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9 multiple-choice questions on Conic Sections and Parametric Equations, about 6% of the High School Pre-Calculus bank. Every one carries a written rationale.
Conic Sections and Parametric Equations is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 9 of the bank's 150 multiple-choice questions — roughly 6% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
5 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
Period of y = 3sin(πx):
Answer: B — 2 (period = 2π/|b|; here b = π, so period = 2π/π = 2)
y = A·sin(Bx + C) + D has period 2π/|B|. B = π → period 2π/π = 2. Amplitude |A| = 3. Phase shift -C/B. Vertical shift D. Pre-Calc trig transformations.
Convert the polar point (4, π/2) to Cartesian coordinates.
Answer: A — (0, 4)
A) x = r cos θ = 4 · 0 = 0; y = r sin θ = 4 · 1 = 4. B) Used cos at θ = 0 instead of π/2. C) Sign error. D) Didn't convert.
Parametric equations: x = cos(t), y = sin(t) for t ∈ [0, 2π). The curve is:
Answer: C — Unit circle (cos²t + sin²t = 1 = x² + y²)
Eliminate parameter: x² + y² = cos²t + sin²t = 1, the unit circle. Traversed counterclockwise from (1,0) at t=0. Parametric form useful for motion, projectile paths, conic sections.
If v = ⟨3, 4⟩, what is |v|?
Answer: C — 5
C) |v| = √(3² + 4²) = √25 = 5. A) Added components instead of using the Pythagorean form. B) Multiplied components. D) Forgot the square root.
If f(x) = (x-3)/(x²-9), there is a HOLE at:
Answer: A — x = 3 (factor: (x-3)/((x-3)(x+3)) = 1/(x+3) for x≠3; cancellation creates hole, not VA)
Hole: when factor cancels (top and bottom). (x-3) cancels at x=3 → hole. (x+3) does NOT cancel → vertical asymptote at x=-3. Pre-Calc rational functions.
These are a sample. The full Conic Sections and Parametric Equations chapter runs 9 items with per-chapter progress tracking, on the web and in the iOS app.
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