Homework Day 3

Pages 39-41
Problems 3-33 every 3rd problem

Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve each of the following exercises.
3.) Number of Squares:  How many squares are in the following figure?

6.) Number of Games:  In a basketball league consisting of 12 teams, each team plays each of the other teams exactly twice.  How many league games will be played?
9.)True-False Test:  In how many ways can you answer a 12-question true or false test if you answer each question with either a "true" or "false"?
12.) Number of Line Segments:  Twenty-four points are placed around a circle.  A line segment is drawn between each pair of points.  How many line segments are drawn?
15.) Change for a Quarter:  How many ways can you make change for $0.25 using dimes, nickels, and/or pennies?

Determine the units digit (ones digit) of the counting number  represented by the exponential expression.
18.) 2^725
21.) Find Sums: Find the following sums without using a calculator.  Hint: Apply the procedures used by Gauss. 
a.) 1+2+3+4+...+397+398+399+400
b.) 1+2+3+4+...+547+548+549+550
c.) 2+4+6+8+...+80+82+84+86

24.) Speed of a car:  A car has an odometer reading of 15,951 miles, which is a palindromic number.  After 2 hours of continuous driving at a constant speed, the odometer reading is next palindromic number.  How fast, in miles per hour, was the car being driven during these 2 hours?
27.) Movie Theatre Admissions:  The following bar graph shows the number of U.S. Canada movie theatre admissions for the years from 2002 to 2009.

a.) Estimate the number of admissions for the year 2009.  Round to the nearest tenth of a billion.
b.) Which year had the least number of admissions?
c.) Which year had the greatest number of admissions?


30.) Votes in an Election:  In a school election, one candidate for class president received more than94%, but less than 100% of the votes cast.  What is the least possible number of votes cast?
33.) Brothers and Sisters:  I have two more sisters than brothers.  Each of my sisters has two more than brothers.  How many more sisters than brothers does my youngest brother have?

Homework Day 2

Page 24
Problems 1-15 & 21

Construct a difference table to predict the next term of each sequence.
1.) 1,7,17,31,49,71, ...
2.) 10,10,12,16,22,30, ...
3.)-1,4,21,56,115,204, ...
4.) 0,10,24,56,112,190, ...
5.) 9,4,3,12,37,84, ...
6.) 17,15,25,53,105,187, ...

Use the given nth-term formula to compute the first 5 terms of the sequence.

Determine the nth-term formula for the number of square tiles in the nth figure.

Homework Day 1

Page 11-14
#3-39 every 3rd

Use Inductive Reasoning to predict the next number in each list:
3.) 3,5,9,15,23,33,?
6.) 80,70,61,53,46,40,?
9.) 2,7,-3,2,-8,-3,-13,-8,-18,?

Use Inductive Reasoning to decide whether each statement is correct. Note: The numbers 1,2,3,4,5,... are called counting numbers or natural numbers.  Any Counting number n divided by 2 produces a reminder of 0 or 1.  If n/2 has a reminder of 0, then n is an even counting number.  If n/2 has a remainder of 1, then n is an odd counting number.
Even counting numbers: 2,4,6,8,10, ...
Odd counting numbers: 1,3,5,7,9, ...
12.) The product of an odd counting number and an even counting number is always an even counting number.
15.) Pick any counting number.  Multiply the number by 6.  Add 8 to the product.  Divide the sum by 2.  Subtract 4 from the quotient.  The resulting number is twice the original number.

Use both images above  to answer #18. 
18.) Determine the distance a ball rolls, on an inclined alone 2, during each of the following time intervals.
a) 1st second : t = 0, t = 1 second
b) 2nd second : t = 1, t = 2 second
c) 3rd second : t = 2, t = 3 second
d) 4th second : t = 3, t = 4 second
e) 5th second : t = 4, t = 5 second

Use Inductive Reasoning  and the data in the incline plane time-distance table to predict the answer to each question.
21.) If the time a ball is allowed to roll on an incline plane is doubled, what effect does this have on the distance the ball rolls?
24.) How far will a ball roll on incline plane 1 in 1.5 seconds?

Determine whether the argument is an example of induction reasoning or deductive reasoning.
27.) Every English Setter likes to hunt.  Duke is an English setter, so Duke likes to hunt.
30.) The Atlanta Braves have won five games in a row.  Therefore, the Atlanta Braves will win their next game.

Find a number that provides a counterexample to show that the given statement is false.
33.) For all numbers x, x> 1/x.
36.)For all numbers x, |x+3|=|x| +3

Find a pair of numbers that provides a counterexample to show that the given statement is false.
39.) If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even counting number.