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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

The questions on this test are the property of the Ohio Department of Education and are used with its permission.

The solutions are a result of a collaboration of the Fitch High School Math Department.

All explanations of solutions and the format of this program are the property of Tom Reardon. C 2006 Reardon Electronic Gifts, Inc.

Your comments and suggestions would be appreciated.

E-mail: [email protected]

Web: www.TomReardon.com

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This program is designed to assist students to prepare to successfully pass the mathematics section of the Ohio Graduation Test.

THIS IS A HIGH SCHOOL GRADUATION REQUIREMENT!

Paper and pencil is required to take this test.

Only OGT CALCULATORS are allowed.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

DIRECTIONS

- At the top of your paper, make two columns:
- CORRECT INCORRECT
- Number the problems on your paper and show some work for each problem. Then choose the answer that best matches yours.
- CLICK on the LETTER of the answer that you want
- If you get the correct answer, then place a mark in the CORRECT column. Then proceed to the next problem.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

DIRECTIONS

- If the response that you select is incorrect, you will be told why it is incorrect and/or you will be given a hint to how to successfully answer the question. Then make a mark under the word INCORRECT at the top of your paper.
- Notice that you are keeping track of your score.
- This is to be a learning experience so try your best to learn from your mistakes… and to learn from what you know!
- Keep in mind that these are ACTUAL OGT TEST questions!!
- Good Luck!

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

For additional help, I

suggest that you consider

the book to the right.

It can be purchased at

most Barnes and Nobles

or online at

www.amazon.com

ISBN 0-7641-2369-6

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

- If this is your FIRST TIME doing this set of problems, then
- click HERE to start with number 1.

- If you have done some of these already, then click on the number of the problem that you wish to start with below:

- To start with problem 4, CLICK HERE.
- To start with problem 8, CLICK HERE
- To start with problem 12, CLICK HERE
- To start with problem16, CLICK HERE.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A. 11 days

B. 16 days

C. 18 days

D. 20 days

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

All work must be shown on your paper.

Try to learn from what you get right and from what you get wrong.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Are you …

TAKING YOUR TIME?

Careless errors are costly!

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

In order for this program to work,

you MUST read each solution and explanation.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Do the problem on your paper. Then click HERE

to see a correct solution. This problem is worth 2 points. Show all work.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

CAUTION!

The wrong answers can look VERY good.

The makers of these tests know all the “common mistakes” that students make and put those wrong answers in the test.

BE CAREFUL!!!!

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.circle graph

B. double line graph

C. box-and-whisker plot

D. back-to-back stem-and-leaf plot

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A. Click A for one way

B. Click B for 2nd way

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

CAUTION!

The wrong answers can look VERY good.

The makers of these tests know all the “common mistakes” that students make and put those wrong answers in the test.

BE CAREFUL!!!!

Click HERE to go to the next page

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Once you have done your work on your paper,

Click HERE to see a possible solution.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

A.

B.

C.

D.

OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Sorry, no.

It looks like you did the following:

Suggestion: subtract 175,000.

Then divide by 108,000.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Yes, great!

First subtract 175,000:

2000000 = 108000n

Then divide by 108000

which is, at most, 16 days.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Sorry, no.

It looks like you divided:

Suggestion: subtract 175,000.

Then divide by 108,000.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Sorry, no.

It looks like you divided:

Suggestion: subtract 175,000.

Then divide by 108,000.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This is incorrect.

The data shows that the tallest flower is

over 8 feet tall.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This is incorrect.

This data is not actually on the graph.

On the horizontal axis, the largest

amount of rain is 4.0 centimeters.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This is incorrect.

The top four heights occur when the

rainfall is between 2.5 and 3.0

centimeters.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Super!

The top four heights of sunflowers (about

8 centimeters) occurs when the rainfall is

between 2.5 and 3.0 centimeters.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Area of a rectangle = length times width

Correct!

