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10 multiple-choice questions and 20 flashcards on Sequences, Series, and Probability, about 7% of the High School Pre-Calculus bank. Every one carries a written rationale.
Sequences, Series, and Probability is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 10 of the bank's 150 multiple-choice questions — roughly 7% 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.
Asymptotes of hyperbola x²/9 - y²/16 = 1:
Answer: C — y = ±(4/3)x (form y = ±(b/a)x for horizontal hyperbola; here b=4, a=3)
Hyperbola x²/a² - y²/b² = 1: asymptotes y = ±(b/a)x. a=3, b=4: y = ±(4/3)x. Foci at (±c, 0) with c² = a² + b² = 25, c = 5.
20th term of the arithmetic sequence with a₁ = 4 and d = 5:
Answer: C — 99
C) aₙ = a₁ + (n − 1)d = 4 + 19·5 = 4 + 95 = 99. A) Used n instead of n − 1: 4 + 100. B) 4 + 20·5 (off by one + one extra). D) Forgot to add a₁.
Sum of infinite geometric series with a = 1, r = 1/2:
Answer: B — 2 (S = a/(1-r) = 1/(1-1/2) = 1/(1/2) = 2; converges since |r|<1)
Infinite geometric series converges iff |r| < 1. Sum = a/(1-r). a=1, r=1/2: S = 1/(1/2) = 2. Verify partial sums approach 2: 1, 1.5, 1.75, 1.875, ... → 2.
Sum of the infinite geometric series 9 + 3 + 1 + 1/3 + ... :
Answer: A — 27/2
A) a = 9, r = 1/3 (|r| < 1, converges). S = a/(1 − r) = 9/(2/3) = 27/2 = 13.5. Both A and D equal 13.5 — but A is shown in fraction form (preferred). B) |r| < 1 ensures convergence. C) Off arithmetic.
Inverse trig: arcsin(1/2) = ?
Answer: B — π/6 (sin(π/6) = 1/2; principal branch [-π/2, π/2])
Principal arcsin range: [-π/2, π/2]. sin(π/6) = 1/2 (30°). Inverse trig functions have restricted ranges to be functions: arcsin ∈ [-π/2, π/2], arccos ∈ [0, π], arctan ∈ (-π/2, π/2).
4 cards from the 20 in this chapter.
What is the formula for the nth term of an arithmetic sequence?
aₙ = a₁ + (n − 1)d.
What is C(n, k)?
n! / (k!(n−k)!) — the number of ways to choose k items from n.
What is the sum of an infinite geometric series with |r| < 1?
S = a₁/(1 − r).
Evaluate lim_{x→2} (x² − 4)/(x − 2) by factoring.
(x − 2)(x + 2)/(x − 2) = x + 2 (for x ≠ 2). Limit = 4.
These are a sample. The full Sequences, Series, and Probability chapter runs 30 items with per-chapter progress tracking, on the web and in the iOS app.
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