STPM Mathematics 954 study guide
STPM Mathematics 954 · Work through your exam, one topic at a time.
STPM Mathematics 954 is the mathematics paper in Sijil Tinggi Persekolahan Malaysia, the pre-university qualification taken after SPM and widely used for university admission in Malaysia and abroad. It suits candidates who need a rigorous, proof-aware mathematics background for science, engineering, computing, economics or actuarial pathways. The STPM Mathematics 954 study guide has 6 sections and about 1,885 words.
01Algebra and Functions
Algebra and Functions underpins Paper 1: functions and graphs, composite and inverse functions, polynomials (remainder and factor theorems), partial fractions, binomial expansion of (1 + x)^n for rational n, and sequences and series including AP, GP and sums to infinity. A function has an inverse only if it is one-one.
312 words, about 2 min02Calculus
Calculus carries a large mark share: differentiation by product, quotient, chain, implicit and parametric rules; integration by substitution, parts and partial fractions; definite integrals, areas and volumes of revolution; and first-order differential equations solved by separating variables. d/dx(ln x) = 1/x, d/dx(e^{kx}) = ke^{kx}; the chain rule applies inside every composite.
297 words, about 1 min03Vectors and Geometry
Vectors in two and three dimensions: addition, scalar multiples, position and unit vectors, magnitude; the scalar product for angles and perpendicularity; the vector product for areas and normals; equations of lines and planes, plus angles and intersections between them. a·b = a b cos θ, so a·b = 0 exactly when a and b are perpendicular.
307 words, about 2 min04Statistics
Descriptive statistics: measures of location and dispersion for raw and grouped data, quartiles from cumulative frequency, box-and-whisker plots and skewness, and how linear coding y = ax + b changes summary statistics. Mean x̄ = Σx/n for raw data, Σfx/Σf for grouped data; median and quartiles by interpolation within the cumulative-frequency class.
322 words, about 2 min05Probability and Probability Distributions
Probability rules, conditional probability, independence and tree diagrams; the binomial and Poisson distributions; the normal distribution, including the normal approximation to the binomial and Poisson with continuity correction. P(A∪B) = P(A) + P(B) - P(A∩B); P(A') = 1 - P(A).
286 words, about 1 min06Hypothesis Testing and Inference
Forming H0 and H1, choosing the correct statistic, running one- and two-tailed tests at a stated significance level, interpreting p-values and error types, plus chi-squared goodness-of-fit and independence tests and inference about correlation. H0 always states equality (μ = μ0); H1 fixes the direction ( , < or ≠), taken from the question, not the data.
361 words, about 2 min