252 = 21 times width

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

3B.

Area of a rectangle = length times width

Unfortunately this is wrong.

It looks like you divided 252 by 18 to get 14.

We are not sure why that should be done.

Since area is length times width,

252 = 21 times width.

How do you “undo” multiplication?

Division.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Area of a rectangle = length times width

Unfortunately this is wrong.

It looks like you subtracted: 252 – 21 to get 231, which is not correct.

Since area is length times width,

252 = 21 times width.

How do you “undo” multiplication?

Division.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Area of a rectangle = length times width

Unfortunately this is wrong.

It looks like you added 252 to 21 to get 273,

which is incorrect.

Since area is length times width,

252 = 21 times width.

How do you “undo” multiplication?

Division.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Lawn Care DepotTractors-R-Us

$169$210

10% discount:1/3 off:

(169)(.10) = 16.90210 divided by 3 = 70

Sale price: Sale price:

169.00 – 16.90 = $152.10210 – 70 = $140

Tractors-R-Us is the most economical place.

It is cheaper by $12.10

Remember: you must supply a clear explanation to receive credit!

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Oops!

In order to get the same number on two

consecutive spins, the probability would be:

But we already know that the first spin is a 2.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This is right!

Since we already know that a 2 is the first spin,

the probability of getting a 2 on the next spin

is one out of four, because each of the four

numbers is equally likely.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Oops!

Since we already know that a 2 is the first

spin, we need to know the probability of

spinning a 2 on the next spin.Well there are

4 numbers and each one is equally likely.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Oops!

Since we already know that a 2 is the first

spin, we need to know the probability of

spinning a 2 on the next spin.Well there are

4 numbers and each one is equally likely.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

You need to try again.

The graph of a linear equation is a straight

line. This is not a straight line.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

You need to try again.

The graph of a linear equation is a straight

line. This is not a straight line.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Terrific!

The graph of a linear equation is a straight line.

This is the only graph of a line.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

You need to try again.

The graph of a linear equation is a straight

line. This is not a straight line.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Great!

Substituting into the proportion above:

Cross multiply and finish solving:

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Not correct.

Substitute into the proportion above and

solve the proportion.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Not correct.

Substitute into the proportion above and

solve the proportion.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Not correct.

Substitute into the proportion above and

solve the proportion.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This isn’t right.

32.35 x 24 = $776.40 is what Jerry will pay

in 24 months.

It looks like you subtracted:

840 – 776.40 = $63.60

But you forgot about the down payment.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Fantastic!

32.35 x 24 = $776.40. This is the total of

Jerry’s monthly payments.

Add in the down payment:

776.40 + 190.00 = $966.40

Now subtract: 966.40 – 840.00 = $126.40

Nice job.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This isn’t right.

32.35 x 24 = $776.40 is what Jerry will pay

in 24 months.

It looks like you subtracted:

840 – 776.40 = $63.60

Then you added the down payment:

63.60 + 190.00 = $253.60

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This isn’t right.

It looks like you subtracted: 840 – 190 = $650.

You never brought in the 24 monthly

payments.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Incorrect.

A circle graph is a good way to represent how

data compares parts to a whole. For example,

a circle graph could be used to show what

percent of people like certain TV shows.

It is not a good way to compare average

earnings of male and female employees

over time.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Good job!

A line graph is an excellent way to show how

data changes over a time period.

A double line graph would show the male

data and female data separately so that the

data can be compared.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Incorrect.

A box-and-whisker plot is a good way to

illustrate how data is distributed.

It shows how data is spread out over “quarters”.

This is not a good idea to compare the earnings

data between males and females.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Incorrect.

A stem-and-leaf plot is a good way to organize

large amounts of data. They are used to

be able to understand which values are modes

and how the data is spread out.

