Calculus 1 Practice Test: answer key

Every answer, with a link to its step-by-step solution

#	Answer	Lesson	Solution
1	1/(√(1 − x²))	Derivatives of inverse trig functions	Solved step by step
2	3/(1 + (3x + 2)²)	Derivatives of inverse trig functions	Solved step by step
3	2 × 3^2x ln 3	Derivatives of bˣ / Derivatives of logarithms	Solved step by step
4	8/((2x + 1) ln 3)	Derivatives of bˣ / Derivatives of logarithms	Solved step by step
5	(x + 1)²(x − 3)⁴(2/(x + 1) + 4/(x − 3))	Logarithmic differentiation	Solved step by step
6	((x + 1)²(x + 3)³)/((x + 2))(2/(x + 1) + 3/(x + 3) − 1/(x + 2))	Logarithmic differentiation	Solved step by step
7	L(x) = 2 + 14(x − 4)	Linear approximation	Solved step by step
8	0.05	Linear approximation	Solved step by step
9	C 0.6	Differentials	Solved step by step
10	3%	Differentials	Solved step by step
11	B −2 and x = 1	Absolute maximum and minimum	Solved step by step
12	B 0 and x = 3	Absolute maximum and minimum	Solved step by step
13	C c = 2	The mean value theorem / Rolle's theorem	Solved step by step
14	c ≈ 0.58	The mean value theorem / Rolle's theorem	Solved step by step
15	(1, −2)	Concavity and inflection points	Solved step by step
16	(−2, −16), (0, 0)	Concavity and inflection points	Solved step by step
17	A 16	Optimization	Solved step by step
18	108 cm²	Optimization	Solved step by step
19	C 1	L'Hôpital's rule	Solved step by step
20	2	L'Hôpital's rule	Solved step by step
21	C root ≈ 1.41667	Newton's method	Solved step by step
22	1.73205	Newton's method	Solved step by step
23	f(x) = x² + 4	Initial value problems	Solved step by step
24	y = 2x³ − 3x² + 5x + 1	Initial value problems	Solved step by step
25	x² + 1	The Fundamental Theorem, part 1	Solved step by step
26	2 e^2x	The Fundamental Theorem, part 1	Solved step by step
27	5	Average value of a function	Solved step by step
28	3	Average value of a function	Solved step by step
29	amount = 52 litres	Net change	Solved step by step
30	displacement = 6 m	Net change	Solved step by step

Grade

Count your right answers and divide by the number of questions: A 90% or more, B 80%, C 70%, D 60%, F below 60%.