PSAT / Intermediate
PSAT/NMSQT Math
Discovery Lab
Targeted practice in algebra, advanced math, data analysis, geometry and trigonometry.
Preparation: Comfort with fractions, signed numbers and basic equations. Use foundation links whenever you need a smaller step.
Current coverage: 4 domains, 20 focused lessons, original practice and two checkpoint forms per domain.
LEVEL 1 · DIFFICULTY 3/5 within this course
Algebra: Models & Constraints
Represent relationships with equations, lines, systems and inequalities.
Explore 4 knowledge islands
Choose an island to read its lesson.
4 stages · 32 library problems · 112 checked variations · 2 × 8 assessment questions
Read the lessons →LEVEL 2 · DIFFICULTY 3/5 within this course
Advanced Math: Expressions & Functions
Connect equivalent expressions, nonlinear solutions and function models.
Explore 6 knowledge islands
Choose an island to read its lesson.
- MINI QUEST PSAT 2.1Rational Exponents & RadicalsRead the lesson
- MINI QUEST PSAT 2.2Quadratic Formula & Completing the SquareRead the lesson
- MINI QUEST PSAT 2.3Rational Equations & Domain RestrictionsRead the lesson
- MINI QUEST PSAT 2.4Radical Equations & Extraneous RootsRead the lesson
- MINI QUEST PSAT 2.5Lines & Parabolas: Nonlinear SystemsRead the lesson
- MINI QUEST PSAT 2.6Exponential Growth, Decay & TablesRead the lesson
6 stages · 48 library problems · 168 checked variations · 2 × 12 assessment questions
Read the lessons →LEVEL 3 · DIFFICULTY 3/5 within this course
Data Analysis: Evidence & Predictions
Use data displays, probability, sampling, rates and units to reason carefully.
Explore 6 knowledge islands
Choose an island to read its lesson.
- MINI QUEST PSAT 3.1Standard Deviation, Center & OutliersRead the lesson
- MINI QUEST PSAT 3.2Dot Plots, Histograms & Frequency TablesRead the lesson
- MINI QUEST PSAT 3.3Scatterplots & Lines of Best FitRead the lesson
- MINI QUEST PSAT 3.4Two-Way Tables & Conditional ProbabilityRead the lesson
- MINI QUEST PSAT 3.5Samples, Population Estimates & LimitsRead the lesson
- MINI QUEST PSAT 3.6Rates, Units & Percent ChangesRead the lesson
6 stages · 48 library problems · 168 checked variations · 2 × 12 assessment questions
Read the lessons →LEVEL 4 · DIFFICULTY 3/5 within this course
Geometry & Trigonometry: Applications
Connect measurements, similarity and right-triangle ratios.
Explore 4 knowledge islands
Choose an island to read its lesson.
4 stages · 32 library problems · 112 checked variations · 2 × 8 assessment questions
Read the lessons →Progress earned through practice
Earn two independent practice stars and one application star, then complete the library skill check for that stage. The check covers the stage’s library prompts, so changing numbers alone is not enough. Hints help you learn; your existing stars and earned rewards stay yours. Clear every stage to clear a level.
Every stage includes an explanation, two worked examples and eight library practice problems, plus checked variations with changing numbers and applications. Each level also has a separate unit test and a later review form. Parents see actual attempts, hint use and results.
These are independently authored core-skills courses, with the current scope listed for each course. They do not reproduce complete textbook contents. Difficulty describes the teaching sequence within each course; course preparation matters when comparing subjects. This site is not affiliated with or endorsed by AoPS. Results reflect these exercises and are not standardized scores. Content release math-courses-2026.09.27-university-guides-v2.