This course has 11 chapters with 14,357 multiple-choice questions. Each question is tied to a topic from the chapter and comes with the correct answer and an explanation. Open a chapter to see its topics and a free sample of its questions, or read the sample from the whole book below.
10 sample questions with the correct answer and an explanation. Try to answer each one before reading the explanation.
Answer: C.√(2x − 1)/(x + 3) is built from x using finitely many algebraic operations (addition, subtraction, multiplication, division, roots), so it is algebraic; the others involve exponential, logarithmic, trigonometric or hyperbolic parts.
Answer: D.Differentiate both sides w.r.t. x and solve for dy/dx: dy/dx = −F_x/F_y, where F = LHS − RHS has F_x = 2x sin y + y² sin x and F_y = x² cos y − 2y cos x; this gives (−2x sin y − y² sin x)/(x² cos y − 2y cos x).
Answer: C.The x-intercepts are −2, 1, 3. Integrate |f| over each interval between consecutive intercepts and add: 253/12 square units; the signed integral over the whole span would be 125/12 because parts below the axis count negatively.
Answer: B.The book defines a differential equation as an equation that involves at least one derivative of a dependent variable with respect to an independent variable.
Answer: C.Both pass through the mid-point of the side, but the median also passes through the opposite vertex while the right bisector is perpendicular to the side; they coincide only in an isosceles triangle.
Answer: A.The net displacement is zero (the starting point is regained), so the average velocity is 0/1.5 = 0 km/h even though the average speed was 5.33 km/h.
Answer: B.Because f is convex here, only a moves: 1.1905, 1.3603, 1.4808, 1.5517 (the book's table, rounded at each step, differs slightly from the full-precision values in the fourth decimal).
Answer: B.The angle is tan⁻¹(30/40), the tower being 30 m high; the angle is = 36.9°, using the inverse function with the given sides (standard knowledge of right-triangle trigonometry).
Answer: C.Write sin u = −1/2 with u = 4x: u = 7π/6 and 11π/6 + multiples of the period; dividing by 4 and keeping x in [0, 2π) gives 7π/24, 11π/24, 19π/24, 23π/24, 31π/24, 35π/24, 43π/24 and 47π/24.
Answer: A.v(π/6) = ⟨12π/(144 + π²), π³/27 − 1⟩ and a(π/6) = ⟨72(144 − π²)/(20736 + 288π² + π⁴), 2π²/3⟩, so v·a = 2(−(27 − π³)(144 + π²)(20736 + 288π² + π⁴)π + 5038848 − 34992π²)π/(81(144 + π²)(20736 + 288π² + π⁴)) > 0: the speed is increasing.
Choose a chapter or topic, take timed or instant-feedback practice exams and see which topics need more work.