JC 2 Mathematics

Students will define vectors, understand their representation in 2D and 3D, and perform basic vector operations.

Students will calculate vector magnitudes, find unit vectors, and use position vectors to describe points in space.

Students will understand the scalar product, its geometric interpretation, and its application in finding angles between vectors.

Students will learn the vector product, its properties, and its use in finding a vector perpendicular to two given vectors and calculating area.

Students will derive and apply vector and Cartesian equations for lines in three-dimensional space.

Students will derive and apply vector and Cartesian equations for planes, including normal vectors.

Students will solve problems involving the intersection of lines with lines, lines with planes, and planes with planes.

Students will calculate the angles between two lines, a line and a plane, and two planes.

Students will calculate distances between points, a point and a line, a point and a plane, and between parallel/skew lines.

Students will define imaginary numbers, complex numbers, and perform basic arithmetic operations.

Students will understand complex conjugates and use them to perform division of complex numbers.

Students will represent complex numbers geometrically on an Argand diagram and convert to modulus-argument form.

Students will perform multiplication and division of complex numbers using their modulus-argument forms.

Students will apply De Moivre's Theorem to find powers and roots of complex numbers.

Students will find the nth roots of complex numbers and represent them geometrically.

Students will sketch and interpret loci of complex numbers satisfying given conditions.

Students will use complex numbers to find roots of polynomial equations, especially those with real coefficients.

Students will review fundamental integration rules and techniques, including indefinite and definite integrals.

Students will apply the method of substitution to integrate more complex functions.

Students will use integration by parts to integrate products of functions.

Students will decompose rational functions into partial fractions to facilitate integration.

Students will integrate various trigonometric functions, including powers and products.

Students will evaluate improper integrals with infinite limits or discontinuous integrands.

Students will apply integration to calculate areas between curves and volumes of solids of revolution.

Students will define differential equations and solve first-order separable differential equations.

Students will solve first-order linear differential equations using the integrating factor method.

Students will formulate and solve differential equations to model real-world phenomena.

Defining sequences and series and understanding sigma notation.

Exploring the properties of sequences with constant differences and their sums.

Exploring the properties of sequences with constant ratios and their sums.

Students will calculate the sum to infinity for convergent geometric series and understand its conditions.

Expanding binomials with positive integer powers using Pascal's triangle and the binomial theorem.

Applying the binomial theorem to expand expressions with positive integer powers, including finding specific terms and coefficients.

Students will apply the binomial theorem for non-positive integer and fractional powers, understanding its conditions for validity.

Students will use binomial expansion for approximations and solving related problems.

Reviewing fundamental probability definitions, events, and sample spaces.

Using permutations and combinations to solve complex counting problems.

Understanding conditional probability and the concept of independent events.

Students will apply Bayes' Theorem to update probabilities based on new evidence.

Defining discrete random variables and their probability distributions.

Calculating the expected value and variance for discrete random variables.

Modeling scenarios with a fixed number of independent trials and two possible outcomes.

Students will model the number of events occurring in a fixed interval of time or space.

Students will understand and apply the Poisson approximation to the binomial distribution.

Students will understand the properties of the normal distribution and calculate probabilities using z-scores.

Students will apply the normal approximation to the binomial distribution, including continuity correction.

Students will apply the normal approximation to the Poisson distribution, including continuity correction.

Students will understand sampling methods and the concept of a sampling distribution of the sample mean.

Students will understand and apply the Central Limit Theorem to sample means.

Students will define null and alternative hypotheses, and understand Type I and Type II errors.

Students will perform one-sample hypothesis tests for the population mean using the normal distribution.

Students will perform one-sample hypothesis tests for the population proportion.

Constructing and interpreting scatter diagrams to visualize relationships between two variables and drawing lines of best fit.

Students will calculate and interpret the product moment correlation coefficient and the equation of the least squares regression line.

Students will interpret regression results, understand extrapolation, and identify limitations of linear models.