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Worksheets

CALCULUS

Total questions: 131

Worksheet time: 6hrs 55mins

Name
Class
Date
1.

A geometry student wants to draw a rectangle inscribed in a semicircle of radius 7. If one side must be on the semicircle's diameter, what is the area of the largest rectangle that the

student can draw?

a)

49

b)

42

c)

14

d)

7√7

2.

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

a)

100ft x 200ft

b)

102ft x 196 ft

c)

50 ft x 300 ft

d)

50 ft x 175 ft

3.
If y=2x-8, what is the minimum value of the product xy?
a)
-16
b)
-8
c)
-4
d)
2
4.
The volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?
a)
2 3√2
b)
2√2
c)
4
d)
2 3√4
5.
A rectangular  page is to contain 144 sq. inches of print. the margins on each side are 1 inch. Find the dimensions of the page that would use the least paper
a)
16, 16
b)
15,15
c)
14,14
d)
13,13
6.
We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft3, determine the dimensions that will minimize the amount of material used.
a)
w=2.027ft, h=4.055ft, l=6.082ft
b)
w=1.488ft, h=3.347ft, l=6.694ft
c)
w=2.231ft, h=3.347ft, l=6.694ft
d)
w=0.485ft, h=2.111ft, l=4.222ft
7.
Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?
a)
3 ft/sec
b)
-7.2 ft/sec
c)
7.2 ft/sec
d)
12
8.
(3 min) The area of a circular region is increasing at a rate of 96 π square meters per second. When the area of the region is 64 π square meters, how fast, in meters per second, is the radius of the region increasing?
a)
6
b)
8
c)
16
d)
4√3
9.
What are the intervals of the graph increasing for f(x) = 2x4- 4x2 + 1
a)
(-1,0)
b)
(0,1)
c)
(-∞,-1) and (1,∞)
d)
(0,1) and (-1,0)
10.
Find the point(s) of inflection for f(x) = 2(x)1/5 + 3
a)
None
b)
x = 0
c)
x = 0, 2
d)
x = -2, 0, 2
11.

Given x3 -3x - 4, the numbers 1 and -3 are

a)

terms

b)

coefficients

c)

variables

d)

constants

12.

State another name for additive inverse

a)

Negative

b)

Opposite

c)

Reciprocal

d)

Constant

13.

Letters in an expression

a)

variables

b)

coefficients

c)

exponents

d)

constant

14.

Given 3/7, 7 is called

a)

numerator

b)

coefficient

c)

expression

d)

denominator

15.

Given x2 - 3x + 4, x2 and -3x are ______ terms.

a)

variable

b)

reciprocal

c)

denominator

d)

constant

16.

A collection of letters and real numbers combined using addition, subtraction, multiplication, division, and exponentiation is

a)

terms

b)

expression

c)

coefficients

d)

constants

17.

Another name for multiplicative inverse

a)

denominator

b)

expression

c)

reciprocal

d)

opposite

18.

1/3 is the ___________ inverse of 3.

a)

expression

b)

multiplicative

c)

variable

d)

additive

19.

Real numbers in an expression are called ___________

a)

constants

b)

terms

c)

coefficient

d)

numerator

20.

x2 -3x - 7, 7 is the ______ term

a)

reciprocal

b)

term

c)

variable

d)

constant

21.

9 is the __________ inverse of -9

a)

multiplicative

b)

constant

c)

additive

d)

reciprocal

22.

Parts of an expression that are separated by addition symbols

a)

variable

b)

denominator

c)

numerator

d)

terms

23.

