Mathematics Basic study plan
Mathematics Basic · Give each week a clear focus.
8 weeks · About 6 hours per week
Algebra
Solve linear equations and inequalities in one variable, including those with fractions and parentheses, and check each solution by substitution
Rearrange formulas and literal equations to isolate any named variable
Translate short word problems into a single equation or inequality and interpret the answer in context
Build a one-page error log listing every mistake made this week with its cause
Your checkpoint
A timed 20-question linear equations and inequalities set scored at 80 percent or higher, with the error log attached
Algebra
Apply the exponent rules and simplify expressions with integer and rational exponents
Factor polynomials by common factor, difference of squares, and trinomial methods
Solve quadratic equations by factoring, completing the square, and the quadratic formula, and choose the most efficient method for a given equation
Simplify rational expressions and solve proportions arising from rate problems
Your checkpoint
A 15-question algebra set covering factoring, quadratics, and rational expressions, scored and corrected, with a written note on which method you chose and why for each quadratic
Algebra & Functions
Solve systems of two linear equations by substitution, elimination, and graphing, and classify the system as consistent, inconsistent, or dependent
Identify domain and range from an equation and state restrictions for rational and radical expressions
Evaluate and interpret function notation, including composite and inverse operations on simple functions
Sketch linear, quadratic, and absolute value functions from their key features without a calculator
Your checkpoint
A two-page function summary sheet: for each of the four parent functions, list the equation, domain, range, graph shape, and one worked transformation example
Functions
Interpret slope and intercepts of a linear model in a real context and use them to make a prediction
Recognize and model exponential growth and decay from a table or a verbal description
Convert between verbal, tabular, graphical, and symbolic representations of the same relationship
Identify the effect of parameter changes on a graph, such as shifts, stretches, and reflections
Your checkpoint
A mid-plan timed mixed set of 25 questions drawn from Number, Algebra, and Functions, scored against a 70 percent target, with every missed item reworked in full
Geometry and Measurement
Solve for missing lengths and angles in triangles using the Pythagorean theorem and similar-triangle ratios
Compute perimeter, area, and volume for rectangles, triangles, circles, cylinders, and rectangular solids, keeping units consistent
Apply the angle relationships for parallel lines cut by a transversal and for interior angles of polygons
Convert within and between measurement systems and carry units through multi-step calculations
Your checkpoint
A 12-problem geometry problem set with a labeled sketch and full unit tracking for each problem, scored at 75 percent or higher
Geometry and Measurement & Statistics and Probability
Use the distance, midpoint, and slope formulas on the coordinate plane to classify figures
Compute mean, median, mode, and range from a data set and from a frequency table
Read and construct histograms, box plots, and scatter plots, and describe the shape of a distribution
Distinguish correlation from causation when interpreting a scatter plot trend
Your checkpoint
A one-page data display project: collect or use a 20-value data set, compute all summary statistics, draw a box plot and histogram by hand, and write three interpretive sentences
Statistics and Probability & Number and Quantity
Compute simple and compound probabilities for independent and dependent events, including complementary events
Count outcomes using the fundamental counting principle and simple permutations and combinations
Perform operations with rational numbers, ratios, proportions, and percents in applied settings
Estimate with scientific notation and judge the reasonableness of a computed answer
Your checkpoint
A 20-question probability and number-sense set scored at 80 percent or higher, plus a half-page list of the estimation shortcuts you actually used
Number and Quantity & Algebra & Functions & Geometry and Measurement & Statistics and Probability
Complete two full-length timed practice tests under exam conditions and record the score for each domain
Rank your five domains by accuracy and rework every missed item from the two weakest domains
Rebuild your error log into a one-page formula and concept sheet you can review in ten minutes
Simulate pacing by completing a 30-question set in the allotted time without stopping to relearn content
Your checkpoint
Two scored practice tests with a domain-by-domain accuracy table and a final one-page review sheet
Milestones
Week 2: Score 80 percent or higher on an untimed 20-question Algebra set covering linear equations, factoring, and quadratics, with no repeated error type from week 1
Week 4: Score 70 percent or higher on a timed 25-question mixed set from Number, Algebra, and Functions, and show full worked corrections for every miss
Week 6: Score 75 percent or higher on a 12-problem Geometry and Measurement set with correct units on every answer, and submit the completed data display project
Week 8: Score 75 percent or higher on each of two full-length timed practice tests, with no domain below 65 percent accuracy and the final review sheet completed