Pancyprian Core Math study plan

Solve linear equations and inequalities in one variable, including those with fractions and parentheses, and express solution sets in interval notation.

Graph linear functions, determine slope and intercepts, and write equations of lines in point-slope and slope-intercept form.

Solve systems of two linear equations by substitution and elimination, and interpret the solution graphically.

Factor quadratic expressions and solve quadratic equations by factoring, completing the square, and the quadratic formula.

Apply the discriminant to determine the number and type of roots of a quadratic equation.

Compute limits of polynomial, rational, and piecewise functions algebraically, including one-sided limits.

Determine continuity at a point and identify types of discontinuities from a graph or equation.

Differentiate polynomial, rational, and radical functions using power, product, quotient, and chain rules.

Find equations of tangent lines and solve basic related-rates problems.

Locate critical points and classify local extrema using the first derivative test.

Sketch graphs of polynomial, rational, exponential, and logarithmic functions, identifying key features such as asymptotes, intercepts, and end behavior.

Solve exponential and logarithmic equations, including applications to growth and decay.

Apply the Fundamental Theorem of Calculus to evaluate definite integrals.

Compute indefinite integrals using basic antiderivatives and substitution.

Solve optimization problems involving maxima and minima in applied contexts.

Compute and interpret measures of center (mean, median, mode) and spread (range, IQR, standard deviation) for raw data sets.

Construct and interpret histograms, box plots, and scatter plots to describe distributions and identify outliers.

Calculate probabilities using the addition and multiplication rules, including conditional probability and independence.

Apply the binomial and normal distributions to solve probability problems, including using z-scores and tables.

Design and analyze a simple statistical study, identifying sampling methods and sources of bias.

Perform operations with real numbers, including exponents, radicals, and absolute value, without a calculator.

Convert between fractions, decimals, and percents, and solve percent increase/decrease problems.

Simplify expressions involving integer and rational exponents, and rationalize denominators.

Solve ratio, proportion, and variation problems, including direct and inverse variation.

Apply number theory concepts (divisibility, prime factorization, GCD, LCM) to solve problems.

Solve problems involving perimeter, area, and volume of polygons, circles, and solids, including composite figures.

Apply the Pythagorean theorem and distance and midpoint formulas in coordinate geometry.

Use similarity and congruence criteria to prove geometric relationships and solve for unknown lengths.

Define the six trigonometric functions and evaluate them for special angles (30°, 45°, 60°) and quadrantal angles.

Solve right triangles using trigonometric ratios and the Law of Sines and Law of Cosines.

Translate verbal problems into algebraic equations or inequalities and solve them, including mixture, work, and distance problems.

Identify and use patterns and sequences (arithmetic and geometric) to model and solve problems.

Apply logical reasoning to evaluate the validity of arguments and identify fallacies in mathematical contexts.

Use estimation and dimensional analysis to check the reasonableness of solutions.

Solve multi-step problems by breaking them into simpler parts and selecting appropriate strategies.

Review and reinforce key concepts from algebra, statistics, and calculus through mixed practice.

Complete a full-length timed practice exam under test conditions.

Analyze errors from the practice exam and create a personalized review list.

Revisit weak areas identified in the error analysis with targeted exercises.

Finalize a concise reference sheet of formulas and theorems for quick recall.