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Quantitative Literacy
Logical and Numerical Reasoning

1
Patterns, Connections, and Inductive Reasoning

Problem 1

Use inductive reasoning to find the next term in the sequence.

  1. \(5, 8, 11, 14,\, \ldots\)

  2. \(\vartriangle, \triangleright, \triangledown, \triangleleft,\, \ldots \)

  3. \(1, 4, 9, 16,\, \ldots\)

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Mr. Perez
Brooke
Brooke
Lauren
Lauren
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Edwin
Problem 2

Each sequence shown here is an arithmetic sequence. Find the next two numbers in each sequence.

a. 10, 16, 22, . . .

b. \(\displaystyle\frac{1}{2}\), 1, \(\displaystyle\frac{3}{2}\), . . .

c. 5, 0, \(-5\), . . .

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Mr. Perez
Mr. Perez
Betsy
Betsy
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Gordon
Problem 3

Each sequence shown here is a geometric sequence. Find the next number in each sequence.

a. 2, 10, 50, . . .

b. 3, \(-15\), 75, . . .

c. \(\displaystyle\frac{1}{8}\), \(\displaystyle\frac{1}{4}\), \(\displaystyle\frac{1}{2}\),. . .

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Mr. Perez
Mr. Perez
Betsy
Betsy
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Edwin
Problem 4

Find the number of bees in the tenth generation of the family tree of a male honeybee.

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Mr. Perez
Mr. Perez
Lauren
Lauren
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Gordon
Problem 5

Find the first \(4\) terms of the sequence whose general term is \(a_n=2n-1\)

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Mr. Perez
Mr. Perez
Betsy cc
Betsy
Brooke
Brooke
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Edwin
Problem 6

Find the first \(4\) terms of the sequence whose general term is \(a_n=\displaystyle\frac{1}{n+1}\)

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Mr. Perez
Mr. Perez
Stefanie cc
Stefanie
Brooke
Brooke
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Cynthia

2
Deductive Reasoning

Problem 1

Identify the hypothesis and conclusion in each statement.

a. If a and b are positive numbers, then -a(-b) = ab.

b. If it is raining, then the streets are wet.

c.

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Mr. Perez
Mr. Perez
Problem 2

For the statement below, write the converse, the inverse, and the contrapositive.

     If it is raining, then the streets are wet.

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Mr. Perez
Mr. Perez
Problem 3

If the statement "If I always tell the truth, then I never have to remember what I said" is true, give another statement that must also be true.

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Mr. Perez
Mr. Perez
Problem 4

If the following statement is true, what other conditional statement must also be true?

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Mr. Perez
Mr. Perez
Problem 5

Write the following statement in "if/then" form.

         Romeo loves Juliet.

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Mr. Perez
Mr. Perez
Problem 6

Ava is deciding whether to go for a run based on the weather conditions. We'll create a truth table to help make this decision. Suppose we have two conditions that influence our decision:

1.  Condition A:  Is it sunny?

2.  Condition B:  Is it not raining?

And she wants to decide whether she should go for a walk based on these conditions. Let's assume that she'll go for a walk only if both conditions are met. In this case, our logical expression is "A AND B" (both conditions must be true for Ava to go for a walk).

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Mr. Perez
Mr. Perez

3
Unit Analysis and Scientific Notation

Problem 1

A rider on the first Ferris Wheel would travel at approximately \(39.3\) feet per minute. Convert feet per minute to miles per hour.

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Mr. Perez
Betsy
Betsy
Aaron
Aaron
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Edwin
Problem 2

A ski resort in Vermont advertised their new high-speed chair lift as the worlds fastest chair lift, with a speed of 1,100 feet per second. Show why the speed cannot be correct.

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Mr. Perez
Mr. Perez
Betsy cc
Betsy
Gordon
Gordon
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Gordon
Problem 3

A snapshot appeared in USA Today in November of 2005 that shows the rate of births and deaths in the United States. There is one birth every seven seconds. How many births are there in one week?

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Mr. Perez
Betsy
Betsy
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Aaron
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Edwin
Problem 4

The pacific plate is moving \(519\) km every 5 million years. What is the rate of movement in cm/tear?

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Mr. Perez
Betsy
Betsy
Gordon
Gordon
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Gordon
Problem 5

Pyroclastic flows travel at speeds of 10 meters/second to 100 meters/second. Could you outrun a pyroclastic flow on foot, on a bicycle, or in a car?

