STPM Mathematics 954 study plan

Differentiate composite, implicit, and parametric functions from first principles and standard rules, then verify each derivative by an independent method

Construct a one-page decision tree for choosing between product, quotient, and chain rules when a function is layered three or more deep

Solve ten limit problems involving indeterminate forms using L'Hopital's rule where valid, and state why the rule fails where it does

Sketch curves by locating stationary points, inflection points, and asymptotes, and classify each stationary point with the second derivative test

Integrate standard forms, linear substitutions, and products requiring integration by parts, choosing the substitution before writing any working

Evaluate definite integrals and apply them to areas between curves, volumes of revolution, and arc length

Set up and solve first-order separable differential equations from a stated physical or geometric context

Diagnose and correct the three most common integration slips: missing constant, wrong limits after substitution, and sign errors in by-parts

Solve polynomial, modulus, and rational inequalities and express solution sets on a number line and in interval notation

Decompose rational functions into partial fractions, including repeated and irreducible quadratic factors

Apply the binomial theorem to expand powers and extract a specified coefficient without full expansion

Determine domain, range, and inverse of composite functions, and test one-to-one behaviour algebraically

Perform vector addition, scalar multiplication, dot product, and cross product in two and three dimensions and interpret each geometrically

Find equations of lines and planes in vector, parametric, and Cartesian form and convert between them

Compute angles between lines and planes and distances from a point to a line and to a plane

Solve intersection problems for pairs of lines and for line-plane systems, distinguishing unique, parallel, and skew cases

Compute mean, variance, and standard deviation for raw and grouped data and interpret each measure in context

Calculate and interpret quartiles, interquartile range, and outliers using a stated rule

Compute Pearson and Spearman correlation coefficients and explain when each is appropriate

Fit a least-squares regression line, interpret slope and intercept, and predict with an explicit statement of extrapolation risk

Apply the addition and multiplication rules, including conditional probability and independence tests, to multi-stage problems

Use tree diagrams and two-way tables to compute conditional probabilities and check answers by a second method

Recognise and compute binomial, Poisson, and normal probabilities, including continuity correction and standardization

Decide which distribution fits a described random process and justify the choice in one sentence

Formulate null and alternative hypotheses for one- and two-tailed tests about means and proportions

Carry out z-tests and t-tests, compute test statistics and p-values, and state conclusions in context

Construct confidence intervals for means and proportions and relate interval width to sample size and confidence level

Distinguish Type I and Type II errors and describe one design change that reduces each

Complete two full-length timed papers under exam conditions and record time spent per question

Re-solve every question missed in weeks 1 to 7 and classify each error as conceptual, procedural, or careless

Rewrite the weakest formula sheet section from memory and check it against the original

Rank remaining weak topics by expected marks gained per hour and schedule the top three before exam day