MB Pre-Calculus 40S study plan

Convert fluently among degrees and radians and locate exact trigonometric ratios for special and quadrantal angles without a calculator

Sketch sine, cosine, and tangent graphs and label amplitude, period, phase shift, and vertical displacement

Solve first-degree trigonometric equations over a stated interval and express the general solution

Apply the primary trigonometric ratios to solve right-triangle and oblique-triangle word problems

Derive and apply the sum, difference, and double-angle identities to simplify expressions

Prove at least six trigonometric identities showing each algebraic step

Model and solve real-world periodic situations such as tides or Ferris-wheel height using sinusoidal equations

Verify solutions to trigonometric equations graphically and reject extraneous roots

Graph exponential and logarithmic functions and describe domain, range, asymptote, and intercepts

Apply the laws of logarithms to expand, condense, and evaluate expressions

Solve exponential equations by rewriting bases and logarithmic equations by exponentiating

Translate compound-interest and half-life contexts into exponential models and interpret the results

Identify and graph the parent functions and apply vertical and horizontal stretches, reflections, and translations

Write the equation of a transformed function from a described sequence of transformations and from a sketch

Determine the inverse of a function algebraically and confirm it by reflecting across the line y equals x

Connect transformations of exponential and logarithmic graphs to their equations

State the domain and range of radical and rational functions and locate vertical and horizontal asymptotes

Solve radical equations and check for extraneous solutions

Simplify rational expressions and solve rational equations including applications

Graph rational functions showing intercepts and asymptotic behaviour

Apply the fundamental counting principle and distinguish permutations from combinations in context

Compute permutations and combinations with and without repetition and solve arrangement problems with restrictions

Expand binomial powers using the binomial theorem and identify a specified term

Solve pathway and selection problems that combine multiple counting strategies

Distinguish arithmetic and geometric sequences and generate terms from recursive and explicit formulas

Compute sums of finite arithmetic and geometric series and apply the infinite geometric series formula with its convergence condition

Interpret sigma notation and evaluate or rewrite given series

Model real-world growth, depreciation, and accumulation situations with series

Derive and use standard and general forms of circles, parabolas, ellipses, and hyperbolas, identifying centre, vertices, foci, and axes

Convert conic equations between general and standard form by completing the square

Complete two full-length mixed practice exams under timed conditions and log every error by domain

Re-drill the three weakest domains identified from error logs until accuracy reaches 85%