MATH 110A PRACTICE FOR FINAL EXAM
This is not all you need to know. In addition to this practice final, you should go over all handouts and
your reviews for exam 1 and exam 2. It is also a good idea to re-do your quizzes, practice exams and exams.
Determine whether the following statements are true or false. If the statement is true, put a T in the blank. If
the statement is false, put an F in the blank and provide a brief explanation or a counterexample. You will
not receive credit if you fail to defend your response.
1.
The sum of two negative numbers is a positive number.
2.
The product of two negative numbers is a positive number.
3.
2 is a multiple of 6,335,783,750.
4.
6,335,783,750 is a multiple of 2.
5.
4 divides 444,444,284.
6.
444,444,284 divides 4.
7.
9 is a divisor of 6,642,954.
8.
6,642,954 is a divisor of 9.
9.
3.3 divided by 100 is 0.033.
10.
100 divided by 3.3 is 0.033.
11.
2.8 is the product of 28 and 0.1.
12.
2.8 is the quotient of 28 and 0.1.
13.
The product of two positive rational numbers that are less than one is a positive
rational number that is greater than one.
14.
The sum of two positive rational numbers that are less than one is a positive
rational number that is less than one.
15.
The greater the numerator, the greater the fraction.
16.
The product of an odd number and an even number is an even number.
17.
The sum of an odd number and an even number is an even number.
18.
The sum of odd numbers is odd.
19.
The sum of even numbers is even.
20.
Every composite number is even.
Math 110A Final Exam Practice (cont.)
21.
A number can have an infinite amount of multiples.
22.
If a number is divisible by 6 and 3, then it is divisible by 18.
23.
The set of whole numbers is closed for the operation of subtraction.
24.
The set of real numbers is closed for the operation of addition.
25.
The set of whole numbers is a subset of the set of digits.
26.
The set of fractions is a subset of the set of rational numbers.
27.
The cardinality of the set of natural numbers is 10.
28.
Division is a commutative operation.
29.
Complete each of the following statements by using an appropriate form of the word or
phrase.
sum
divided by
subtrahend
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
product
difference
quotient
dividend
divisor
divides
divisible
factor
times
multiple
subtrahend
minuend
addend
minuend
minus
plus
subtracted from
least common multiple
greatest common factor
expression
equation
additive inverse
multiplicative inverse
Some of the ______________________ of 14 are 14, 28, 42, 56, and 70.
32 ______________________ 43 is 11.
The ______________________ of 6 and 4 is 24.
In the statement 72  9  8 , 72 is called the ______________________ , 9 is called the
______________________, and 8 is called the ______________________.
The ______________________ of 35 and 5 is 30.
80 ______________________ 16 is 64.
The ______________________ of 26 and 10 is 130.
12 ______________________ 60.
60 is ______________________ by 12.
60 ______________________ 6 is 12.
30.
Find a number that is
a) natural, an integer, rational, and real.
b) an integer, rational, and real.
c) rational and real.
d) irrational and real.
31.
Let a, b, c, and d represent real numbers, with a and b nonzero.
Identify the property of real numbers illustrated by the example.
1
ab   1
a)
b) a  b  c  b  c  a
c) a  b  c   a  b  c
ab
d) ab1  ab
f) a  bc  d   c  d a  b
e)  ab  ab  0
2
Math 110A Final Exam Practice (cont.)
32.
On the left below, there is an illustration of some of the steps that could be used to solve the
equation 5x  2  3x . To the right of each step, identify the property of real numbers that
is being illustrated on the left.
5x  2  3x
5x  10  3x
5x  5x  10  3x  5x
 10  2x
 1
 1
   10      2 x 
 2
 2
5 x
33.
Given
__________________________________________________
__________________________________________________
Simplify.
__________________________________________________
Simplify.
Let U  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, where U is the universal set.
Let A  0, 1, 3, 5, 7 , B  4, 9 , and C  0, 2, 4, 6, 8 .
For parts (a) through (d), use set roster notation to list the following:
a) A C 
b) A  B 
c) A C 
d) B  C 
e) B  C
34.
f) Find n  B 
g) Find n  B  C 

h) Find n B  C

a) Use standard written English to describe how to read the mathematical sentence 6  2  8 .
b) Describe two techniques you can use to teach a student to add the numbers 6 and 2.
