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 sheet
3. Book
4. Reference sheet/planner
5. Calculator, optional
6. 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
1 3
1
 x  5  10
2 8
2
#2. Solve and check
0.02 x  4  0.01x  2  6.3
#3. Solve and check
x  5x  4( x  2)  3x  8
#4. Simplify
2 x  10x
2x
2
#5. Simplify. TEAM QUESTION
2
2
3
2
b db
3f d
(

)
3
2
d
4
b
#6.
Avogadro’s number is represented by 6.02 x1023
Writing this number as a product, which value
would have to be in the exponent of the
expression 6.021015 10 2 ?

 
#7. TEAM QUESTION
The formula to convert degrees Fahrenheit to
degrees Celsius is
5
C
9
F  32 
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
#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
#17
The 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
10,000
20,000
30,000
40,000
Tread Depth
20 mm
16 mm
12 mm
8 mm
#19
Explain the difference between the following:
1 & 1
#20
2g
Explain why
2g  6
1
simplified to .
6
cannot be
#21.
Which expression is not
6

1
equivalent to 3rd  1 ?
r d
a)  3rd 1
b)  3r
d
c)
d)
 3d
r
3
r 1d
#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 slopeintercept form of a line that
passes through the points
(14, -3) and (-6, 9).
#26
Student A
Student B
 6 x  3x  5
 6 x  3x  5
 2 x  1x  7
 2 x  1x  7
 4x  4x  2
 4 x  3x  1x  2
3
2
3
3
2
3
2
3
3
2
#27
Write a polynomial expression for the
perimeter of the triangle. Simplify the
polynomial and give your answer in
standard form.
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.
Date
1.1.04
1.1.05
1.1.06
1.1.07
Doug
$300
$400
$200
$25
Jane
$375
$410
$50
$200
Use your book to answer part a and b.
#30
Using a horizontal format, find the sum:
9x
3
 

 12  16x  4x  2
3