ConcepTests For Math 110

1
ConcepTests For Math 110
Prepared by Richard Cangelosi and Mariamma
Varghese
2
If the sum of two numbers is 14, and their
difference is 2, what is the product of the two
numbers?

• 24
• 28
• 40
• 45
• 48
• None of these.

3
Compare the quantity in Column A with the
quantity in Column B given the condition
Column A Column B

• The quantity in Column A is greater
• The quantity on Column B is greater
• The two quantities are equal
• The relationship cannot be determined from the
  information given

4
Which of the following equals the reciprocal of
where ?

• .
• .
• .
• .
• .

5
Which of the following could be a graphical
representation of
6
Compare the quantity in Column A with the
quantity in Column B given the following
condition.
Column A Column B

• The quantity in Column A is greater
• The quantity on Column B is greater
• The two quantities are equal
• The relationship cannot be determined from the
  information given

7
Compare the quantity in Column A with the
quantity in Column B given the condition
Column A Column B

• The quantity in Column A is greater
• The quantity on Column B is greater
• The two quantities are equal
• The relationship cannot be determined from the
  information given

8
Compare the quantity in Column A with the
quantity in Column B given the condition
Column A Column B

• The quantity in Column A is greater
• The quantity on Column B is greater
• The two quantities are equal
• The relationship cannot be determined from the
  information given

9
Solve for x given

• -5.8, 5.8
• -4.6, 4.6
• 21
• -11, 11
• None of these

10
Solve for x given

• 1/5
• -2/5
• 1/5, -2/5
• 1/10
• None of these

11
Determine the domain of

• .
• .
• .
• .
• None of these

12
Below is part of the graph of . What
is the average rate of change of f between
?

• .
• .
• .
• .
• . None of these.

13
The graph to the right gives a complete
representation of the function, .
For what values of x is ?

• . -3, -2, -1
• . -3, -2, -1, 2, 3
• .
• .
• .
• . None of these.

14
Determine which of the following graphs are even
functions.
I II III

• I only
• II only
• III only
• None of these

15
Compare the quantity in Column A with the
quantity in Column B given the condition
The perimeter of a rectangular desktop is 10
feet. Its length is 1 foot greater than its width.
Column A Column B
The area of the desktop
5 sq. ft.

• The quantity in Column A is greater
• The quantity on Column B is greater
• The two quantities are equal
• The relationship cannot be determined from the
  information given

16
In the figure below, ABCD and QRST are rectangles
where QR ½ AB and RS ½ BC. What fraction of
the region bounded by ABCD is NOT shaded?
C
(A) (B) (C) (D) (E)
17
A machine can stamp 20 envelops in 4 minutes.
How many of these machines, working
simultaneously, are needed to stamp 60 envelops
per minute?

• 5
• 10
• 12
• 20
• 24

18
Draw a graph to represent the following
situation. Label axes and intercepts.
A boy who is 4 inches tall is growing at a rate
of 2 inches per year.
19
Draw a graph to represent the following
situation. Label axes and intercepts.
A person pays 10 per week to a friend in order
to pay off a 100 loan.
20
It takes Carla three hours to drive to her
brothers house at an average speed of 50 miles
per hour. If she takes the same route home, but
average speed is 60 miles per hour, how long does
it take her to get home?

• 2 hours
• 2 hours and 14 minutes
• 2 hours and 30 minutes
• 2 hours and 45 minutes
• 3 hours

21
Which of the following operations will affect the
zeros of ? Assume .
(i) (ii) (iii) (iv)

• (i) and (ii) only
• (ii) and (iv) only
• (i), (ii) and (iii) only
• (ii), (iii) and (iv) only
• All of them
• None of them

22
If y f(x) is an even function, then which of
the following functions are also even?
(i) Kf(x) (ii) f(x K) (iii) f(x) K

• (i) only
• (ii) only
• (ii) and (iii) only
• (i) and (ii) only
• (i) and (iii) only
• All are even functions

23
If y f(x) is an odd function, then which of the
following functions are also odd?
(i) Kf(x) (ii) f(x K) (iii) f(x) K

• (i) only
• (ii) only
• (iii) only
• (i) and (ii) only
• (ii) and (iii) only
• All are odd functions

24

• True or False (Explain your answers.)
• Every line has two distinct intercepts.
• Every line can be written in slope intercept
  form.
• Two lines with the same slope but different x
  intercepts must have the same y intercept.
• Two lines with different slopes and the same x
  intercept must have the same y intercept.
• If you know the x intercept and the y
  intercept you can determine the equation of the
  line.

25
The y-intercept of is

• .
• .
• .
• .
• .