You may include illustrations to support your explanation.
c) Use standard written English to describe how to read the mathematical sentence 7  4  3 .
d) Describe two techniques you can use to teach a student to subtract 4 from 7.
You may include illustrations to support your explanation.
4
5
and .
5
6
35.
Find two fractions between
36.
a) Find two unit fractions that have a sum of
1
.
30
b) Find two unique unit fractions that have a sum of
37.
1
.
30
4 1
 .
5 3
1 1
b) Use diagrams to illustrate how you could teach students to subtract  .
2 3
a) Use diagrams to illustrate how you could teach students to multiply
3
Math 110A Final Exam Practice (cont.)
38.
39.
40.
41.
3
a) Demonstrate how you could compute 2  10 using the distributive property.
5
1
3
b) Demonstrate how you could mentally determine that 4  5  10 .
2
5
2
Draw three different diagrams that could be used to illustrate the fraction .
3
Fully describe how you could respond to a student who writes the following mathematical
1
1
sentence on an exam: 6  6  36 .
4
4
a) Explain the difference between prime factoring a number and listing all of the factors of
a number.
b) Illustrate two techniques for prime factoring using the number 2640.
c) List all of the natural number factors of 320.
42.
a) What does it mean to find the greatest common factor of a set of numbers?
Provide an example to support your response.
b) Find the greatest common factor of 1245 and 3720.
c) What does it mean to find the least common multiple of a set of numbers?
Provide an example to support your response.
d) Find the least common multiple of 156, 84, and 294.
43.
Suppose that the LCM of two numbers is 90, and the GCF is 15. Find a pair of numbers that
fit this description.
44.
a) What is the greatest prime number that must be checked to determine whether 2581 is a
prime number? Explain your response.
b) List all the prime numbers larger than 120 but smaller than 150.
5
.
12
In order to solve the problem, the student must be able to perform multiplication. After you
write the problem, clearly demonstrate at least one strategy for solving the problem.
45.
Write a meaningful word problem for an elementary aged student for which the answer is
46.
Write a meaningful word problem for an elementary aged student for which the answer is
5
.
12
In order to solve the problem, the student must be able to perform addition or subtraction.
After you write the problem, clearly demonstrate at least one strategy for solving the problem.
47.
Create a 15 digit natural number that is a perfect square and divisible by 4, 5, and 11.
4
Math 110A Final Exam Practice (cont.)
48.
a) Write 685 in base 5.
b) Write 345 in base 2.
49.
a) Write 1011002 in base 10.
b) Write 4235 in base 10.
Use any problem solving strategy to solve the following word problems.
50.
Kamal begins grading papers at 11:00 a.m. He can grade, on the average, 4 problems per
minute. Each exam contains 60 problems and he has 30 exams to grade. If he works at a
steady rate and takes a 30 minute break after every 3 hours, at what time will all of the exams
be graded? Answer in terms of hours and minutes.
51.
What is the remainder when 541 is divided by 3?
52.
Elise and Matthew have walkie talkies. The walkie talkies only work if they are less than 1
mile apart. Elise and Matthew begin walking away from each other at exactly 7:00 a.m. Elise
walks at a steady 2.5 miles per hour due north. Matthew walks at a steady 3 miles per hour
due west. At what time will Elise and Matthew lose contact?
53.
There were 78 cookies in the cookie jar at the Dawson household. James Dawson came home
2
from school and ate half of the cookies in the jar. Later that day, his father ate
of the
3
cookies that were left in the jar. After this, how many cookies were left in the jar?
54.
Carole is planning to retile her kitchen. For an 11 foot by 12 foot rectangular section of the
kitchen, she wants to use rectangular tiles that are 3 inches by 4 inches. The tiles cost $2.59
each. How much will Carole spend on tiles if she buys exactly what she needs for the job?
55.
Find the sums of the following:
a) 1  2  3  4  ...  497  498  499  500
b) 2  4  8 16  ... 1024
56.
Using the symbols  ,  ,  , and  , fill in the following blanks to make a true statement. You
may use parentheses if needed.
6 _____ 6 _____ 6 _____ 6 _____ 6 _____ 6 = 38
57.
Suppose you wanted to make a track of matchstick squares like the following:
a) How many matchsticks would it take to create a track of 500 squares?
b) How many matchsticks would it take to create a track of n squares?
5