Links to practice problems for distance between two points and area of a triangle defined by three points, one of which is (0, 0)

Here is the link to the practice problems.

More practice
Here are four points. Distances should be given in simplified square root form and approximated to the nearest thousandth,

(0, 0), (6, 3), (10, 1), (-4, -5)

a) Distance from (0, 0) to (6, 3)
b) Distance from (0, 0) to (10, 1)
c) Distance from (0, 0) to (-4, 5)
d) Distance from (6, 3) to (10, 1)
e) Distance from (6, 3) to (-4, -5)
f) Distance from (10, 1) to (-4, -5)

g) the area of the triangle defined by the points (0, 0), (6, 3) and (10, 1)
h) the area of the triangle defined by the points (6, 3), (10, 1) and
(-4, -5)

answers in the comments.
 

Links to triangle classification with angles

Other problems are included, but you can find problems like the homework due on 1 July 2015 on these pages.

Simultaneous equation practice with Kramer's rule

6x + 5y = 18
2x - y = -4

3x + 7y = 12
2x + 5y = -18

Answers in the comments.

100 coin (or ticket) problems

a) 100 coins, all quarters and pennies, total = $13.72

b) 100 tickets, all children ($6) and adult ($12), total =$912

c) 100 coins, all quarters and nickels, total = $8.20

d) 100 coins, all dimes and pennies, total = $3.79

e) 100 coins, all dimes and nickels, total = $7.85

f) 100 coins, all quarters and dimes, total = $14.65

Answers in the comments

The Richter scale: From two readings, the relative strength and vice versa

In class last week, we learned how to find out how much stronger one quake is compared to another given the two Richter scale readings. For example, on June 28, the strongest quake in the U.S. was a 3.4 in Oklahoma, while the strongest in North America was a 5.4 in Niltepec, Mexico. What is the difference in levels of energy? Here are the steps.

Step 1: Subtract little from big. In our case, 5.4 - 3.4 = 2.0.
Step 2: multiply difference by 1.5. 2.0 * 1.5 = 3.0.
Step 3: Raise 10 to the power of the answer from Step 2: 10^3.0 = 1,000. The Mexican quake was 1,000 times stronger than the Oklahoma quake.

Let's ask the question in the opposite direction. Let's say we have a reading for a quake and we know another quake was x times stronger. Again, it will be a three step process, but now we will take the inverse of our three steps above in reverse order. Let's say we have a quake 350 times stronger than the one in Niltepec.  Here are our steps.

Step 1: Take the log of the strength multiplier. Log is the inverse of raising 10 to a power, just like addition is the inverse of subtraction and division is the inverse of multiplication. log(350) = 2.544...,
Step 2: divide the answer from Step 1 by 1.5 and round this answer to the nearest tenth. 2.544/1.5 = 1.696..., which rounds to 1.7. We round to the nearest tenth because the Richter scale rounds to the nearest tenth.
Step 3: Add the answer from Step 2 to the Richter reading we know. In this case, it would be 5.4+1.7 = 7.1, the reading of the stronger quake. If instead we were told a quake was 350 times weaker than Niltepec, it would be 5.4-1.7 = 3.7

Here are some practice questions. The answers are in the comments.

1. 16 times stronger than a 6.1
2. 250 times stronger than a 6.7
3. 8 times weaker than a 5.8

Link to the computer science biographies

Click on this link for the biographies of the five computer scientists. There will be questions on them on the midterm tomorrow.

Links to notes for 22 and 23 June

Notes on changing from decimal to binary and back, binary to hexadecimal and back and decimal to binary and back.

Notes for bitwise operators using binary notation.

Links to notes for 17 and 18 June 2015

Notes for percent and other scales based on powers of 10.

Practice for rates and scientific notation.

Links to all scientific notation posts.

Topics not covered in class that will be covered on Thursday and on homework 2.


Changing repeating decimals to fractions in lowest terms from 2012.

Changing repeating decimals to fractions in lowest terms from 2011. (Different practice problems.)
 


 
 

Links to homework 1, due Wednesday 17 June 2015

Link for prime factorization and all factors, with practice examples.

Roman and Hindu-Arabic numerals, fractions and decimals.

Practice for Roman to Hindu-Arabic and vice versa, fractions and decimals.

Practice for time conversion.

The following problems are in the form minutes:seconds. If the answer gives more than 60 minutes, write the answer as hours:minutes:seconds. Answers to the question below are in the comments.

 18:34
- 6:58


 42:23
 41:07
 43:01
 42:18
+42:17
 
 

Link to the four great mathematician biographies

Here is the link to the biographies of Archimedes, Newton, Euler and Gauss.