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Mr. Perez
Betsy
Betsy
Aaron
Aaron
CJ
CJ
Problem 6

A bottle of vitamin C contains \(50\) tablets. Each tablet contains \(250\) milligrams of vitamin C. What is the total number of grams of vitamin C in the bottle?

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Mr. Perez
Betsy
Betsy
Gordon
Gordon
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Gordon
Problem 7

The engine in a car has a \(2\)-liter displacement. What is the displacement in cubic inches?

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Mr. Perez
Betsy
Betsy
Aaron
Aaron
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Edwin
Problem 8

Write \(376,000\) in scientific notation.

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Mr. Perez
Betsy
Betsy
Gordon
Gordon
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Gordon
Problem 9

Write \(4.52\times 10^3\) in expanded form.

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Mr. Perez
Betsy
Betsy
Aaron
Aaron
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Edwin
Problem 10

Multiply \(\left(4\times 10^7\right)\left(2\times 10^{-4}\right)\)

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Mr. Perez
Betsy
Betsy
Gordon
Gordon
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Gordon
Problem 11

Divide \(\dfrac{9.6\times 10^{12}}{3\times 10^4}\)

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Ana
Ana
Betsy cc
Betsy
Aaron
Aaron
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David
Problem 12

Simplify \(\dfrac{\left(6.8\times 10^5\right)\left(3.9\times 10^{-7}\right)}{7.8\times 10^{-4}}\)

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Mr. Perez
Graham
Graham
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David
Problem 13

The distance across the Cone Nebula is about \(2.5\) light-years. If we assume light travels \(186,000\) miles in one second, find the distance across the nebula.

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Mr. Perez
Betsy
Betsy
Aaron
Aaron
CJ
CJ

4
Sets and Venn Diagrams

Problem 1

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cup B\).

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Suhas
Suhas
Katrina cc
Katrina
Logan cc
Logan
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Edwin
Problem 2

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap B\).

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Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 3

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap C\).

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Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
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Edwin
Problem 4

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(B\cup C\).

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Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
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Julieta
Problem 5

If \(A=\{1, 2, 3, 4, 5, 6\}\), find \(A=\{x\mid x\in A \text{ and } x\geq 4\}\).

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Breylor cc
Breylor
Stephanie cc
Stephanie
Nathan cc
Nathan
Mr. Perez
Mr. Perez
Problem 6

Locate the numbers \(-4.5\), \(-0.75\), \(\dfrac{1}{2}\), \(\sqrt{2}\), \(\pi\), and \(4.1\) on the real number line.

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Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
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Edwin
Problem 7

For the set \(\left\{-5, \,-3.5, \,0, \,\frac{3}{4}, \,\sqrt{3}, \,\sqrt{5}, \,9\right\}\), list:

  1. whole numbers

  2. integers

  3. rational numbers

  4. irrational numbers

  5. real numbers

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Mr. Perez
Katrina cc
Katrina
Graham
Graham
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Edwin
Problem 8

Factor \(525\) into the product of primes.

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Preston
Preston
Katrina
Katrina
Breylor cc
Breylor
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Cynthia
Problem 9

Reduce \(\dfrac{210}{231}\) to lowest terms.

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Julieta spanish language icon
Julieta
Problem 10

Suppose a sample space is a deck of \(52\) playing cards. Let set \(A=\{ \text{Aces} \}\) and \(B=\{ \text{Kings} \}\) and use a Venn diagram to show that \(A\) and \(B\) are mutually exclusive.

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Mr. Perez
Joshua cc
Joshua
Stephanie cc
Stephanie
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Julieta
Problem 11

Use a Venn diagram to show the intersection of the set \(A=\{\text{Aces}\}\) and \(B=\{\text{Spades}\}\) from the sample space of a deck of playing cards.

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Mr. Perez
Mr. Perez
Logan cc
Logan
Stephanie cc
Stephanie
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Julieta
Problem 12

Use Venn diagrams to check the following expression. \[A\cap(B\cup C)=(A\cap B)\cup (A\cap C)\]

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Mr. McKeague
Julieta cc
Julieta
Logan cc
Logan
Mr. Perez
Mr. Perez
Problem 13

Let \(A\) and \(B\) be two intersecting sets, neither of which is a subset of the other. Use a Venn diagram to illustrate the set \[\{x\mid x\in A\text{ and }x\notin B\}\]

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Mr. McKeague
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Stephanie
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Mr. Perez
Julieta spanish language icon
Julieta
Problem 14
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Problem 15
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Mr. Perez
Mr. Perez