Given 2/7, 2 is called the

a)

denominator

b)

term

c)

numerator

d)

expression

24.
a)
cosx
b)
-cosx
c)
-sinx cosx
d)
sinx cosx
25.
a)
sinx
b)
-sinx
c)
-cscx cotx
d)
sec2x
26.
a)
cscx cotx
b)
secx tanx
c)
sec2x
d)
-cscx cotx
27.
a)
secx tanx
b)
sec2x
c)
cscx cotx
d)
-cscx cotx
28.
a)
secx tanx
b)
-secx tanx
c)
tan2x
d)
cscx cotx
29.
a)
-cscx cotx
b)
cscx cotx
c)
-csc2x
d)
csc2x
30.
a)
-ln |cosx| + C
b)
ln |cosx| + C
c)
ln |sinx| + C
d)
-ln |sinx| + C
31.
a)
sin x + C
b)
-sin x + C
c)
ln |sinx| + C
d)
-ln |sinx| + C
32.
a)
secx tanx + C
b)
-ln |secx + tanx | + C
c)
ln |secx + tanx| + C
d)
-secx tanx + C
33.
a)
-ln |cscx + cotx| + C
b)
ln |cscx + cotx| + C
c)
-cscx cotx + C
d)
cscx cotx + C
34.
a)
-ln |cosx| + C
b)
ln |cosx| + C
c)
-ln |sinx| + C
d)
ln |sinx| + C
35.
a)
-ln |cosx|
b)
ln |cosx|
c)
cosx
d)
-cosx
36.
Find the limit as x approaches 3 from the left
a)
4
b)
3
c)
2
d)
DNE
37.
Find the limit of the function as x approaches 2+.
a)
1
b)
-1
c)
5
d)
DNE
38.
What is the limit of the function as x approaches -4 from the left?
a)
2
b)
-4
c)
DNE
d)
-2
39.
What is the limit of the function as x approaches 1 from the left?
a)
DNE
b)
1
c)
4
d)
-2
40.
What is the limit of the function as x approaches 1 from the right?
a)
DNE
b)
1
c)
4
d)
-2
41.
Find the limit of the function as x approaches 4 from the right.
a)
-1
b)
2
c)
-2
d)
DNE
42.
What is the limit as x approaches -1
a)
0
b)
Infinity
c)
-Infinity
d)
What are you talking about?!?!?
43.
Find the limit as x approaches 0-
a)
0
b)
∞
c)
-∞
d)
1
44.
a)
0
b)
-2/9
c)
Infinity
d)
-5/6
45.
Find the derivative of the given function using the definition of derivative.
f(x) = 1 - x2
a)
1 - 2x
b)
-2x
c)
-2
d)
-1
46.
Find the derivative of the given equation using the definition of derivative.
f(x) = -4x 
a)
4
b)
x
c)
-4
d)
0
47.
Find the derivative using the definition. y = 3x2 - 4x + 2
a)
6x-6
b)
6x-2
c)
4-6x
d)
6x-4
48.
a)
3/2 or 1.5
b)
3
c)
0
d)
D.N.E
49.
a)
1
b)
1.5
c)
0
d)
Does not exist
50.
Evaluate the limit: 
a)
0
b)
1
c)
-9/4
d)
∞
51.
Find the derivative of f(x)=(x3-2x)2
a)
6x5 - 12x3+8x
b)
6x5 - 16x3+8x
c)
x6-4x4+4x2
d)
6x5 - 16x3-8x
52.
Determine the derivative:
a)
A
b)
B
c)
C
d)
D
53.
Find dy/dx for
y = 32x+5 
a)
dy/dx = 3(2x+4)
b)
dy/dx = (3(2x+4)) ln 3
c)
dy/dx = 3(2x+5) ln3
d)
dy/dx = (3(2x+5)) (ln 3) (2)
54.
a)
A
b)
B
c)
C
d)
D
55.
Find dy/dx for y=-(3x2+5x)5
a)
y=-5(x+5)4
b)
y=-5(6x+5)(3x2+5x)4
c)
y=-6x+5(3x2+5x)4
d)
y=-6x(3x2+5x)4
56.
Differentiate:
f(x) = x3e4x
*You will need to remove the Greatest Common Factor
a)
f '(x) = 3x2e4x
b)
f '(x) = 3x2e4x+3x2e4x
c)
f '(x) = x2e4x(4x+3)
d)
f '(x) = xe4x(4x2+3x)
57.
Differentiate y = √(x² - 1)
a)
√(x² -1)
b)
(1/2x)(x² - 1)^(-1/2)
c)
x(x² - 1)^(-1/2)
d)
x(x² - 1)^(1/2)
58.
d/dx (sin2x) = ?
a)
2sin x
b)
2(sin x)(cos x)
c)
2cos x
d)
2x(cos x)
59.
Find the derivative:
y=4ex²
a)
y'=8xe
b)
y'=8xex²
c)
y'=8xe2x
d)
y'=8xe4x²
60.
Find the derivative:
y=5x2e3x
a)
y'=10xe3x(2x+3)
b)
y'=5xe3x(3x+2)
c)
y'=10ex3x(3x+2)
d)
y'=5xe3x(2x+3)
61.
Find the derivative:
y=11x²
a)
y′=11x²(2x)(ln11)
b)
y′=2x(ln11)
c)
y′=11x²(2x)(lnx)
d)
y′=11x²(x)(ln11)
62.
.
a)
(3x^2-2)cos(x^3-2x)
b)
-(3x^2-2)cos(x^3-2x)
c)
cos(2x^2-2)
d)
sin(2x^2-2)
63.
Find the derivative of f(x) = x2sinx
a)
f'(x) = 2xsinx - x2cosx
b)
f'(x) = 2xsinx + x2sinx
c)
f'(x) = 2xsinx + x2cosx
d)
f'(x) = 2xcosx
64.
Find the derivative f(x) = tanxcosx
a)
f'(x) = sec2xcosx - tanxsinx
b)
f'(x) = sec2xcosx + tanxsinx
c)
f'(x) = sec2xsinx
d)
f'(x) = sec2xcosx - tanxcosx
65.
What is f'(x) if f(x) = cos(5x4)?
a)
f'(x) = sin(20x3)
b)
f'(x) = 20x3 sin(5x4)
c)
f'(x) = -sin(20x3)
d)
f'(x) = -20x3 sin(5x4)
66.
The equation of the tangent to y=1/x at x=3 is
a)
y=-1/9x+2/3
b)
y=1/3x+1/3
c)
y=1/9x+9
d)
y=1/9x
67.
The position function x(t)=t3+6t2+16t-18 is given on the interval of 0<x<9. What is the velocity at t=6?
a)
197
b)
190
c)
18
d)
196
68.
Find the derivative of g(x)=(3x-2)/(x2+2)
a)
9x2+2
b)
3(x2+2)/(x2+2)2
c)
(-3x2+4x +6)/(x2+2)2
d)
(-3x2+10)/(x2+2)2
69.
Find the second derivative of f(x) = x2 + ex  - cosx
a)
f"(x) = 2 + ex + cosx
b)
f"(x) = 2x + ex + cosx
c)
f"(x) = 2x + xex - cosx
d)
f"(x) = 2x + ex + sinx
70.

