Free CSCA lessons

Week 1 of the ACE CSCA course, free to read: how the paper is scored and planned, sets, inequalities and the basics of functions. Each lesson has the formulas, drawn diagrams, worked examples and a practice question with hints.

1. Day 2 · Lesson 1.1–1.2 · About 9 minutesHow the CSCA math paper works + your plan by trackHow a CSCA paper is built and scored: 48 questions in 60 minutes, the three bands, a pacing plan for each band, and what a study day looks like.
2. Day 2 · Lesson 1.3–1.4 · About 13 minutesSets: ∈ or ⊆, number sets, ∩ and ∪When to write ∈ and when ⊆, the number sets, and how to find A ∩ B and A ∪ B for finite sets and intervals, endpoints included. Worked examples and practice.
3. Day 3 · Lesson 1.5–1.6 · About 14 minutesQuadratic and rational inequalitiesSolve quadratic and rational inequalities with the “between or outside the roots” rule and write the answer in interval notation. Worked examples and practice.
4. Day 3 · Lesson 1.7 · About 8 minutesInequality properties: test with numbersWhich inequality rules always hold, which break for negative numbers or zero, and how a few test numbers find the statement that must be true.
5. Day 4 · Lesson 1.8–1.9 · About 14 minutesDomain and rangeFind the domain of a function from its formula, including composite functions such as f(2x−1), and its range with the right method for each type.
6. Day 4 · Lesson 1.10 · About 10 minutesOdd and even functionsDecide whether a function is even, odd or neither, use the symmetry to find unknown values and parameters, and avoid the domain trap.
7. Day 5 · Lesson 1.11 · About 10 minutesInverse functionsFind an inverse function and its domain, evaluate f⁻¹(k) without a formula, and use the mirror image of a graph in the line y = x.
8. Day 5 · Lesson 1.12–1.13 · About 13 minutesMonotonicity and the same-function testFind where a function increases or decreases, use monotonicity to solve inequalities and find parameters, and tell whether two functions are the same.