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10 multiple-choice questions and 20 flashcards on Exponential and Logarithmic Functions, about 7% of the High School Pre-Calculus bank. Every one carries a written rationale.
Exponential and Logarithmic Functions 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.
4 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.
If sin(x) = 3/5 in Q1, what is cos(x)?
Answer: A — 4/5 (Pythagorean: cos² = 1 - 9/25 = 16/25; cos = 4/5 in Q1 where cos > 0)
Use sin² + cos² = 1: cos² = 1 - (3/5)² = 1 - 9/25 = 16/25. cos = ±4/5. Quadrant 1: cos > 0, so cos(x) = 4/5. Classic 3-4-5 right triangle ratios.
What is the period of y = sin(2x)?
Answer: A — π (period = 2π/|b| = 2π/2 = π)
y = sin(bx) has period 2π/|b|. With b=2: period = π. Compresses graph horizontally. Pre-calc graphing of transformed trig functions.
If log₃(x) = 4, then x =
Answer: C — 81
C) log₃(x) = 4 means 3⁴ = x = 81. A) Multiplied base by exponent. B) Used 4³ instead of 3⁴. D) Added base and exponent.
Solve 4·e^(2x) = 100 for x (exact form).
Answer: D — x = ln(25)/2
D) Divide: e^(2x) = 25. Take ln: 2x = ln(25). x = ln(25)/2. A) Forgot to divide by 2 after taking the log. C) Used log₁₀ instead of ln (inverse of e is ln, not log). B) Mixed exponential and log operations.
4 cards from the 20 in this chapter.
State the product rule of logs.
log_b(MN) = log_b M + log_b N.
Evaluate log_2(8).
3, since 2³ = 8.
What is an exponential function f(x) = aᵇˣ's graph?
Smooth curve through (0, a). For b > 1, increasing; for 0 < b < 1, decreasing.
Solve: 2ˣ = 16.
x = 4.
These are a sample. The full Exponential and Logarithmic Functions chapter runs 30 items with per-chapter progress tracking, on the web and in the iOS app.
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