Find dy/dx

a)

A

b)

B

c)

C

d)

D

71.
a)
1/(3x2+5)1/4
b)
(3x)/(2(3x2+5))
c)
(2(3x2+5)3/4)/(3x)
d)
(3x2+5)1/4
72.
a)
(5(1-4x))/(12x3)
b)
5(x+1)(3x3-4x2+4x-4)
c)
(5(x3+16))/(x(x3+4))
d)
(5(x+1)(-3x3+4x2-4x+4))/(3x4(x3+4))
73.
a)
((3x2-5)(x2+1))/(10x2(3x4-5))
b)
(2(-3x4-5))/(5x(3x4-5))
c)
(3x2-1)/(60x3)
d)
((3x2-5)(-x2-1))/5
74.
a)
1/(cos(5x2))
b)
-(10xsin(5x2))/(cos(5x2))
c)
-1/(10xsin(5x2))
d)
cos(5x2)
75.
a)
1/(2x5)
b)
1/(10x4)
c)
2x5
d)
5/x
76.
In the equation (x-3)2+(y-2)2=16, the center of the circle is...
a)
(3,2)
b)
(-3, -2)
c)
(-2, -3)
d)
(2, 3)
77.
The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.
a)
(x - 2)2 + (y + 5)2 = 36
b)
(x - 5)2 + (y + 2)2 = 6
c)
(x + 5)2 + (y - 2)2 = 36
d)
(x + 2)2 + (y - 5)2 = 6
78.
What is the center of the shifted ellipse?
a)
(0,0)
b)
(-3,1)
c)
(1,-3)
d)
(3,-1)
79.
See Picture
a)
A
b)
B
c)
C
d)
D
80.
What are the vertices of the ellipse?
a)
(0, 0)
b)
(7, 1) and (-1, 1)
c)
(3, -5) and (3, 7)
d)
(3, 1)
81.
What is the center of the hyperbola?
a)
(0, 4)
b)
(4, 0)
c)
(-4, 0)
d)
(0, -4)
82.
What are the vertices of the hyperbola?
a)
(0, 3) and (0, -3)
b)
(-4, 3) and (-4, -3)
c)
(0, 1) and (0, -1)
d)
(4, 0) and (-4, 0)
83.

