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CSCA Mathematics syllabus

Every topic in the ACE CSCA course for the CSCA Mathematics paper, week by week, in the order we teach it: 58 short video lessons over 8 weeks, about an hour a day.

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Week 1 Start here · Sets and inequalities · Function basics Free

  1. 1.1 How the CSCA Math exam works
  2. 1.2 The 60-minute plan and the top traps
  3. 1.3 Sets: elements, subsets, ∅ and number sets
  4. 1.4 Intersections and unions with intervals
  5. 1.5 Quadratic inequalities
  6. 1.6 Rational inequalities
  7. 1.7 Inequality properties
  8. 1.8 Domain, including composite domains
  9. 1.9 Range
  10. 1.10 Odd and even functions
  11. 1.11 Inverse functions
  12. 1.12 Increasing and decreasing functions
  13. 1.13 The “same function” test

Week 2 Trigonometry I: values, ratios, identities, reduction, graphs

  1. 2.1 Radians and special-angle values
  2. 2.2 Ratios from a point on the terminal side
  3. 2.3 Same-angle identities and quadrant signs
  4. 2.4 Reduction formulas
  5. 2.5 Sine and cosine graphs
  6. 2.6 The tangent graph

Week 3 Trigonometry II: sum, difference, double and half angle

  1. 3.1 Sum and difference formulas
  2. 3.2 Double-angle formulas
  3. 3.3 Half-angle formulas and the sign rule
  4. 3.4 Homogeneous ratios
  5. 3.5 Trig trap clinic

Week 4 Coordinates and lines

  1. 4.1 Quadrants, symmetric points, points on axes
  2. 4.2 Distance between two points
  3. 4.3 Slope and inclination angle
  4. 4.4 Equations of a line
  5. 4.5 Intersections and concurrent lines
  6. 4.6 Parallel and perpendicular lines
  7. 4.7 Perpendicular line through an intersection

Week 5 Sequences

  1. 5.1 Arithmetic sequences: the general term
  2. 5.2 Geometric sequences: term and ratio
  3. 5.3 Arithmetic and geometric means
  4. 5.4 General term from a pattern; which type
  5. 5.5 Finding aₙ from Sₙ
  6. 5.6 Recursions and the reciprocal trick
  7. 5.7 Sums: index properties and grouping

Week 6 Conics

  1. 6.1 Circles: standard form
  2. 6.2 Circles: general form
  3. 6.3 Parabolas
  4. 6.4 Ellipses: a, b, c and e
  5. 6.5 Ellipses from conditions
  6. 6.6 Hyperbolas

Week 7 Exponentials and logs · Vectors · Complex numbers · Probability

  1. 7.1 Exponential functions
  2. 7.2 Logarithm rules
  3. 7.3 Log functions and log inequalities
  4. 7.4 Comparing powers, exponentials and logs
  5. 7.5 Vectors
  6. 7.6 Complex numbers
  7. 7.7 Classical probability

Week 8 Insurance topics · Exam mode

  1. 8.1 Derivatives basics (insurance)
  2. 8.2 3D coordinates and simple solids (insurance)
  3. 8.3 Mean and variance (insurance)
  4. 8.4 Normal distribution basics (insurance)
  5. 8.5 The Repeat drill
  6. 8.6 The trap catalogue
  7. 8.7 How to review a mock

Week 8’s “insurance” topics come up rarely. They’re there so nothing on the paper is new to you.

What’s free, and what’s Premium

The diagnostic and all of Week 1 are free, with a free account for Week 1. Premium opens Weeks 2–8, a weekly test at the end of each week, six full mocks, and a written solution for every question.

Start with the diagnostic. 48 questions, 60 minutes, and your weak topics at the end.

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