 exercises.

Apply the binomial and normal distributions to 15 problems, including continuity correction and standardisation.

Calculate and interpret expectation, variance, and standard deviation for discrete and continuous random variables.

Solve 8 permutation and combination counting problems and justify the choice of formula in each.

Complete three full past-paper-style papers under timed conditions, allocating marks per question before starting each.

Review every incorrect or skipped question and classify each error as conceptual, procedural, or careless.

Re-attempt all misclassified conceptual errors unaided until solved correctly without hints.

Practise presenting solutions with clear intermediate steps, defined variables, and stated units to secure method marks.

Condense all notes into a final two-page revision sheet covering the highest-frequency methods from weeks 1-6.

Re-solve the 20 hardest problems previously marked wrong, targeting full marks within the time allowance.

Complete two final timed papers under exam conditions and compare scores against the week-4 and week-7 baselines.

List remaining weak areas and schedule targeted practice for the days before the exam.