Is the hyperbola opening vertically or horizontally?

a)

Vertically

b)

Horizontally

84.
What are the vertices of the hyperbola with the equation 8x² - 9y² = 72?
a)
(±2√2, 0)
b)
(±3, 0)
c)
(0, ±3)
d)
(0, ±2√2)
85.

Write an equation of a circle if the ends of the diameter are (18,-13) and (4,-3)

a)

(x+11)2+(y-8)2=√74

b)

(x-11)2+(y+8)2=74

c)

(x+11)2+(y-8)2=74

d)

(x-11)2+(y+8)2=√74

86.

What are the vertices of the ellipse with equation

x2+9y2-4x+54y+49=0

a)

(8,-3) and (-4,-3)

b)

(2,3) and (2,-9)

c)

(4,-3) and (0,-3)

d)

(2,-5) and (2,-1)

87.

Identify the conic from the equation: y2 -4x -2y -2 = 0

a)

circle

b)

ellipse

c)

parabola

d)

hyperbola

88.

Identify the conic from the equations: 4x2 -15y2 + 6x - 8y -72 = 0

a)

circle

b)

ellipse

c)

parabola

d)

hyperbola

89.

Convert the equation x2 + 4y2 + 2x + 24y + 21 = 0 into standard form.

a)
b)
c)
d)
90.

Write the equation for the parabola if it contains the point (7, 1)

a)

-1/4(y-2)2 + 3 = x

b)

-1/16(y-2)2 + 3= x

c)

-1/4(x-3)2 + 2 = y

d)

-1/16(x-3)2 + 2 = y

91.
Find the equation of the figure shown.
a)
(x-5)2 + (y-3)2 = 25
b)
(x+5)2/4 + (y+3)2/9 = 1
c)
(x-5)2/2 + (y-3)2/3 = 1
d)
(x-5)2/4 + (y-3)2/9 = 1
92.

Find the equation of the figure shown.

a)

(x-1)2/16 - (y+2)2/4 = 1

b)

(x+1)2/16 - (y-2)2/4 = 1

c)

(y+2)2/4 - (x-1)2/16 = 1

d)

(x-1)2/4 - (y+2)2/2 = 1

93.
Which conic's equation has only 1 squared term?
a)
Parabola
b)
Circle
c)
Ellipse
d)
Hyperbola
94.

Using the vertical line test. Is this a function?

a)

Yes

b)

No

95.

Using the vertical line test. Is this a function?

a)

Yes

b)

No

96.

Which of the relations below is a function?

a)

{(2, 3), (3, 4), (5, 1), (5, 4)}

b)

{(-2, 3), (3, 4), (6, 2), (9, 3)}

c)

{(-2, 3), ( -3, 4), (6, 2), (-3, 3)}

97.
For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
a)
D: {1, -3, -4,}
R: {0, 1, 2, -4}
b)
D:{0, 1, 2, -4}
R:{1, -3, -4}
c)
D:{0, 1, 2, 3, 4}
R:{1, -3, -4}
d)
D:{0, 1, 2, 3}
R:{0, 1, 2, 3, 4}
98.

What is g(-2) if:

a)

-7

b)

7

c)

1

d)

-1

99.
What is the RANGE?
a)
(-∞, +∞)
b)
(-2, +∞)
c)
[-2, +∞)
d)
(-∞, 0) U (0, +∞)
100.

Given f(x) = 3x2 + 1, what is f(t + 2)?

a)

3t2 + 3

b)

(3t + 2)2 + 1

c)

3(t + 2)2 + 1

d)

none of these

101.