This is not a good graph to compare earnings

data.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

One way: system of equations

F = number of 5 point questions

T = number of 2 point questions

F + T = 38 Times – 2 - 2F + - 2T = - 76

5F + 2T = 100 5F + 2T = 100

Adding 3F = 24

F = 8

T = 30

The number of 5 point questions is 8.

The number of 2 point questions is 30.

Check: 5(8) + 2(30) = 40 + 60 = 100.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

2nd way: make a table of guesses

# of 5 pt # of 2 pt Total points

Guess 10 28 10(5) + 28(2) = 50 + 56

= 106 (too high)

929 9(5) + 29(2) = 45 + 58

= 103 (still too high)

8 30 8(5) + 30(2) = 40 + 60

= 100 (just right!)

Therefore 8 5-point questions and 30 2-point questions

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Unfortunately this is wrong.

This figure has only triangles as faces and

there are clearly 3 rectangles in the original

figure.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Unfortunately this is wrong.

The original figure has 3 rectangles and 2

triangles. The figure in B has a rectangle and

4 triangles.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Unfortunately this is wrong.

The original figure has 3 rectangles and 2

triangles. The figure in C consists of 4

triangles.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Correct!

The original figure has 3 rectangles and 2

triangles.

The figure in D has 3 rectangles and 2

triangles.

Good job.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Super!

BF is half of DC, so BC is 3.

BE is half of AD, so BE is 4.

Triangle EBF is a right triangle, so the

Pythagorean theorem applies.

Also you may recognize the Pythagorean

Triple: 3 : 4 : 5. EF = 5 in.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

You need to try again.

BF is half of DC, BF = 3.

BE is half of AD, BE = 4.

Hint: use the Pythagorean theorem to find EF.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

You need to try again.

BF is half of DC, BF = 3.

BE is half of AD, BE = 4.

Hint: use the Pythagorean theorem to find EF.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

You need to try again.

BF is half of DC, BF = 3.

BE is half of AD, BE = 4.

Hint: use the Pythagorean theorem to find EF.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This isn’t right.

To find the volume of a rectangular solid,

aquarium, V = length x width x height.

But that is the volume if the aquarium if full.

It is only two-thirds full.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This isn’t right.

To find the volume of a rectangular solid,

aquarium, V = length x width x height.

But that is the volume if the aquarium if full.

It is only two-thirds full.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Hurray!

To find the volume of a rectangular solid,

aquarium, V = length x width x height.

But that is the volume if the aquarium if full.

It is only two-thirds full.

V = 36,000. One third of that is 12,000.

Two-thirds of that will be 24,000 cubic

centimeters.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

This isn’t right. You forgot to use the 2/3.

To find the volume of a rectangular solid,

aquarium, V = length x width x height.

But that is the volume if the aquarium if full.

It is only two-thirds full.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Sorry, no.

The number of successes is 2 + 5 = 7,

because there are 2 music CDs and 5

picture CDs.

The total number of possibilities is 10 (CDs).

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Sorry, no.

The number of successes is 2 + 5 = 7,

because there are 2 music CDs and 5

picture CDs.

The total number of possibilities is 10 (CDs).

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Good job!

The number of successes is 2 + 5 = 7,

because there are 2 music CDs and 5

picture CDs.

The total number of possibilities is 10 (CDs).

Probability = 7 out of 10.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Sorry, no.

The number of successes is 2 + 5 = 7,

because there are 2 music CDs and 5

picture CDs.

The total number of possibilities is 10 (CDs).

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Row 6 16 17 18 19 20 21

Row 7 22 23 24 25 26 27 28

Row 8 29 30 31 32 33 34 35 36

This is incorrect.

Check to see that you obtained the correct

numbers for Row 8 (above). Make sure you

got the right pattern.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Row 6 16 17 18 19 20 21

Row 7 22 23 24 25 26 27 28

Row 8 29 30 31 32 33 34 35 36

This is incorrect.

