PEI Math 521A study plan

Diagnose your current algebra level by completing a timed 25-question self-made pretest covering linear, quadratic, polynomial, rational, radical, exponential, and logarithmic equations, then score it by error type.

Rewrite each missed algebra item into a corrected worked solution and label the underlying rule (factoring, exponent laws, domain restrictions, inverse operations) that was violated.

Build a one-page reference sheet of function-family properties (domain, range, symmetry, end behavior, asymptotes) for linear, quadratic, absolute value, exponential, and logarithmic functions.

Solve 15 composition and inverse-function problems and verify each inverse by checking that f(f⁻¹(x)) = x symbolically.

Factor and solve 20 mixed polynomial and rational equations, stating excluded values before clearing denominators.

Graph 10 functions by hand using transformations (shifts, stretches, reflections) and confirm key points against a graphing tool.

Solve 12 inequality problems, expressing solution sets in interval notation and on a number line, including sign-chart methods for rational inequalities.

Apply the factor and remainder theorems to determine polynomial roots and construct a polynomial from given zeros.

Prove and apply the Pythagorean theorem, similarity criteria, and circle theorems (inscribed angle, tangent-radius, chord relationships) across 15 problems.

Compute areas and volumes of composite 2D and 3D figures, including sectors, frustums, and solids with a removed section.

Derive the distance, midpoint, and slope formulas from coordinate geometry and use them to classify quadrilaterals given four vertices.

Write equations of circles and parabolas in standard form by completing the square, then identify center, radius, vertex, and directrix.

Evaluate all six trigonometric functions at standard and quadrantal angles without a calculator, and convert fluently between degrees and radians.

Solve 12 triangle problems using the law of sines, law of cosines, and area formulas, identifying the ambiguous case when it arises.

Prove 8 trigonometric identities by manipulating one side only, and solve 8 trigonometric equations over a stated interval.

Sketch sine and cosine graphs with amplitude, period, phase shift, and vertical shift, and write an equation from a given graph.

Evaluate limits algebraically (factoring, rationalizing, common denominators) and identify where a function is discontinuous and why.

State the limit definition of the derivative and use it to differentiate three functions from first principles.

Apply the product, quotient, and chain rules to 20 composite functions, showing each intermediate step.

Solve 10 applied optimization and related-rates problems by defining variables, writing a constraint equation, and justifying the optimum.

Compute definite integrals using antiderivatives and the Fundamental Theorem of Calculus, and interpret each result as a signed area.

Sketch curves and compute the area between two curves and the volume of a solid of revolution for 6 problems.

Distinguish and compute mean, median, mode, variance, and standard deviation for grouped and ungrouped data sets, showing the computation.

Construct and interpret histograms, box plots, and normal-distribution probability statements using z-scores and the empirical rule.

Solve 10 probability problems using the addition and multiplication rules, conditional probability, and independence, stating assumptions explicitly.

Apply permutations and combinations to count outcomes in 10 scenario problems and distinguish when order matters.

Compute expected value and interpret it in a decision context, including a simple expected-value comparison of two options.

Write truth tables for compound statements and test 6 arguments for validity using direct proof, contradiction, or counterexample.

Build and interpret a mathematical model for a real scenario (linear, exponential, or quadratic), stating domain restrictions and the meaning of each parameter.

Critique three given models for reasonableness by checking units, extrapolation limits, and sensitivity to assumptions.

Complete two full-length timed mock exams under exam conditions and score each by domain to identify remaining gaps.

Consolidate all error logs and reference sheets into a single final review document covering the highest-weight domains.