Given f(x) = 3x+2x−1\frac{3x+2}{x-1}  , what is the domain of f(x)?

a)

All real numbers greater than or equal to 1

b)

All real numbers except 1

c)

x = 1

d)

All real numbers

102.

What is the domain of y = x\sqrt{x}  ?

a)

All real numbers

b)

All real numbers greater than 0

c)

All real numbers less than 0

d)

All real numbers greater than or equal to 0

103.
When is this function increasing?
a)
−2.5 < x < 2.5
b)
0 < x < 5
c)
0 < x < 55
d)
−5 < x < 0
104.

y = x (x – 3)2 decreases for the values of x given by :

a)

1<x<31<x<3

b)

x<0x<0

c)

x>0x>0

d)

0<x<320<x<\frac{3}{2}

105.
The function shown in the graph is:
a)
even
b)
odd
c)
neither even nor odd
d)
both even and odd
106.
The function in the graph is:
a)
even
b)
odd
c)
neither even nor odd
d)
both even and odd
107.
The function shown in the graph is:
a)
even
b)
odd
c)
neither odd nor even
d)
both odd and even
108.

Find the Relative Maximum and Minimum. Round to nearest tenth.

a)

A

b)

B

c)

C

d)

D

109.
Find the average rate of change over the given interval.
a)
3
b)
1.5
c)
1
d)
0.67
110.
Find the average rate of change over the given interval.
a)
3
b)
1.5
c)
1
d)
0.67
111.
f(x) = 2x2 + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].
a)
2
b)
1/2
c)
-2
d)
-1/2
112.
5a - 6b + 4a + 3b
a)
9a - 3b
b)
a + b
c)
6ab
d)
-b + a
113.
Simplify the expression.
5y - 3r + 7r - 5
a)
5y + 4r + (-5)
b)
5y + 10r + (-5)
c)
15ry + (-5)
d)
9ry + (-5)
114.
Simplify the expression by combing like terms. 9x+7x-9+1
a)
16x-10
b)
16x-8
c)
16x+10
d)
16x+8
115.
What is the value of the expression
x2 + y2 + x - y 
when x = -1 and y = 3
a)
6
b)
8
c)
12
d)
16
116.
Factor:
x2 + 7x - 30
a)
(x + 10)(x - 7)
b)
(x - 10)(x + 3)
c)
(x + 10)(x + 3)
d)
(x + 10)(x - 3)
117.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
118.
CW.1.2 What is the domain and range of the function graphed behind this question?
a)
(-4, ∞)
b)
(-∞, -4)
c)
(0, ∞)
d)
[-∞, ∞]
119.
CW.1.2: Where is the graph behind this question increasing?
a)
(2,∞)
b)
(0,4)
c)
[0,4]
d)
(4,∞)
120.

What is the degree of the polynomial function below?

y = x3 + 4x - 5

(a)  

121.

What is the degree of the following function?

y = 25 - x2

(a)  

122.
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
123.
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
124.
______________________________ arranges the terms by degree in descending numerical order.
a)
degree of polynomial
b)
polynomial 
c)
terms
d)
standard form of polynomial
125.
Classify by number of terms:
7x3 – 8x2 -4x+ 9
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
126.

Which one is trinomial

a)

3x - 4

b)

12z

c)

14v8w

d)

3x2y4 −15z +123x^2y^4\ -15z\ +12  

127.
Which one is written in Standard form
a)
4 + 5b3
b)
4n3 - n + 6n2
c)
2a2 + 9
d)
2h5 - 5h3 - 8 + 3h
128.

Simplify:

5(3x+2)

a)

3x+10

b)

15x+10

c)

15x-10

d)

3x-10

129.
Simplify:
2x ( -2x -3)
a)
-4x - 3
b)
x2 - 3
c)
-4x2 - 6x
d)
-4x - 6
130.
(x + 5)(x + 4)
a)
x2 + x + 20
b)
x2 + 20x + 9
c)
x2 + 9x + 20
d)
x2 - 9x + 54
131.
The monomial 7 has a degree of...
a)
7
b)
1
c)
0
d)
It has no degree

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