NEW
Font size
WorksheetsMrs. Ballard's Praxis/ACT Math Review
Total questions: 45
Worksheet time: 54mins
The derivative of a constant function is ______________.
d/dx (c) = 0
d/dx (c) = x
d/dx (c) = c
d/dx (c) = 1
The derivative of f(x) = 5 is ________.
1
5c
5x
0
Find the slope of the tangent line to the graph of the function at the given point.
f(x) = 5 - x2 (3,-4)
m = -6
m = 6
m = 5
m = 3
The derivative of f + g (or f - g) is the sum (or difference) of the derivatives of f and g.
True
False
What is the derivative of y = 1/x2 ?
y' = 3x2
y' = -2/x3
y' = 1/3x
y' = 1/2x
What is the derivative of f(x) = 5x2?
f'(x) = 10x
f'(x) = 5x
f'(x) = 2x5
f'(x) = 10x2
Before differentiating functions involving radicals, what should we do first?
Differentiate directly.
Simplify the terms with radicals.
Multiply/Divide the radicals.
Rewrite the function with rational exponents.
The term indefinite integral is a synonym for antiderivative.
True
False
How can we say that a function F is an antiderivative of f on an interval I?
when F(x) = f(x) for all x in I
when F'(x) = f(x) for all x in I
when f'(x) = F(x) for all x in I
when F'(x) = f'(x) for all x in I
Another way of finding the area of a region is to use a definite integral.
True
False
How do we approximate the area of a plane region?
By taking the limit of the summation of all n-rectangles as n approaches infinity.
By taking the derivative of the function.
By multiplying length and width.
By using Chain Rule.
Who were credited for creating calculus?
Niels Henrik Abel & Evariste Galois
Joseph-Louis Lagrange & Michel Rolle
Thomas Simpson & George Friedrich Riemann
Isaac Newton & Gottfried Wilhelm Leibniz
What is the Fundamental Theorem of Calculus?
∫[f(x) dx] = f(a - b) (lower limit=a; upper limit=b)
∫[f(x) dx] = F(a - b) (lower limit=a; upper limit=b)
∫[f(x) dx] = F(b) - F(a) (lower limit=a; upper limit=b)
∫[f(x) dx] = F(a) - F(b) (lower limit=a; upper limit=b)
Create a definite integral for y = x2 - 6x having a lower limit of 2 and upper limit of 4.
∫(x2 - 6x) dx (lower limit=4; upper limit=2)
∫(x2 - 6x) + C (lower limit=4; upper limit=2)
∫(x2 - 6x) dx (lower limit=2; upper limit=4)
∫(x2 - 6x) (lower limit=2; upper limit=4)
Evaluate the following definite integral:
∫ (x2-3) dx a=1, b=2
-2/3
1/2
14
5
∫ (6x) dx a=0, b=2
11
12
15
10
∫ (2x +1) dx a=0, b=1
3
2
-1
2
∫ x2 dx a=0, b=3
8
10
9
6
2 only
2 and 4
0 and 2 only
0, 1 and 2
0, 1, 2, and 4.
1
3
7
10
None
Does not exist
-7/5
-5/9
-1/2
y=-x(x+2)(x-1)
