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Calculus (DATU)

Total questions: 35

Worksheet time: 51mins

Name
Class
Date
1.
factor:x2 - 25
a)
( x + 5 ) ( x - 5 ) 
b)
( x - 5 ) ( x - 5 ) 
c)
( x + 5 ) ( x + 5 ) 
d)
Prime
2.

It is the point equidistant from the points on the edge of a circle.

a)

Radius

b)

Center

c)

Minor Arc

d)

Major Arc

3.

It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

a)

Radius

b)

Diameter

c)

Secant

d)

Chord

4.

It is the set of all points equidistant from the fixed point.

(a)  

5.

It is the distance from the center to any point on the circle.

a)

Radius

b)

Diameter

c)

Secant

d)

Tangent

6.

 lim⁡x→5x3\lim_{x\rightarrow5}x^3  

a)

15

b)

125

c)

20

7.

A rabbit population has invaded a local farm. The farmer, by tagging and counting the rabbits he's caught, models their growth by the function f(x) = 8 (1.26)x.

a)

The rabbits are getting sick from the farmer's produce.

b)

The farmer is catching less of the rabbit population over time.

c)

The rabbit population is growing exponentially.

d)

None of the above

8.

A pond, where a population of frogs has found a habitat, is polluted and severely destroyed by a storm.


The equation modelling the frog population after the storm is f(x) = 100 (0.82)x.

What is happening to the frog population?

a)

Exponential growth by a rate of 82%

b)

Exponential decay by a rate of 18%

c)

Exponential growth by a rate of 182%

d)

None of the above

9.
What is Mrs. Gordon's rate from 0 to 2 seconds?
a)
2.5 feet per second
b)
.4 feet per second
c)
5 feet per second
d)
.2 feet per second
10.

Carmen is learning to drive, so this weekend she practiced driving 5 5/10 miles with her mother and another 3 4/10 miles with her father. How far did Carmen drive in all?

a)

8 9108\ \frac{9}{10} miles

b)

9 miles

c)

5 9105\ \frac{9}{10} miles

d)

8 miles

11.

Choose the fractions that are equivalent to  3143\frac{1}{4}  

a)

 1941\frac{9}{4}  

b)

 124\frac{12}{4}  

c)

 2542\frac{5}{4}  

d)

 134\frac{13}{4}  

12.

The art club used 5 gallons of paints to decorate 12 chairs. How much paint was used on each chair?

a)

1/2 of a gallon

b)

5/12 of a gallon

c)

1 gallon

d)

12/5 of a gallon

13.
Given that f(x) = x2 + x and g(x) = 3x + 1, find the value of g(f(-2)).
a)
-14
b)
20
c)
6
d)
7
14.
f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))
a)
-42
b)
-26
c)
-18
d)
None of these.
15.
Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))
a)
19
b)
23
c)
-10
d)
None of these.
16.

M(t) represents the number of math problems your AP Calculus class has solved after t minutes.

What does M''(20) = -2 represent?

a)

At t = 20 minutes the rate at which the math class is solving problems is decreasing at a rate of 2 problems per minute per minute.

b)

At t = 20 minutes the rate at which the math class is solving problems is increasing at a rate of 2 problems per minute per minute.

c)

At 20 minutes, the math class is solving problems at a rate of 2 problems per minute.

d)

At 20 minuets the math class has solved -2 problems.

17.

H(t) represents the number of hats purchased at a store after t hours. What does the above notation represent ?

a)

The number of hats sold on the time interval 4 to 8 hours was 32.

b)

The number of hats sold at t = 8 hours was 32.

c)

The rate at which hats were sold on the interval 4 to 8 hours was 32.

d)

The number of hats sold at t = 4 hours was 32.

18.

The rate at which the temperature outside is changing is represented by the function O(t). What does the following represent?

a)

The temperature after 12 minutes is 15 degrees.

b)

The temperature has increased 15 degrees on the time interval 5 to 12 minutes.

c)

The rate of change of temperature on the interval 5 to 12 minutes is 15.

d)

The temperature at 5 minutes is 15 degrees.

