Math 30-2 Diploma study plan
Math 30-2 Diploma · Give each week a clear focus.
8 weeks · About 6 hours per week
Logical Reasoning
Define and distinguish inductive and deductive reasoning using at least three original examples of each
Construct truth tables for negation, conjunction, disjunction, conditional, and biconditional statements
Identify and correct common logical fallacies (e.g., converse error, inverse error) in written arguments
Translate everyday statements into symbolic logic notation and back
Your checkpoint
A one-page reference sheet of truth tables and fallacy definitions, plus 10 self-written practice problems with worked solutions
Logical Reasoning
Apply Euler diagrams to test the validity of syllogisms and categorical arguments
Determine whether a given argument is valid, invalid, sound, or unsound
Solve multi-step logical puzzles (e.g., ordering, grouping) using systematic deduction
Explain the difference between a counterexample and a formal proof
Your checkpoint
A set of 8 solved logic problems (mixed truth tables, Euler diagrams, and puzzles) with a short written justification for each answer
Probability
Compute experimental and theoretical probabilities from given data sets and sample spaces
Distinguish between independent and dependent events and calculate probabilities for each
Apply the addition rule (mutually exclusive vs. non-mutually exclusive) and multiplication rule
Construct and interpret Venn diagrams and two-way tables for probability problems
Your checkpoint
A two-way table and Venn diagram problem set (6 problems) with fully worked probability calculations
Probability
Calculate conditional probabilities and interpret them in context
Solve problems involving permutations and combinations, distinguishing when order matters
Determine probabilities using the fundamental counting principle
Analyze real-world scenarios (e.g., lottery, medical testing) using probability concepts
Your checkpoint
A 10-question mixed probability quiz (self-created) with answer key and brief explanations
Relations and Functions
Identify domain and range from equations, graphs, and tables
Determine whether a relation is a function using the vertical line test and mapping diagrams
Evaluate and interpret function notation in context
Sketch and analyze linear and quadratic functions, including intercepts and vertex
Your checkpoint
A graphic organizer summarizing domain/range, function tests, and key features of linear and quadratic functions, with 5 example problems
Relations and Functions
Model real-world situations with linear, quadratic, and exponential functions
Compare characteristics of linear, quadratic, and exponential growth using tables and graphs
Perform transformations (translations, reflections, stretches) on parent functions
Solve problems involving arithmetic and geometric sequences as functions
Your checkpoint
A mini-project: create three real-world scenarios (one linear, one quadratic, one exponential), model each with an equation and graph, and write a paragraph interpreting the model
Trigonometry
Convert between degrees and radians and use arc length and sector area formulas
Define and apply the six trigonometric ratios in right triangles
Solve right triangles using trigonometric ratios and the Pythagorean theorem
Use the unit circle to evaluate trigonometric functions at special angles
Your checkpoint
A unit circle diagram (hand-drawn) with all special angles labeled in degrees and radians, plus 8 solved right-triangle problems
Logical Reasoning & Probability & Relations and Functions & Trigonometry
Review and synthesize key concepts from all four domains through mixed practice
Complete a full-length practice exam under timed conditions
Identify and remediate weak areas using error analysis
Create a personalized formula sheet and test-taking checklist
Your checkpoint
A completed practice exam with error log and a one-page formula sheet, plus a reflection on areas for further review
Milestones
Week 4: Score at least 80% on a self-created 20-question mixed quiz covering Logical Reasoning and Probability, with written corrections for any missed questions
Week 8: Complete a full-length practice exam (all four domains) with a score of 75% or higher, and submit an error log showing analysis of every incorrect answer