26
Consider the function, .
Assume a gt 0.Which of the following statements
are true?Increasing the value of a will
(i) increase the minimum value of f (ii)
change the vertex (iii) change the yintercept
(iv) not change the minimum value of f

• (i) and (ii) only (D) All are true
• (i), (ii) and (iii) only (E) All are false
• (iii) and (iv) only

27
A horticulturist has determined that the number
of inches a young oak tree grows in one year is a
function of the annual rainfall, r, given by
What is the maximum number of inches a young
oak can grow in a year? The number of maximum
inches is

• Less than 1 (D) between 1 and 2
• Between 2 and 3 (E) between 3 and 4
• Between 4 and 5

28

• True or False (Explain your answers.)
• All even degree polynomials are even functions.
• All polynomials have at least on real zero.
• All polynomials of odd degree have all real
  numbers as their domain.
• A polynomial of degree 3 can have 4 real zeros.
• All polynomials have a y intercept.
• A polynomial of degree 4 has 4 real zeros.

29
The graph of the polynomial function, is given
below. The constant term of is

• Greater then zero
• Equal to zero
• Less then zero
• Cannot be determined from graph

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31
If , which of the following rational
functions have only one vertical asymptote?
(1) (2) (3)

• . (1) only
• . (2) only
• . (3) only
• . (2) and (3) only
• . All of them
• . None of them

32
Which of the following functions could have the
graph shown below?

• .
• .
• .
• .
• .

33
If P(x) is a polynomial of degree , then
the degreeof the quotient of is

• Less than 2
• Exactly 2
• Greater than or equal to 2
• Exactly 3
• None of these.

Q(x) is called the quotient, D(x) is the divisor
and R(x) is the remainder.
Recall
34
Given and a gt 0, which of the
followingstatements are true? Changing a will
(i) changes xintercept (ii) changes
yintercept (iii) changes horizontal asymptote.

• (i) and (ii) only
• (I) and (iii) only
• (ii) only
• (iii) only
• None of these.

35
Match the function in Column I with the
appropriate statement in Column II.
Column I (1) (2) (3) (4) (5)
Column II (A) The x-intercept is (B) The
vertical asymptote is (C) The horizontal
asymptote is y 4 (D) The y intercept is (E)
There is a hole in its graph at
36
An insect population is increasing according to
the exponential function defined by P 3e0.03t,
where P is in thousands and t is the number of
years since 2004. Match the question given in
Column I with the correct equation given in
Column II.

• Column I
• How long will it take the insect population to
  double?
• When will the population reach 5 thousand?
• How large will be the insect population be in the
  year 2007?
• How large is the population 3 months since 2004?

Column II (1.) (2.) (3.) (4.)
37
Compare the quantity in Column A with the
quantity in Column B given the condition
Column A Column B

• The quantity in Column A is greater
• The quantity on Column B is greater
• The two quantities are equal
• The relationship cannot be determined from the
  information given

38
Mia has an investment that doubles in value
every 7 years. What will be the value of the
investment 21 years after it has a value of
10,000?

• 50,000
• 60,000
• 70,000
• 80,000
• 90,000

39
Below is the graph of y f(x) whereWhich of the
following must be true?
(i) (ii) (iii) (iv)

• (i) and (iii) only
• (i) and (iv) only
• (ii) and (iii) only
• (ii) and (iv) only

40
Which of the following functions have an inverse?

• 1 only
• 2 only
• 3 only
• 1 and 3 only
• 2 and 3 only
• All have inverses

1. 2. 3.
41
If f(x)log(xa) has a value of 1 when x 1,
then a must equal

• 1
• e
• 9
• 10
• Not possible to determine with the given
  information.
• None of these.

42
If , what is the value of
?

• .
• 343 a
• a4
• 22
• None of these.

43
What is the domain of
?What is the domain of ?
What implications does your answers to the
above have with regard to the solution of the
equation
44
Critique the following solution to the equation
45
Do you expect the graph of and the graph of
to be identical? Explain.
Do you expect the graph of and the graph of
to be identical? Explain.
46
Let b be a positive real number (not equal to 1)
and let a be its reciprocal. Discuss the
relationship between the graphs of and
47
True / False. The functions represented by the
graphs below are inverse functions.
48
Discuss why stretching / shrinking and vertical
translations are the same for logarithmic
functions.Thats is, consider the
transformation where
and
49
There are 20 rows of seats in an auditorium. If
the first row has 20 seats and each successive
row has 6 more seats than the previous row, how
many seats are there in the auditorium?

• 1600
• 1540
• 1440
• 1200
• 1040

50
Suppose that satisfies the equation
Then the value of is

• 1
• 1
• 3/2
• Not possible to determine with the given
  information
• None of these.

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