Calculus I assumes three high-school skills are as automatic as arithmetic — and never re-teaches them. This check tests all three directly. Work on paper, no calculator, no formula sheet, no looking anything up: the point is to measure what you can produce, not what you can find. Score yourself honestly at the end.

Part 1 — Algebra (5 minutes)

  1. Simplify: (x² − 9)/(x − 3), and state any restriction on x.
  2. Expand completely: (x + h)³.
  3. Rewrite with exponent notation: √x + 1/x².
  4. Solve for x: 2ˣ = 8^(x−1).

Answers: 1) x + 3, with x ≠ 3  ·  2) x³ + 3x²h + 3xh² + h³  ·  3) x^½ + x⁻²  ·  4) x = 3x − 3 → x = 3/2.

Part 2 — Functions (5 minutes)

  1. Given f(x) = x² and g(x) = 2x + 1, write f(g(x)) and g(f(x)). Are they equal?
  2. State the domain of √(4 − x²).
  3. For f(x) = x², compute [f(x + h) − f(x)]/h and simplify fully.

Answers: 1) (2x + 1)² and 2x² + 1 — not equal; composition order matters  ·  2) −2 ≤ x ≤ 2  ·  3) 2x + h.

Part 3 — Trigonometry (5 minutes)

  1. From memory: sin, cos and tan at 0, π/6, π/4, π/3 and π/2.
  2. Sketch sin x and cos x for one full period, labelled.
  3. Simplify 1 − cos²x using the Pythagorean identity.

Answers: 1) the standard unit-circle table  ·  2) sin starts at 0, cos starts at 1, both period 2π  ·  3) sin²x.

Scoring yourself

In each part, count a question as solid only if you finished it in about two minutes with no peeking. That distinction matters — slow-but-correct under no pressure collapses at exam time.

  • Mostly solid everywhere: your foundations are ready for Calculus I. Put your effort into the course itself, and start the Calculus I guide at Chapter 2.
  • One weak part: that's your leak, and it's cheap to fix — two to three weeks of twenty-minute daily reps on that skill, in parallel with your course. The gap-closing guide has the repair order.
  • Two or three weak parts: don't panic and don't pause your semester. This is the most common picture I see, and it's exactly what the Foundation track is built for — current course in the centre, foundation repair around it.

Want the full picture?

This page tests three skills in fifteen minutes. The full diagnostic is a 90-minute session where you solve problems out loud — algebra, functions, limits and early derivatives — and you leave with a one-page report: topic-by-topic readiness, your biggest bottleneck, and the path forward. It's required before any program, and it starts with a free 30-minute consult.