Pancyprian Advanced Math study plan

Sketch graphs of polynomial, rational, exponential and logarithmic functions from their defining features without a graphing aid

Solve inequalities involving absolute values, rational expressions and exponentials, writing solution sets in interval notation

State and apply domain/range and inverse-function conditions to decide when an inverse exists

Reconstruct the standard transformation rules and justify each graphically

Evaluate limits algebraically, including indeterminate forms handled by factoring, rationalizing and conjugates

Classify discontinuities and test continuity at a point and on an interval using the three-part definition

Apply the intermediate value theorem to justify existence of roots

Compute derivatives from the limit definition for polynomial, radical and rational functions

Differentiate products, quotients, composites and implicit relations fluently

Differentiate exponential, logarithmic, trigonometric and inverse-trigonometric functions

Solve related-rates problems by setting up the geometric constraint before differentiating

Find tangent and normal lines and use linearization to estimate function values

Locate critical points, inflection points and asymptotes, then produce a complete curve sketch

Apply the first and second derivative tests to classify extrema

Solve optimization problems with a stated domain and verify endpoints

Prove simple inequalities and root-count results using monotonicity

Compute antiderivatives using substitution, by parts and partial fractions

Evaluate definite integrals and apply the fundamental theorem correctly, including sign conventions

Set up and evaluate area between curves and volumes of revolution

Apply the mean value theorem for integrals and interpret average value

Test series for convergence using comparison, ratio, root and integral tests, stating the condition that justifies each conclusion

Expand binomial powers with positive and negative or fractional indices and state the validity range

Perform arithmetic in Cartesian, polar and exponential form and convert between them

Solve polynomial equations over the complex numbers and apply De Moivre's theorem for roots and powers

Solve 3D line and plane problems, including intersections, angles and distances

Identify a conic from its equation, find foci, directrices and asymptotes, and sketch it

Compute conditional probability and apply the binomial and normal distributions with continuity correction where needed

Interpret mean, variance and standard deviation in context and standardize values for normal calculations

Complete two full-length timed mock papers under exam conditions and self-mark against a rubric

Re-derive from memory every formula on the personal sheet and flag the ones that fail

Re-solve, without notes, the 15 problems most often missed across weeks 1-7

Allocate remaining time by domain weight and rehearse a fixed per-question time budget