Mathematics – Secondary Grade 2

Course highlights

• Find the domain and range of real functions, decide even/odd and one-to-one, study monotonicity, compose functions, sketch curves with translations, reflections and stretches, and solve absolute-value equations and inequalities
• Apply the laws of rational exponents, graph exponential functions and solve aˣ = b, find inverse functions, define and graph y = logₐx, use the laws of logarithms and solve exponential and logarithmic equations and growth problems
• Recognise indeterminate forms, find limits by substitution, factorisation, rationalisation and the rule lim (xⁿ − aⁿ)/(x − a) = n aⁿ⁻¹, find limits at infinity and of trigonometric functions, use one-sided limits and decide continuity
• State and apply the sine rule (incl. a/sin A = 2r) and the cosine rule to find unknown sides and angles and to solve triangles in applied problems
• Find the resultant of concurrent coplanar forces, resolve forces into components, state conditions for the equilibrium of a particle/rigid body under concurrent forces, and solve problems of equilibrium on rough horizontal and inclined planes using friction and the angle of friction
• Describe points, lines and planes in space, recognise pyramids and cones, calculate the lateral and total areas and volumes of right pyramids and cones, and find and use the equation of a circle in standard and general form
• Generate sequences from a general term or a recurrence, use Σ notation, and find terms and sums of arithmetic and geometric sequences and series, including the sum to infinity of a convergent geometric series
• Use the fundamental counting principle, factorials, permutations ⁿPᵣ and combinations ⁿCᵣ (and their properties) to count arrangements and selections
• Find average and instantaneous rates of change, differentiate polynomial, product, quotient, composite and trigonometric functions, write tangent and normal equations, and find indefinite integrals of polynomials
• Solve elevation/depression problems, and use the sum, difference, double-angle and half-angle formulas
• Describe straight-line motion (displacement, velocity, relative velocity), and apply the equations of uniformly accelerated motion including free fall and vertical projection
• Compute momentum and its change, and apply Newton's three laws to motion on horizontal planes, in lifts and on smooth and rough inclined planes

Course content

• 14units
• 56sessions
• 13quizzes

The lecturer