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Faculty of Science Handbook, Academic Session 2025/2026
SYNOPSIS OF COURSES Assessment:
Continuous Assessment: 40%
SIX1016 Summative Assessment: 60%
STATISTICS (FACULTY OF SCIENCE)
SIM1002
Introduction to statistics; Experimental and CALCULUS I
observational studies; Display and
organisation of data; Descriptive statistics; Functions and their graphs, combining
Population and samples; Sampling functions, trigonometric functions. Rate of
methods; Basic probability theory; Useful change and tangent lines to curves, limits of
probability distributions: binomial, Poisson functions and limit laws, the precise
and normal; Sampling distributions; Central definition of a limit, one-sided limits,
Limit Theorem; Point estimation and continuity, limits involving infinity and
confidence interval; Hypothesis testing for asymptotes of graphs. Tangent lines and
mean and proportion in one and two the derivative at a point, the derivative as a
populations; Chi-square tests; Simple linear function, differentiation rules, derivatives
regression and correlation analysis. of trigonometric functions, the chain rule,
implicit differentiation. Extreme values of
Assessment: functions, the mean value theorem,
Continuous Assessment:100% monotonic functions and the first derivative
test, concavity and curve sketching,
SIM1001 antiderivatives. Sigma notation and limits of
BASIC MATHEMATICS finite sums, the definite integral, the
fundamental theorem of calculus,
Introductory logic. Mathematical indefinite integrals and the substitution
statements. Quantifiers. Rules of inference. method, the definite integrals, substitution
Mathematical induction, binomial theorem. and the area between curves, logarithms
Sets, Cartesian products, equivalence functions, exponential functions,
relations, functions, bijections, inverse indeterminate forms and L’Hôpital’s rule.
functions. Integers, rational numbers, real
numbers. Complex numbers. De Moivre’s Assessment:
theorem and roots of unity. Polynomials Continuous Assessment: 40%
and equations. Remainder theorem, Summative Assessment: 60%
fundamental theorem of algebra, conjugate
roots. SIM1003
CALCULUS II
Systems of linear equations, row reduction,
echelon forms. Matrix operations, algebraic Inverse trigonometric functions, hyperbolic
properties of matrices, inverses, functions, inverse hyperbolic functions.
elementary matrices, linear independence Basic integration formulas, integration by
and homogeneous linear systems, matrices parts, trigonometric integrals,
with special forms. Determinants, cofactor trigonometric substitutions, integration of
expansion, properties of determinants, rational functions by partial fractions,
Cramer’s rule, eigenvalues, eigenvectors, improper integrals. Sequence, infinite
and diagonalization. series, the integral test, comparison tests,
absolute convergence, the ratio and root
tests, alternating series test, conditional
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