math-lessons

Math Lessons

Short interactive lessons for a 9th grader preparing for the PreACT 9, built around the questions missed on a practice test. Each lesson takes 5–10 minutes: read the worked examples, then try the quiz and get feedback right away.

Start with the study plan. It ranks the lessons by payoff: questions at stake × how fast the habit can be fixed.

Lessons, in study-plan order

1. Finish every section, never leave a blank: pacing, time caps and guessing (all sections)
2. Reading: spot the trap answer: answers that are too strong, too narrow or about the wrong paragraph
3. Science: read the data exactly: the right row, the right units and the passage’s own definitions
4. English: four grammar rules: subject–verb agreement, commas before names, dash pairs, semicolons
   • Follow-up: Extra info comes in pairs: titles before names, comma pairs around descriptions, closing a dash
   • Follow-up: Who, which, that: when a who/which clause gets commas, and why that never does
5. Science: conflicting viewpoints: one line per student before answering
6. English: what’s the question’s job?: add/delete, conclusions, transitions, sentence placement

Math

• The missing-letter rule: putting a triangle’s sides and angles in order
• SOH CAH TOA, and when to divide: choosing sin, cos or tan, and whether to multiply or divide
• Math practice test: a full 34-question, 45-minute section with the same skills in the same order as ACT’s free PreACT 9 practice form, with new numbers, a pacing timer and results by skill

Reference

• Study plan: the ranked plan and how to use it
• Triangles cheat sheet: both math methods on one printable page

Read or watch

• ACT, “Preparing for the ACT Test” 2025–26: official tips for every section, plus a practice test
• ACT, Preparing for PreACT 9 Secure: official PreACT 9 timings and format
• ACT, Description of the Science Test: the three Science passage types, including Conflicting Viewpoints
• Purdue OWL: Transitional Devices: transition words grouped by meaning
• Math Open Reference: side lengths and angles: drag the corners of a triangle and watch the rule hold
• Khan Academy: Ordering triangle sides and angles: short video on the same rule
• Lippman & Rasmussen, §5.5 Right Triangle Trigonometry: free open textbook; Example 3 is the “divide” case

Using the lessons

The lessons are plain HTML files with no build step. Open them from the website or in any browser. They load KaTeX from a CDN to display the math, so they need an internet connection.