Counting, Matrices and Differential Equations
Permutations and combinations, linear systems, and equations that describe change.
01CountingThe multiplication principle, permutations and combinations and how to tell them apart, arrangements with repeated letters or restrictions, circular arrangements, and probability including conditional and independent events.100 questions02Matrices and Systems of Linear EquationsThe determinant of a 3 × 3 matrix, cofactors and the adjoint, the inverse and when it exists, solving a system of three equations by matrix inversion or row reduction, and deciding whether a system has one solution, none, or infinitely many.100 questions03Differential Equations and ModellingSolving first-order equations by separating the variables and by the integrating factor, second-order equations with constant coefficients through the auxiliary equation, particular integrals, and using all of this to model growth, decay and cooling.100 questions