Syllabus for Summer 2015

Math 15: Math for Liberal Arts Summer 2015 (L1 30451)
Instructor: Matthew Hubbard
Email: mhubbard@peralta.edu
Text: no required text. If you want a text, personal recommendations can be made
Class website: http://mathlibarts.blogspot.com/
Class hours MTWTh: 10:00 am - 12:05 pm, G-211
Office hours: Math lab G-201
TTh 9:25-9:55 am 3:05-3:35 pm (also available by appointment)
Scientific calculator required (TI-30IIXs, TI-83 or TI-84 recommended)

Important academic schedule dates:
Last date to add, if class is not full: Sat., June 21
Last date to drop class without a "W": Sat. June 21
Last date to withdraw from class: Tues., July 23

Holidays: No holidays this session



Midterm and Finals schedule:

Midterm 1__________Thursday, June 25
Midterm 2__________Thursday, July 9
Comprehensive Final ___Thursday, July 23

Quiz schedule (most Tuesdays and Thursdays) no make-up quizzes given

First week: 6/16 and 6/18                       

Second week: 6/23

Third week: 6/30 and 7/2

Fourth week: 7/7

Fifth week: 7/14 and 7/16

Sixth week: 7/21

Grading Policy
Homework to be turned in: Assigned every Tuesday and Thursday, due the next class
(late homework accepted at the beginning of next class period, 2 points off grade)
If arranged at least a week in advance, make-up midterm can be given.

The lowest two scores from homework and the lowest two scores from quizzes will be removed from consideration before grading.

Grading system
Quizzes 25%* best 2 out of three of these grades
Midterm 1 25%* best 2 out of three of these grades
Midterm 2 25%* best 2 out of three of these grades
Homework 20%
Lab 5%
Final 25%

Anyone who misses less than two homework assignments and gets a higher percentage score on the final than the weighted average of all grades combined will get the final percentage instead deciding the final grade.


Anyone with a class grade of 97% out of all work before the final (this grade will be given on the next to last day) does not have to take the final. That grade is worth an A.

Academic honesty: Your homework, exams and quizzes must be your own work. Anyone caught cheating on these assignments will be punished, where the punishment can be as severe as failing the class or being put on college wide academic probation. Working together on homework assignments is allowed, but the work you turn in must be your own, and you are responsible for checking its accuracy. If I see multiple homework assignments turned in with the exact same wrong answers, I will give a warning. If it happens a second time, the student will get a 0 on the assignment and it will be counted towards the grade.

Class rules: Cell phones and beepers turned off, no headphones or text messaging during class
You will need your own calculator and handout sheets for tests and quizzes. Do not expect to be able to borrow these from someone else.

Student Learning Outcomes

• Analyze an argument for validity using simple rules of logic, and if invalid identify the type of mistake made.
• Compute, with sophisticated formulas, such quantities as interest payments for amortized loans.
• Interpret patterns and draw inferences from them.

Students with disabilities
The Disabled Students Program Services (DSPS) should have your academic accommodation with the instructor. After the first day, I will accept these accommodations electronically or by hard copy on paper. If you need academic accommodation and have not yet applied, please call 510-464-3428 for an appointment.

Exam policies
Quizzes will be closed book and closed notes. Some information you will be expected to remember, other formulas and information will be provided. No sharing of calculators is allowed. You are responsible for knowing how to use your calculator to find answers.

The reciprocal relationship

The teacher will be on time and prepared to teach the class.
The students will be on time and prepared to learn.

The teacher will present the material to the best of his ability.
The students will absorb the material to the best of their ability. They will ask questions when topics are not clear.

The teacher will do his best to answer the questions the students ask about the material, either by repeating an answer with more details included or by taking a different approach to the material that might be clearer to some students.
The students will understand if the teacher feels a topic has been covered enough for the majority of the class and will accept questions being answered outside the class, either in extra time or through written communication.

The teacher will do his best to keep the class about the material. Personal details and distractions that are not germane to the class should not be part of the class.
The students will do their best to keep the class about the material. Questions that are not about the topic should be avoided. Distractions like cell phones and texting are not welcome when the class is in session.

The teacher will give assignments that will help the students master the skills required to pass the course.
The students will put in their best efforts to complete the assignments.
When the assignments are completed, the teacher will make every effort to get the assignments graded and back to the students in a timely manner, by the next class session whenever possible.

The teacher will present real life situations where the skills being learned will be used when they exist. In math, sometimes a particular skill is needed in general to solve later problems that will have real life applications. Other skills have the application of “learning how to learn”, of committing an idea to memory so that committing other ideas to memory becomes easier in the long run.

The student has the right to ask “When will I use this?” when dealing with mathematical topics. Sometimes, the answer is “We need this skill for the next skill we will learn.” Other times, the answer is “We are learning how to learn.” Both of these answers are as valid in their way as “We will need this to understand perspective” or “We use this to balance our checkbooks” or “Ratios can be used to figure out costs” or other real life applications.