Check to see that you obtained the correct

numbers for Row 8 (above). Make sure you

got the right pattern.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Row 6 16 17 18 19 20 21

Row 7 22 23 24 25 26 27 28

Row 8 29 30 31 32 33 34 35 36

This is incorrect.

Check to see that you obtained the correct

numbers for Row 8 (above). Make sure you

got the right pattern.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Row 6 16 17 18 19 20 21

Row 7 22 23 24 25 26 27 28

Row 8 29 30 31 32 33 34 35 36

Yes, great!

Adding the numbers from Row 8 (above):

29 + 30 + 31 +32 + 33 + 34 + 35 + 36 = 260

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Team ATeam B

90100

87 87

85 (median) 87 (median)

83 78

80 78

Sum is 425Sum is 430

Mean is 425/5 = 85Mean is 430/5 = 86

Team B scored better in the contest because it had a higher

mean and higher median than Team A.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Using your OGT calculator:

Oops!

It looks like you took the cubed root of 27

instead of the square root of 27.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Using your OGT calculator:

This is right!

Good job.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Using your OGT calculator:

Oops!

It looks like you divided 27 by 3

instead of taking the square root of 27.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Using your OGT calculator:

Oops!

It looks like you divided 27 by 2

instead of taking the square root of 27.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Equation of a line:

y = m x + b

m is the slope, b the y-int.

Incorrect.

The y-intercept is 0. But the slope is not 4.

Use the ordered pairs, (12, 80) and (0, 0) to

approximate the slope.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Equation of a line:

y = m x + b

m is the slope, b the y-int.

Terrific!

The y-intercept is 0. And the slope is 6.5.

Use the ordered pairs, (12, 80) and (0, 0) to

approximate the slope.

m = 80/12 or about 6.7, which is closest to 6.5

Good job.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Equation of a line:

y = m x + b

m is the slope, b the y-int.

Incorrect.

The y-intercept is 0, not 10.

Use the ordered pairs, (12, 80) and (0, 0) to

approximate the slope.

Please try again.

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OGT Math March 2006 www.TomReardon.com C 2006 Reardon Gifts, Inc.

Equation of a line:

y = m x + b

m is the slope, b the y-int.

Incorrect.

The y-intercept is 0, not 10.

Use the ordered pairs, (12, 80) and (0, 0) to

approximate the slope.

Please try again.

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Not correct.

Angles 1 and 3 are congruent corresponding

angles. But angles 2 and 3 are supplementary,

not necessarily congruent.

Please try again.

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Not correct.

Angles 1 and 5 are congruent alternate

exterior angles.

But angles 2 and 5 are supplementary and not

necessarily congruent.

Please try again.

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Fantastic!

Angles 1 and 3 are congruent corresponing

angles.Angles 3 and 5 are congruent vertical

angles.By the transitive property, angles

1, 3, and 5 are all congruent to each other.

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Not correct.

Angles 1 and 5 are congruent alternate

exterior angles.

But angles 4 and 5 are supplementary and not

necessarily congruent.

Please try again.

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You need to try again.

2,400,000 is standard notation for this number

in scientific notation:

So close. Please try again.

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You need to try again.

In scientific notation, the power on 10 is the

number of places you must “move” the

decimal point in 2.4 to the right.

Please try again.

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You need to try again.

In scientific notation, the power on 10 is the

number of places you must “move” the

decimal point in 2.4 to the right.

Please try again.

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Super!

In scientific notation, the power on 10 is the

number of places you must “move” the

decimal point in 2.4 to the right.

Good job.

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I hope that you did well. Keep in mind that around 70% correct would be a passing score.

More importantly, I hope that you learned some good mathematics – enough so that you will pass the real 10th grade Ohio Graduation Test (OGT) the next time that you take it.

GOOD LUCK!!!

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For additional help, I

suggest that you consider

the book to the right.

It can be purchased at

most Barnes and Nobles

or online at

www.amazon.com

ISBN 0-7641-2369-6

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