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MCV4U Final Exam Review Flashcards | StudBud
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MCV4U Final Exam Review
MCV4U Final Exam Review
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MCV4U Final Exam review #calculus #derivatives #vectors #limits #rateofchange
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Questions
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Answers
1
Given A(2,2,1) and B(5,4,3), then vector AB is ?
AB = (3, 2, 0)
AB = (3, 2, 1)
AB = (-3, 2, -2)
AB = (3, 2, 2)
2
Determining the values of x when f'(x) = 0 is finding the _______________ ?
roots
local min/max. points
inflection points
asymptotes
3
The rate of change of a function is the _________________ ?
reciprocal
absolute value
slope
inverse
4
Given the following parametric equations, state the symmetric equation ?
(x-2)/1 = (y+1)/-5 = (z-3)/6
(x-2)/-1 = (y+1)/5 = (z-3)/-6
(x+2)/1 = (y+1)/5 = (z-3)/6
(x-2)/1 = (y-11)/-5 = (z+3)/6
5
The cross product of (1,1,0) and (1,0,1) is
(1,0,0)
(1, -1, -1)
(1,1,2)
(0,0,0)
6
Given the function f(x) = 3
x
, the derivative f'(x) = ?
3ex
x3
x . (3x-1)
ln 3 . (3x)
7
In the interval x ϵ [0,7], Point E and F are _________________?
global minimums
local minimums
global maximums
local maximums
8
What is the direction vector of the vector equation r = (3,0,1) + t (-2,1,5)
(3,0,1)
(5,1,-2)
(1,-1,-4)
(-2,1,5)
9
Given the function f(x) = x
4/5
, the derivative of the function f'(x) = ?
4x-1/5 / 5
5x-1/5 / 4
4x-3/5 / 5
5x-4/5 / 4
10
Dot product is also referred to as _____, and the cross product is also referred to as ____.
none of these
both of these
square product, triangle product
scalar product, vector product
11
What is the Product Rule ?
(f ')(g) - (g')(f)
none
(f ')(g) + (g')(f)
(f )(g) + (g')(f')
12
Given the function g(x) = ∛x , the derivative of the function g'(x) = ?
x-2/3 / 3
x-1/3
2x-1/3 / 3
x2/3
13
Given the function f(x) = sin x
, the derivative f'(x) = ?
sin2x
-cos x
cos x
-sin x
14
The normal of the plane given the Cartesian Equation 2x -3y +7z = -4
-4
4
(2,-3,7)
(-2,3,-7)
15
If the displacement function is given as s(t) = t
4
, then the acceleration function is ?
a(t) = 4t3 + t2
a(t) = 4t2
a(t) = 4t3
a(t) = 12t2
16
The limit of the following function ?
0
undefined
5
7
17
Determining the values of x when f"(x) = 0 is finding the _______________ ?
asymptotes
inflection points
y-intercept
local min/max. points
18
What type of asymptote is found when you find the limit f(x) as x-----> ±∞
slant asymptotes
vertical asymptotes
horizontal asymptotes
oblique asymptotes
19
Determine the dot product of (2,0,3) and (1,4,0) ?
2
0
4
-2
20
Given the planes x + y - 2z + 4 = 0 and -2x -2y +4z -8 = 0, these planes ?
skew
coincident
perpendicular
parallel
21
Given the function h(x) = -17 , the derivative of the function h'(x) = ?
0
-17x-1
17
-17
22
The process of finding a derivative by using limits and f(x+h)-f(x) is called ?
factoring
rationalizing
first principles
optimization
23
The process of setting the derivative of a function equal to zero and solving it is called ?
optimization
tangent
first principles
dependence
24
Given the following system, the two sets of intersecting lines are ?
coincident
parallel
perpendicular
skew
25
Given the function f(x) = cos x
, the derivative f'(x) = ?
-sin x
-cos x
cos x
sinx
26
log
3
x + 2log
3
y - log
3
z =
log3(xy/2z)
log3(xy2/z)
any of these
log3(x2y/z)
27
Given the function f(x) = x
100
+ 100x
-2
, the derivative of the function f'(x) = ?
100x99 - 200x-3
100x99 +100
100x99 + 200x-3
100x99 - 200x-1
28
Point A is a _________________?
local minimum
global maximum
local maximum
global minimum
29
Given the function f(x) = -3x
3
+ x
2
+ 1, the derivative of the function f'(x) = ?
-9x2 + 2
-9x2
-9x2 + 2x + 1
-9x2 + 2x
30
The vector (4,-1,0) exists in what plane ?
yz - plane
xy- plane
xz-plane
xyz-plane
31
Determine the |(2,-1, 3)| (magnitude)
√14
14
√12
√8
32
The ______________ is when a tangent is used to find the rate of change (at only one point).
average rate of change
y"
instantaneous rate of change
secant
33
Given the function f(x) = e
x
, the derivative f'(x) = ?
1/x
f'(x) = ex
1
0
34
When two normals have a dot product equal to zero, the planes are ______?
perpendicular
coincident
skew
parallel
35
What is the Chain Rule?
a way to determine the derivative of a composite function
all of these
dy/du . du/dx
f'(g(x) . g'(x)
36
If the displacement function is given as s(t) = t
4
, then the velocity function is ?
v(t) = 4t3 + t2
v(t) = 12t2
v(t) = 4t2
v(t) = 4t3
37
What is the value of ln e ?
none of these
e
0
cos x
38
Given the function f(x) = sin(4x)
, the derivative f'(x) = ?
cos(4x)
4cos x
-4sinx
4cos(4x)
39
What is the derivative of the function f(x) = (2x
3
+ 1)
5
?
5(2x3 +1)4
2x15 + 1
5(2x3 +1)4 (6x2)
5(6x2 )4
40
The limit of the following function, as x ---> 3, is ______________
3
dne (does not exist)
1
4
41
Given the function f(x) = 4x
5
, the derivative of the function f'(x) = ?
x2
5x4
80x3
20x4
42
Given the function f(x) = e
-x
, the derivative f'(x) = ?
e-x
1
xex
-e-x
43
Another notation to represent derivative is ?
dx/dy
dy/dx
y"
df
44
Point B is a _________________?
local maximum
global minimum
local minimum
global maximum
45
Given the planes x + y - 2z + 4 = 0 and -2x -2y +4z + 8 = 0, these planes ?
skew
coincident
perpendicular
parallel
46
Given the following symmetric equation, state the parametric equation for the y component?
y=1+ 4t
y = 2+5t
y = 3 + 6t
y = 1+ 5t
47
Given the function f(x) = ln(4x)
, the derivative f'(x) = ?
4x
1/x
1/4
ln e
48
What is the Quotient Rule?
{(f ')(g) + (f)(g')} / g2
{(f )(g') - (f ')(g)} / g2
{(f ')(g) - (f)(g')} / g2
(f ')(g) + (f)(g')
49
Point D is a _________________?
global maximum
global minimum
local maximum
local minimum
50
Given the function f(x) = ln x
, the derivative f'(x) = ?
x-2
x2
ex
1/x
