Calculus 3 Practice Test: answer key

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

#	Answer	Lesson	Solution
1	D d = 13	Points and distance in space	Solved step by step
2	d ≈ 5.4	Points and distance in space	Solved step by step
3	v = (3, 4, 0)	Vectors in space	Solved step by step
4	v = (1, 2, 3)	Vectors in space	Solved step by step
5	12	Dot product and angle in space	Solved step by step
6	61.9°	Dot product and angle in space	Solved step by step
7	B (−3, 6, −3)	Cross product and area	Solved step by step
8	(14, −7, 0)	Cross product and area	Solved step by step
9	x = 1 + 3t	Lines in space	Solved step by step
10	z − 1−3	Lines in space	Solved step by step
11	B 12	Planes in space	Solved step by step
12	13	Planes in space	Solved step by step
13	2xy	Partial derivatives	Solved step by step
14	f_yx = −2	Partial derivatives	Solved step by step
15	z = 2x + 4y − 5	Tangent planes and linear approximation	Solved step by step
16	z = 12x − 2y − 15	Tangent planes and linear approximation	Solved step by step
17	15t⁴	Chain rule with several variables	Solved step by step
18	36t³ + 24t²	Chain rule with several variables	Solved step by step
19	(4, 1)	Gradient and directional derivative	Solved step by step
20	5	Gradient and directional derivative	Solved step by step
21	(2, −3)	Local maximum, minimum and saddle points	Solved step by step
22	(3, 1)	Local maximum, minimum and saddle points	Solved step by step
23	1	Double integrals over rectangles	Solved step by step
24	163	Double integrals over rectangles	Solved step by step
25	C 112	Double integrals over general regions	Solved step by step
26	14	Double integrals over general regions	Solved step by step
27	8π	Double integrals in polar form	Solved step by step
28	20π	Double integrals in polar form	Solved step by step
29	92	Triple integrals	Solved step by step
30	6	Triple integrals	Solved step by step
31	2	Line integrals and work	Solved step by step
32	92	Line integrals and work	Solved step by step
33	C 2	Green's theorem	Solved step by step
34	2	Green's theorem	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%.