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ECHS 20-2 Final Exam Review

I.

Unit 1: Inductive & Deductive Reasoning

Questions

1. Austin created a pattern with blocks. Predict the next figure that he is likely to sketch.

2. Ashley likes to create number sequences. Explain the sequence she created and predict the next number in her pattern..

_____

3. Toney’s Uncle had a safety deposit box at a bank in the capital city of San Salvador, El Salvador. Inside the deposit box is a lock box containing a solid gold chain weighing 20 ounces of 24 karat gold. The current melt price of the gold chain is $1,028.05. Toney is to inherit the chain at his 21 birthday but can only obtain the chain if he is able to decipher the pattern below and enter the seven digits into the combination of the lock box (no negatives). Explain the pattern to Toney and help him determine the next number thereby providing the seven digit code.

_____

Number and Logic

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4. Make a conjecture about the length of line segment AB with respect to line segment BC.

5. From the pattern below what conjecture is Karan likely to make (if any). Provide an example to support Karan’s idea.

6. Corrine considers the expression . She notices that a pattern is created

if she decides to substitute the numbers 1-9 into the expression for x one digit at a time what solutions did she obtain in each case? Record your answer in the table below and study the pattern. By what means can Corrine move from one number

to the next? Rather than use the formula ( ) to determine the tenth term;

show how the pattern can be utilize to arrive at that term. Explain to Corrine how you did it?

7. Ned used a counterexample to disprove the statement, “All prime numbers are odd”. Define the terms prime and composite numbers. State the status of each number from 1 to 20 (prime or composite). What is the counterexample that Ned might have used?

8. Jovan is confident that he can determine both an example and counterexample for the statement;

All odd numbers can be expressed as the sum of three prime numbers”.

Help Jovan provide one example to support his theory and a counterexample to disprove the idea?

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9. Christian, Houston, Jessica, and Kim live on the first floor of an apartment building. One is a manager, one is a computer programmer, one is a singer, and one is a teacher. Use the statements below to determine which person is the manager. Also, describe the reasoning used to solve this problem.

 Kim and Jessica eat lunch with the singer.

 Christian and Houston carpool with the manager.

 Jessica watches football on television with the manager and singer.

10.State the divisibility test for the numbers “2’ and “3”. After carefully considering the divisibility tests for 2 and 3 Adam declares the conjecture below. Provide three examples that agree with his conjecture and if possible a counterexample in order to disprove Adam’s conjecture;

“Any numbers divisible by 2 and 3 will also be divisible by 6”

Questions

11.Christiana is obsessed with Sudoku subscribing to countless game sights on the internet. Her strategy is to determine which square in a particular matrix cannot hold a number. Explain how this strategy might be used to find the correct number for the grey space in the Sudoku puzzle below.

Number and Logic

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12. Arrange the numbers 1 through 9 on a tic tac toe board such that the numbers in each row, column, and diagonal add up to 15.

13. Using six straight lines, connect all of the sixteen circles shown below:

14.Joe likes to do Sudoku in his spare time. Help Joe find the answer to the grey space in the Sudoku puzzle below:

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15.Kee decided to challenge himself with the NY Times’ set game puzzle found daily in every issue of the famous news paper. There are four characteristics:

 Shape (diamond, oval, squiggle)

 Number of shapes (one, two, three)

 Color (red, green, purple)

 Fill (solid, hollow, stripes)

The rules are simple, you must select three items, of which all three must have all the same or all different with respect to the above characteristics. As the photocopy is not color the letter under each provide a hint as to the color (R is red, G is green, and P is purple). There are six sets that can be found below. Help Kee find one set.

II. Unit 2: Statistical Reasoning

Statistics

2. Demonstrate an understanding of normal distribution, including:Standard Deviation

z-scores. P

P

G

R

P

P

P P

G

G

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Questions

16. In 1905, Alfred Binet created the first workable intelligence scale at Stanford

University. Eventually this work evolved into what is now known as the Stanford-Binet IQ Test. Using the current world population of 6.5 billion, a normal intelligence quotient (IQ) ranges from 85 to 115. Approximately 1% of the people in the world have an IQ of 135 or over.

The table that follows is composed of fourty actual IQ’s scores from a grade eleven classes at a local high school in Edmonton.

113 120 101 108 99 104 100 101 91 119

89 121 107 101 112 108 95 101 95 112

97 86 101 100 125 98 131 103 117 105

96 100 98 102 118 102 118 109 101 105

a) Calculating the Range of raw data makes it easier to estimate a suitable interval in the IQ Ranges in the table below. Determine the range of the forty IQ’s above.

b) How many intervals are appropriate for the IQ data?

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c) Complete the Frequency Distribution Table below.

IQ Range Tally Frequency

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e) Determine the standard deviation using you graphing calculator. Record the results below on the left side of the question response section. On the right side record the required steps.

f) Create a histogram to represent the forty grade eleven IQ’s.

g)Find the score of Leonardo Davinci from the chart below. Determine the z-score of his IQ against the IQ’s of the 24 grade eleven students

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Abraham Lincoln President USA 128

Adolf Hitler Nazi leader Germany 141

Albert Einstein Physicist USA 160

Albrecht von Haller Medical scientist Switzerland 190 Alexander Pope Poet & writer England 180

Andrew Jackson President USA 123

Andy Warhol Pop artist USA 86

Arnold Schwarzenegger Actor/politician Austrian 135 Benjamin Franklin Writer, scientist & politician USA 160

Bill Gates CEO, Microsoft USA 160

Bill (William) Jefferson Clinton President USA 137

Bobby Fischer Chess player USA 187

Buonarroti Michelangelo Artist, poet & architect Italy 180

Charles Darwin Naturalist England 165

Charles Dickens Writer England 180

George Walker Bush President USA 125

George Washington President USA 118

Immanuel Kant Philosopher Germany 175

Sir Isaac Newton Scientist England 190

James Cook Explorer England 160

Johann Sebastian Bach Composer Germany 165

Johann Strauss Composer Germany 170

John Adams President USA 137

John F. Kennedy Ex-President USA 117

John Quincy Adams President USA 153

Joseph Haydn Composer Austria 160

Leonardo da Vinci Universal Genius Italy 220 Louis Napoleon Bonaparte Emperor France 145

Ludwig van Beethoven Composer Germany 165

Ludwig Wittgenstein Philosopher Austria 190 Madame de Stael Novelist & philosopher France 180

Madonna Singer USA 140

Martin Luther Theorist Germany 170

Miguel de Cervantes Writer Spain 155

Nicolaus Copernicus Astronomer Poland 160

Nicole Kidman Actor USA 132

Plato Philosopher Greece 170

Richard Nixon Ex-President USA 143

References

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