Download Math 1302- Test I Review - Angelo State University

Math 1302- Test I Review
The following questions give you an idea of how I ask questions as well as a few examples. This test
review may be similar to the actual exam – it may also be quite different. The topics should be
similar in both. You are responsible for everything we studied in class ; notes, lectures, HW
problems, and quizzes. In some cases ( one or two problems), the ideas that we covered have been
extended somewhat and you may not have seen that type of question but are asked to use what you
have learned to answer the question.
No make-up on Exam I. Do not be alarmed
contains as many types of problems as possible.
about the length of this exam – it is a review and it
As stated in syllabus – you can only attend the review session ( 7:00 – 8:00 PM – Wed ) if you have missed at most one day
and if you have attempted this review – a blank review is not acceptable. If you have a good reason for having two absences
but you have attempted the test review – go ahead and come. This is only for the first exam – on the other exams – only one
absence is acceptable since the last exam.
When you answer the questions – keep in mind that you are studying the topics , the ideas – you are not memorizing the
question. I have a tendency to change the way the question is asked or modify the topic. ( instead of integers I may ask about
whole numbers – instead of commutative, I may ask about distributive, instead of additive inverse, I may ask about
multiplicative identity, ... )
Answers Should be non calculator based – use it to help you but not to provide an answer.
( 3/7,
2 , π are all good answers – their decimal representations are not
1. Identify each of the following sets;
{ 1, 2, 3, ... } → ________________________
set of real numbers that can not be written as fractions → __________________________
Whole numbers greater than 1 that are divisible only by 1 and the number itself → ___________
2. Write down the set
of whole numbers: ___________
of integers: ________________
Find the smallest nonnegative integer _________ smallest counting number ___________
3. Give me an example of the commutative law of addition. __________________
Is putting on your left shoe and then your right shoe commutative ? _____________________ Why or why not ?
Give me an example of something in real life ( like above ) that is not commutative . ___________________
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4. Which property is being used;
3 ( 4 • 5 ) = ( 3 • 4 ) • 5 ______________
Is ( 3 + 4 ) + 5 = ( 4 + 3 ) + 5 the associative law? ___________
5. Show by example
that the set of whole numbers is not associative under division -( division is not associative with whole numbers )
6. What does it mean when we say
the set of real numbers is closed under addition, subtraction, multiplication, and division (with one exception)
Show by example that the set of integers is not closed under the division operation.
7. Find the sum of the first three prime numbers. _________
Find the product of the first three prime numbers ___________
Find xn . if n is the smallest whole number and x is not zero. _________
xn if n is the smallest counting number and x is any real number. _________
8. Find each of the following absolute values.
a) | x 2 | = __________
c) | 4 -
15 | = __________
b) | 4 + x | = _____________ if x is a whole number
d) x + | x | = __________ if x is a whole number
x - | x | = ____________ if x is an integer
e)
x
= ______ if x is a real number
|x|
f)
|
5 • 5 - 6 | = ________
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9. Give me an example of an irrational number different than numbers of the form π and e. __________
of a rational number that is not positive. ____________
Since 4 is a rational number and
2 is not, then what kind of number is 2 +
make a conclusion of the statement above → “ the sum of .... is always ....”
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Is the product of two rational numbers a rational number ? _____________ provide examples or a counterexample
Is the product of two irrational numbers an irrational number ? _________ provide examples to convince me.
10. Find the solution of each of the following equations.
3 + x2 = 3 → _______________
2 – 3 ( x + 1 ) = 1 → __________
x x2

→ __________
3
4
1 - x( 1 – x ) = x2 → ____________
11. Is the set of whole numbers closed under multiplication ? ___________ Explain what this means.
Why is the set { 0, 2, -2 } not closed under addition ?
12. Which is bigger 3/11 or 4/23 ? Show without the use of a calculator -
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13. Find the additive identity of the set of real numbers . _________________ multiplicative identity ? ________
Find the additive inverse of ( - 4 ) . ______________
The multiplicative inverse of ( - 4 ) ? ______
14. Use the rules of exponents to simplify. Simplest type – exponents should be nonnegative.
a) 2x3 • 5x2y4 = ___________
( - 3 x2y4 ) 4 = ___________
c) xy(2xy4) = ___________
12 xy 5
4x 7 y 2
= __________________
15. More exponent problems. More difficult – exponents in final solution should be nonnegative.
a) ( 2x -1 ) -3 = _________
  3x 2 y 2 

c) 
2 7 
 12 x y 
e)
3
= _________
 3x1 / 2 y 1 / 2
= _________
6 x 2 y 1 / 3
  3x 7
g) 
 2y
b) ( -2x-1y4)2 (4x-2y3 )-1 = _____________
d) ( x1/3 ) ( -2x-1/2)(4x1/4y) = ____________
f) ( 2x1/2y-1/3 )-6
0