Short explanation of mathematical logic and links to practice problems.

Here is a link to practice problems for mathematical logic.

There are four major logical operators we will be using.

AND, represented by the symbol ^.
OR, represented by the symbol v.
NOT, represented by the symbol ~
IMPLIES, represented by the symbol => (supposed to be an arrow, but no single symbol availabe to the blogger editor works.

There are only two values in logic, TRUE (represented by 1) and FALSE (represented by 0). A logical variable, often represented by the letters p, q and sometimes r, though other letters are legal, is an ordered list of 1s and 0s, known as a bitstring.

Here are the rules for AND, an operator that needs two variables.
1 ^ 1 = 1
1 ^ 0 = 0
0 ^ 1 = 0
0 ^ 0 = 0


In English, the simplest way to explain AND is to say p ^ q is only true if BOTH p and q are true, otherwise the operation produces a false outcome.


Here are the rules for OR, an operator that needs two variables.
1 v 1 = 1
1 v 0 = 1
0 v 1 = 1
0 v 0 = 0



In English, the simplest way to explain OR is to say p v q is true if EITHER p or q are true, and only false if both are false.


NOT is an operator that applies to a single variable.


~1 = 0
~0 = 1


NOT is like a switch. "NOT true" is the same as "false" and "NOT false" is the same as "true".


Mathematical logic is similar to set theory, where AND is like intersection, OR is like union and NOT is like the complement (or bar over the set).


IMPLIES is an operation in mathematical logic that doesn't have an analog to a basic set theory operator.  The rules are as follows.


1 => 1 = 1
1 => 0 = 0

0 => 1 = 1
0 => 0 = 1


If you have trouble remembering the rules for p => q, it works the same as ~p v q, where the NOT at the beginning only applies to the variable p. (The standard order of operations in logic is left to right, unless there are parentheses and ~ only applies to the variable immediately following it.)

A link to the stories of the five 19th Century British mathematicians who started mathematical logic.

Here is a link to the stories about Boole, Babbage, DeMorgan, Lovelace and Dodgson.

A link to all the posts dealing with binary and hexadecimal representation.

This link goes to three posts that deal with binary and hexadecimal representation. There are practice problems with answers in the comments.

Notes and practice for Venn diagrams and conditional probability

This link is to a post on my statistics blog about what we did today in the lab handout. Like posts here on the Math for Liberal Arts blog, there are problems at the end with answers in the comments.

Link to practice with set theory and cardinality.

Here's a link to some set theory problems.

Practice for contingency tables and time problems

_____________Male____Female__row totals
Facebook______55________________125
no Facebook __________20_____   ______
col. totals___90_____________________grand total

Answer the following probability problems from the completed contingency table. Write the answers first as fractions then rounded to the nearest thousandth.

The inclusion exclusion rule tells us p(A UNION B) = p(A) + p(B) - p(A INTERSECTION B) 

p(Facebook) = _________ ~= __________

p(Male) = _________ ~= __________

p(Male INTERSECTION Facebook) = _________ ~= __________

p(Male UNION Facebook) = _________ ~= __________

Time problems.

a) How many minutes in 3 days?

b) 560 hours is __________ days and ________ hours.


c) 8,086 seconds is ________ hours, ________ minutes and __________ seconds.

d) 8,086 hours is ________ weeks, ________days and __________ hours.

e) After a flu outbreak, a hospital has decided quarantine will last 66 hours. If it starts at 5:00 pm on Tuesday, give the day and time when it will be over.

Day: ________ time: ___________ a.m or p.m? __________

Answers in the comments.
 

Practice for regular polygon angles and pictures of regular tilings

Here is a link to practice problems from 2011 dealing with the angles of regular polygons.

Here are pictures of some mix and match tilings of the planes, which will be on the Tuesday homework.

Here are more regular polygon problems.

The formula for total degrees of the angles on an n-gon is 180(n-2)° or [180n-360]°.

 The formula for the measure of a regular angle is [180-360/n]°.

a) What is the sum of all the angles of a 20-gon?

b) What is the regular angle measure of a 20-gon?

c) What is the sum of all the angles of a 30-gon?

d) What is the regular angle measure of a 30-gon?


Answers to these questions in the comments.

Link to the story of the five computer scientists

Here is the link to the stories of John Von Neumann, Grace Hopper, Alan Turing, Edsger Dijkstra and Donald Knuth.

Order of operations practice

Using the rules of order of operations, find the values of the following expressions.

a) 2(3² - 5)

b) 2(3 - 5)² 

c) 2²(3 - 5)

d) 2 × 3² - 5 

e) (2 × 3)² - 5

f) 2(3² - 5²)

Answers in the comments.