MATSEC AM Applied Mathematics study plan

Derive and apply the five constant-acceleration (suvat) equations to vertical and horizontal motion, selecting the correct equation from the known and unknown quantities

Resolve projectile motion into independent horizontal and vertical components, and compute time of flight, maximum height and range for launch angles between 20° and 70°

Construct and interpret velocity–time and displacement–time graphs, extracting acceleration as gradient and displacement as area

Set up Newton's second law along and perpendicular to an incline, including the component of weight mg sin θ and mg cos θ

Solve connected-particles problems (masses over a pulley, objects joined by a tow-bar) by writing simultaneous equations for each body

Apply the impulse–momentum theorem FΔt = Δ(mv) to collision and rebound problems, choosing a sign convention and stating it explicitly

Apply conservation of linear momentum to one-dimensional collisions and explosions, and classify each as elastic or inelastic using kinetic energy

Compute work done by a constant force as Fd cos θ and by a variable force as the area under a force–displacement graph

Apply the work–energy principle and power P = Fv to problems combining motion and energy

Draw complete free-body diagrams for a particle in equilibrium under three or more coplanar forces, labelling every reaction, tension and weight

Resolve forces in two perpendicular directions and solve the resulting simultaneous equations for unknown tensions and reactions

Apply the principle of moments about a chosen pivot to rigid bodies and beams, including the weight of the beam acting at its centre of mass

Determine the position of the centre of mass of a composite lamina by taking moments about two axes

Apply the friction model F ≤ μR, distinguish limiting from static friction, and solve problems on horizontal and inclined planes

Apply the addition and multiplication rules for probability, including the distinction between independent and mutually exclusive events

Compute conditional probabilities using P(A|B) = P(A ∩ B)/P(B) and interpret them in a two-way table

Use tree diagrams and Bayes' theorem to reverse conditional probabilities in two-stage experiments

Model a binomial random variable, state its parameters, and compute probabilities, mean and variance

Model a Poisson random variable and decide when the Poisson approximation to the binomial is justified

Compute and interpret mean, median, mode, range, interquartile range, variance and standard deviation from raw data and from grouped frequency tables

Construct and read cumulative frequency curves and box plots, and compare two distributions in context

Compute Pearson's product-moment correlation coefficient and interpret its sign and magnitude, noting that correlation does not imply causation

Fit a least-squares regression line of y on x and use it to predict, stating the limits of extrapolation

Standardise a normal variable and use tables to find probabilities and inverse values for the normal distribution

Distinguish a population from a sample, and explain why a statistic is a random variable with a sampling distribution

Apply the central limit theorem to state the distribution of the sample mean and compute standard error

Construct confidence intervals for a population mean with known and unknown variance, and state the meaning of the confidence level correctly

Set up a one-sample hypothesis test: state null and alternative hypotheses, choose the significance level, compute the test statistic and reach a conclusion in context

Carry out a chi-squared goodness-of-fit test, checking expected frequencies and degrees of freedom

Solve multi-stage mechanics problems that chain kinematics, Newton's second law and energy in a single scenario

Solve momentum problems involving two dimensions or a rebound with a specified coefficient of restitution

Handle equilibrium problems where friction and moments act together on a ladder or a hinged rod

Allocate marks and time across a long structured question, showing method even when the final answer is uncertain

Translate a word problem set in a real context into a mathematical model, stating assumptions and their consequences

Critique a model by identifying where its assumptions break down and how the prediction would shift

Complete timed practice on statistics under exam conditions, including a full hypothesis test and a regression question

Revise the formula sheet from memory and identify any remaining gaps by self-testing without notes