Algebraic Olympics

Are you ready?

Are you going to compete?Write your name on a note card for individual

competition and put on the table.Write your name on another note card for team

competition and put on the table.You need:

1. To sit toward the front of the room.2. Problem set sheet3. Book4. Reference sheet/planner5. Calculator, optional6. To be prepared to learn and have fun

Rules • The top 5 competitors will go on to the finals

and be eligible for Gold, Silver, or Bronze medals (prizes).

• Every competitor will get a small prize for participation.

• The Olympic spirit is important. Any competitor not displaying this spirit will be no longer eligible for prizes and subject to disciplinary action by the Olympic committee (Mrs. Byland and the 8th grade team).

If you are NOT competing:

• It is time to work on your problem set silently, without disruption.

• You will NOT be eligible for prizes, so don’t complain.

• You will learn, but won’t have as much fun

#1. Solve and check

2

1105

8

3

2

1 x

#2. Solve and check

3.6201.0402.0 xx

#3. Solve and check

83)2(45 xxxx

#4. Simplify

x

xx

2

102 2

#5. Simplify. TEAM QUESTION

)3

4(

2

232

3

2

b

dfdb

d

b

#6.

Avogadro’s number is represented by Writing this number as a product, which value

would have to be in the exponent of the expression

231002.6 x

?101002.6215

#7. TEAM QUESTION

The formula to convert degrees Fahrenheit to degrees Celsius is

a) Make a table of equivalent degrees Celcius temperature to -4, 32, 50, and 77 degrees Fahrenheit.b) Use the table to make a graph of the relationship.c) Find the slope of the graph

329

5 FC

#8. TEAM QUESTION

A class makes a box and whisker plot to show how many children are in each family. Identify the median, upper and lower quartiles, upper and lower extremes, and the interquartile range.

0 1 2 3 4 5

Children Per Family

#9. TEAM QUESTION

A doctor makes a box and whisker plot to show the number of patients she sees each day. Identify the median, upper and lower quartiles, upper and lower extremes, and the interquartile range.

10 15 20 25 30 35 40 45

Patients Per Day

#10. TEAM QUESTION

Create a data set that meets the following criteria: lower extreme 62, lower quartile 70, median 84, upper quartile 86, and lower extreme 95.

#11. Using a box and whisker plot, which information can you gather?

a) The mode

b) The range

c) The mean

d) The number of data values

#12. TEAM QUESTION

The planets’ distances (in million of miles) from the sun are as follows:

36, 67, 93, 142, 484, 887, 1765 and 2791

Make a box and whisker plot of these distances and determine if any planet’s distance is an outlier.

#13

Find the percent of increase or decrease to the nearest percent from the original price of $2175.00 to the new price of $2392.50.

#14. TEAM QUESTION

Choose an appropriate measure of central tendency to represent the data set. Justify your answer.

12 quiz scores (in percents): 86, 92, 88, 100, 86, 94, 92, 78, 90, 96, 94, 84

#15.A skateboard factory has 467 skateboards

in stock. The factory can produce 115 skateboards per hour.

Write a linear equation in slope-intercept form to represent the number of skateboards in inventory after so many hours if not shipments are made.

#16. Write an equality for the graph below

-9 -7 -5 -3

#17The following chart shows the wear on a

particular brand of tires every 10,000 miles. What is the average rate of wear for this brand of tires?

Mileage Tread Depth10,000 20 mm20,000 16 mm30,000 12 mm40,000 8 mm

#19

Explain the difference between the following:

1 1&

#20

Explain why cannot be

simplified to .

62

2

gg

6

1

#21.

Which expression is not equivalent to

a) c)b) d)

?6

31

1

drrd

13 rd

d

r3r

d3

dr 13

#22. TEAM QUESTION

Jane bought a prepaid phone card that had 500 minutes. She used about 25 minutes of calling time per week.

Write and graph an equation to approximate her remaining calling time y (in minutes) after 9 weeks.

#23

Find the slope of the line that passes through (1, 6) and (3, -4).

#24.

Describe a line that has a slope of 0 and passes through the point (-1, 1).

#25.

Write an equation in slope-intercept form of a line that passes through the points

(14, -3) and (-6, 9).

#26

Student A Student B

244

712

536

23

3

23

xx

xx

xx

2134

712

536

23

3

23

xxx

xx

xx

#27

Write a polynomial expression for the perimeter of the triangle. Simplify the polynomial and give your answer in standard form.

2x + 6

4x + 3

3x + 7

#28

The length of the sidewalk that runs in front of Trina’s house is 3x -16 and the width is 5x + 21. Find the perimeter of the sidewalk.

#29. TEAM QUESTION

The table shows the amounts that Doug and Jane plan to deposit in their savings account. Their savings account has the same annual growth rate g.

Use your book to answer part a and b.

Date 1.1.04 1.1.05 1.1.06 1.1.07

Doug $300 $400 $200 $25

Jane $375 $410 $50 $200

#30

Using a horizontal format, find the sum:

2416129 33 xxx