 = _______

h) ( -2/7 )-2 = ________
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16. What is the x intercept of 2x – y = 4 ? ______________
the y – intercept ? ____________
Give me three points that lie on the line 2x – y = 4. _______________________ Use them to graph the line.
You should include the intercepts above.
17. What is the slope of the lines
2x – y = 4 ? __________
18.
0•x + y = 2 ? __________
3x – 0 •y = 12? _____
simplify – reduce to simplest form
12 • 5/9 = ___________
1–
3/5 - 4/7 = ____________
1/ 2
= ________
3/ 6
4 - 3/5 = ______________
3  x( x  2)
= _________
x2
(1 + 1/x) ÷ ( 1 + 1/x) = _______
19. Write in simpler form
x • 1 = _________
0 + x = _______
x • x = _________
x ÷ x = ______
20. Find all whole number solutions of the equation 2x + 4 = 0. ________________
Find all integer solutions of the equation x ( 2x + 3 ) = 0 . _________________
Find all real solutions of x2 = 1 – x ( 1-x) , _____________________
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21. Find all positive solutions of x4 + 2x2 + 4 = 0 . ______________
22. Find the GCF of
a) 12 and 30 → ___________
b) 240 and 420 → _______________
c) 8x2y6 and 12x3y → _________
d)
5x
and 23y → _____________
23. Find the LCM of (problems above)
a) LCM( 12, 30) = _________
b) LCM(240, 420 ) = _______________
c) LCM ( 8x2y6, 12x3y ) = __________
d) LCM ( 5x, 23y ) = ________________
24. Use a number line to sketch all real numbers that satisfy the following inequalities (three different lines)
x ≤ -2
2x + 3 > 2
-2 < x ≤ 4
25. If x is a number in ( 3, 10] ( this is interval notation),
a) then what is the smallest value of x ? Is there a smallest value ?
b) what is the largest value of x ? Is there a largest value ?
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26. What if anything is wrong with the statement below ?
- 4 < x < - 12
27. How many terms does 3x – y have ? _______________
How many factors does ? ________
28. Which one does a monomial have more of (usually ) terms or factors ? _____________
29. Find a polynomial with three factors and only 1 term. _____________
A polynomial with three terms is called a _________________
30.
Which one of these is not a polynomial ? (circle your best solution(s) )
-3
2x + 3
all are
21/2 x2y + 1
x2 y
2
none are polynomials
31. What is the degree of the following polynomials
2 + x → _________
-2 → ___________
4 + x + x7 → ____________
½ x + x4y3 - y5 → ___________
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32. Simplify by performing the given operation and combining similar terms.
3 2  4 8 = ___________
a) 2i ( 1 – 2i ) = _____________
b)
c) ( 1+2i)(3 – 2i) = ______________
d) ( x + 3)2 = ________________
e) ( 1-x)(1-x)(1-x) = _____________
f) ( 3 – 2i ) - ( 4 – 2i ) = ________
g) a + b ( a + b ) = _______________
h) ( 2x –y)(2x + y) = _________
33. Write in scientific notation
321 = _________________
0.0021 = _______________
34. Find the answer to the following two problems and write your final answer in scientific notation. Try to control
yourself and not use a calculator.
a) ( 3 x 102 ) ( 5 x 103 ) = _______________
b) ( 1.2 x 10-3 ) ÷ ( 1.6 x 102 ) = _______________
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36. Simplify the following by using the properties of radicals. ( simplest )
a)
c)
 64 x12
= ________
y3
3
6
= ________
3
f)
4 3  3 18 = _________
1
h)
= ______________
(16x-8y4 )-1/2 = ________
b)
d)
8x 5 = ____________
2x
g)
x2
8
i)
36 x
16x 6
e) ( 9/25)3/2 = ________
= __________
= _________
37. More radicals.
a)
c)
e)
5
43 4 x 2 = ___________
b)
2x
= ___________
8 x5 y 4
d)
6 •
3
6 = ____________
f)
3
4 x  3 2 x 2 = _________
3
16 x
3
4
2x
2 3
32
= ____________
= ___________
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39. Other problems
a) which is bigger
x 2 or | x | ? explain your answer.
b) Find (assume that x is any real number) – without the use of a calculator.
2 + 3π = ___________
c)
3
x 2 = ______
x 3 = | x | True or False. _________
40. Word Problems
a) 10 % of all students in summer classes miss more than a week’s worth of school. A class consists of 60 students –
how many missed one week or less of school ? Actual number !
b)
A child can walk around a track in 10 minutes – stops along the way several times. The parent walks at 4
minutes per lap and will not stop until they both meet again at the starting line. Use the concepts we studied to
find how long it will be before they meet at the starting line. A single answer will be counted wrong – a list of
numbers (guessing) will also be counted wrong.
c) Use the given examples to find the missing numbers on the third example
What’s next in the pattern
- 5, -10, 10, 100
4, 8, -8, 64
-3, _____, _______, _______
d) When we divide the sum of a number and one by 3 we get 23, what was the original number ? I want an
equation – I do not want the actual number. Set up an equation that correctly models the statement.
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41. Which of these are perfect squares ?
x8,
9,
y25,
x2 + 9,
(2x – 3)2,
1 + 2x + x2,
x2 + 10x + 25
x2 + 12x - 9,
none of them
all are
We will probably be selective on this last two problems – depends on how far we get. We probably will get enough of
#42 below but not #43 or #44.
42. Factor the following polynomials. - whatever factoring we get to.
x2 - 2x = _____________
12x2y3 - 8xy4 = _____________
3x + xy = _____________
12x + 36x2 = __________
x2 – 49 = _____________
3y (x + 2) + 2x( x + 2 ) = ____________
4x2 – 9y2 = ____________
1 + x2 = __________
x3 + 8 = _____________________
x4 - 16 = ______________
1 – 27y3 = _____________________
5x4 + 40 = ______________
x2 - 4x - 5 = ____________
x3 + 8 = ________________
5 + x3 = _____________
x6 - 64 = ____________________
x2 + 2x – 35 = _____________
x2 + x + 100 = __________
x2 + 12x + 36 = ________________
8x3 – 18x = ______________
x2 +12x + 32 = _______
x3 – 2x2 – 3x = ___________
x2 – 6x + 9 = ______________
x3 - 27y3 = ______________
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43. More Factoring
more complicated problems plus trinomials of the form ax2 + bx + c
44. Algebraic fractions – if we get to this section - sum, difference, product, quotient
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