19.

A particle has a negative velocity and a negative acceleration. Which of the following is true?

a)

The speed is increasing.

b)

The speed is decreasing.

c)

The speed is neither increasing or decreasing.

d)

The particle is not moving.

20.

A particle has a positive velocity and a negative acceleration. Which of the following is true?

a)

The speed is increasing.

b)

The speed is decreasing.

c)

The speed is neither increasing or decreasing.

d)

The particle is not moving.

21.

A particle travels along the x-axis. The position of the particle at t = 4 is 10. Which of the following would give you the position of the particle at t = 7?

a)
b)
c)

v(7)

d)

v(4) + v(7)

22.

B(t) represents the temperature of the biscuits after t minutes. What does the following notation represent?

a)

The temperature of the biscuits after 10 minutes.

b)

The average rate of the temperature of the biscuits on the time interval 3 to 10 minutes.

c)

The average temperature of the biscuits on the time interval 3 to 10 minutes.

d)

The temperature of the biscuits on the time interval 3 to 10 minutes.

23.

B(t) represents the temperature of the biscuits after t minutes. What does the following notation represent?

a)

The temperature of the biscuits at 10 minutes

b)

The average temperature of the biscuits on the time interval 3 to 10 minutes.

c)

The average rate of temperature on the interval 3 to 10 minutes.

d)

The change in temperature of the biscuits on the time interval 3 to 10 minutes.

24.

L(t) represents the total number of lollipops that a class has eaten after t minutes. What does L'(10) = 12 represent?

a)

At t = 10 minutes, the class is eating lollipops at a rate of 12 lollipops per minute.

b)

At t = 10 minutes, the class has eaten 12 lollipops.

c)

At t = 10 minutes the rate at which the class is eating lollipops is increasing at a rate of 12 lollipops per minute per minute.

d)

At t = 12 minutes the class has eaten 10 lollipops.

25.

R(t) represents the rate at which people enter a line, measured in people per minute. What does R'(3) = 4 represent?

a)

At t = 3 minutes, people are entering the line at a rate of 4 people per minute.

b)

At t = 3 minutes, the rate at which people are entering the line is increasing at a rate of 4 people per minute per minute.

c)

At t = 3 minutes, there are 4 people in line.

d)

At t = 4 minutes, 3 people are in line.

26.

Look at the picture. From 1 to 10, how confident do you feel with your Math?

4 lines
27.

The result of the following operation is....

 2+3⋅4−202+(5+72)2+3\cdot4-\frac{20}{2}+\left(5+7^2\right)  

a)

unknown

b)

64

c)

58

d)

12

28.

Solve for "y" given the following equation

 45x + 20 =(2⋅3y)245x\ +\ 20\ =\left(\frac{2\cdot3}{y}\right)^2  

a)

 y=3645x+20y=\frac{36}{45x+20}  

b)

 y=36−45x−20y=\sqrt{36-45x-20}  

c)

 y=3645x+20y=\sqrt{\frac{36}{45x+20}}  

d)

 y=36−45x−20y=36-45x-20  

29.
What is f(-2)?
a)
4
b)
1
c)
1
d)
DNE
30.
What is f(-1)?
a)
6
b)
-2
c)
sqrt(2)
d)
DNE
31.
Evaluate f(x) = 6(x - 3) at f(-3)
a)
0
b)
36
c)
-36
32.
Evaluate f(x) = 3x - 4 at f(3)
a)
5
b)
13
c)
2
33.
(x - 8) ( x - 8) = ______
a)
x2 - 64
b)
x2 + 64
c)
x2 - 16x + 64
d)
x2 + 16x + 64
34.

Expand (4x − 5)(4x + 5).

a)

4x2 − 25

b)

4x2 + 25

c)

16x2 + 25

d)

16x2 − 25

35.

Expand (x−4)2.

a)

x2 −8x+16

b)

x2 −8x−16

c)

x2 +8x+16

d)

x2 −16

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