NYS Math study plan
NYS Math · Give each week a clear focus.
8 weeks · About 6 hours per week
Number and Quantity & Algebra
Classify real numbers into rational, irrational, integer, and natural subsets and justify each classification with a written reason
Rewrite radical and rational-exponent expressions in equivalent forms without a calculator
Apply exponent rules to simplify expressions containing negative and fractional exponents
Solve linear equations and inequalities in one variable, including compound inequalities, and graph the solution set on a number line
Your checkpoint
A 20-item self-made error log covering number-sense and linear-equation problems, with each missed item corrected and annotated by error type
Algebra
Factor quadratic expressions by inspection, grouping, and difference of squares
Solve quadratic equations by factoring, completing the square, and the quadratic formula, and verify roots by substitution
Interpret the discriminant to predict the number and type of solutions
Solve systems of two linear equations algebraically and confirm the solution graphically
Simplify polynomial and rational expressions and state excluded values
Your checkpoint
A one-page decision flowchart mapping problem cues to the correct algebraic method, plus 15 solved problems that follow it
Algebra & Functions
Distinguish functions from relations using the vertical-line test and input-output uniqueness
Evaluate and compose functions, and find inverse functions for one-to-one cases
Identify domain and range restrictions from equation structure and from a described context
Write and solve exponential growth and decay models from word problems
Your checkpoint
A table of 12 function families listing equation form, domain, range, key features, and one worked application each
Functions
Graph linear, quadratic, absolute value, and exponential functions and label intercepts, vertex, and asymptotes
Translate between equation, table, graph, and verbal description for the same function
Interpret slope and rate of change in context and compare average rates of change across intervals
Solve equations graphically by locating points of intersection
Your checkpoint
A four-representation portfolio of 8 functions, each shown as equation, table, labeled graph, and contextual sentence, scored against a self-written rubric
Geometry
Prove and apply triangle congruence and similarity criteria to find missing lengths and angles
Apply the Pythagorean theorem and right-triangle trigonometry to solve contextual problems
Compute area and volume of composite figures, keeping units consistent
Perform and describe transformations on the coordinate plane, including dilations and their effect on length and area
Write and evaluate coordinate-geometry proofs using distance, midpoint, and slope
Your checkpoint
A timed 25-minute mixed geometry set of 12 problems, graded with a corrected solution for every miss
Geometry & Statistics and Probability
Derive the equation of a circle from its center and radius, and complete the square to recover center and radius
Distinguish independent and dependent events and apply conditional probability rules
Interpret two-way frequency tables and compute joint, marginal, and conditional frequencies
Decide when to use permutations versus combinations and compute each
Your checkpoint
A two-way table built from self-collected or invented data, with all joint, marginal, and conditional frequencies computed and interpreted in writing
Statistics and Probability
Summarize a data set with mean, median, mode, range, IQR, and standard deviation, and explain when each is preferred
Construct and interpret box plots, histograms, and scatter plots, describing shape, center, spread, and outliers
Fit a line of best fit to bivariate data and interpret slope, intercept, and correlation versus causation
Design a sampling method and identify sources of bias in a described study
Your checkpoint
A full statistical report on one data set including graphs, summary statistics, a line of best fit, and a bias critique
Number and Quantity & Algebra & Functions & Geometry & Statistics and Probability
Assemble a ranked list of your 10 weakest objectives from weeks 1-7 and re-teach each one with a worked example
Complete two full-length timed practice tests under exam conditions and record per-domain accuracy
Analyze every missed item to classify errors as conceptual, procedural, or misreading, then correct each
Build a one-page formula and concept sheet from memory and check it against your notes
Your checkpoint
A final error-analysis report with per-domain accuracy from both practice tests and a written remediation note for each of the 10 weakest objectives
Milestones
Week 2: Score at least 80% on a self-made 15-question algebra quiz covering factoring, the quadratic formula, and systems, with all misses corrected
Week 4: Explain aloud, in under 5 minutes each, how to find domain, range, and key features for a quadratic and an exponential function, recording the explanation for self-review
Week 6: Score at least 75% on a mixed 20-question geometry and probability set, and correctly compute all four frequency types from a two-way table
Week 8: Achieve at least 80% overall on the second full-length practice test with no domain below 70%