BLACK HISTORY MONTH
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These problems were created to be used on the
High School level as warm-up exercises or to fill
in time at the end of a class. There are enough
exercise to take you through 4 weeks with an
extra 3 problems included. They range from
algebra to trigonometry. I hope this will not only
be educational, but fun!
Enjoy your mission…
Ms. Valerie Russell
FYI: Geography: Benjamin Banneker, a self taught
mathematician, was the first African-American to publish an almanac.
He is most noted for being the assistant surveyor on the team that
designed the ten-mile square of Washington D.C.
The White House is located in the center of the square, at the intersection of
Pennsylvania Avenue and New York Avenue. Let –5x+7y=0 represent New
York Avenue and let 3x+8y=305 represent Pennsylvania Avenue.
Your mission today is to find the coordinates for the White House.
MISSION ACCOMPLISHED
-5x+7y=0
3x+8y=305
3(5x+7y)=0
5(3x+8y)=305
-5x=-175
x=35
-15x+21y=0
15x+40y=1525
61y=1525
y = 25
The coordinate for the White House is (35,25).
-5x+7(25)=0
-5x+175=0
FYI:
Wilma Rudolf (1940-1994) was the first African-American woman to win three
gold medals at a single Olympic games. She won the 100-meter sprint, the
200-meter dash, and the 4* 100 meter relay at the 1960 Olympic Games.
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Given:
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The runners in a 200 meter dash race ran around the curve of a track. If
the runners start and finish at the same line, the runner on the outside lane
would run farther than the other runners. To compensate for this situation,
the starting points of the runners are staggered.
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Your Mission:

If the radius of the inside lane is X and each lane is 2.5 ft. wide, find out how
far apart should the officials start the runners in the two inside lanes.
Mission Accomplished
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Inside circle
Pi x
= 3.14x + 2.5(3.14) – 3.14x
= 2.5 (3.14)
= 7.85
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The two runners should start about 7.85 meters apart.
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Outside circle
Pi ( x+ 2.5) -
FYI:
Elmer Simms Campbell was the first African-American cartoonist to work for national
publications. He contributed cartoons and other art work to Esquire, Cosmopolitan, and Redbook, as
well as syndicated features in 145 newspapers.
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Given:
The Lion King was the top-grossing
film of the year, making an estimated
300.4 million at the box office. On a
Saturday afternoon the Johnson and
Olivera families decided to go see The
Lion King together. The Johnson
family, two adults and four children can
afford to spend $30 on movie tickets
while the Olivera family, two adults and
two children can afford to spend
$21.50. Different theatures around
town charge different amounts for adult
and chid tickets.
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Your Mission:
Find out what price can the
Johnson’s and Olivera’s afford
to pay for each adult and each
child .
Mission Accomplished
Let a = 1 adult ticket and

c = 1 child ticket
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
2a + 4c = 30
-( 2a + 2c = 21.50 )
2c = 8.5
2
2
C= $4.25
2a +4 (4.25) = 30
2a + 17 = 30
- 17 -17
2a
= 13
2
2
a = $6.50
They can afford to pay $6.50 for an adult ticket and $4.25 for a
childs ticket.
FYI:
The Moscow Papyrus contains records of early counting and
measuring. It contains 25 problems. Of these, 11 concern
proper portions for making different strengths of beer and bread.
Given: The longest loaf of bread ever baked was 2,132 feet 2.5
inches.
Today’s Mission:
If this loaf were cut into .5 inch slices, find out how many slices
of bread would there have been.
Mission Accomplished
First change 2132 ft. 2.5 in. to inches.
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2132 * 12 = 25,584
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25,584 + 2.5 = 25,586.5 inches
 Next divide by .5
 25,586 / .5 = 51,173
 There would have been 51,173 slices of
bread.
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FYI:
In 1980, there were 1.2 million elephants living in Africa. Because the natural
grazing lands for the elephant are disappearing due to increased population
and cultivation of the land, the number of elephants in Africa has decreased by
about 6.8% per year.
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Your Mission:
A) Write an equation
to represent the
population of the
elephants in Africa.
B) Find the year in
which the population
of Africa dropped by
half of the population
of the year 1980.
Mission Accomplished
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A) Y= c(1-r)^t
= 1.2(1-.086)^t
B) .6 > 1.2( 1- .068)^t
1.2 1.2
1.2(1.086
1.2
1
1.2
1.086
.086)
.5 > .932^t
Log .5 > t log .932
 


t> log .5
log .932
t> 9.8 year
Towards the end of 1989 the elephant population dropped to less
than half that of 1980.
t
tt
FYI: The Babylonians computed 2 to determine the diagonal of a
square of side 1. This indicates, and other texts confirm that the
Babylonians knew the Pythagorean theorem over a millennium
before Pythagoras lived. They did not prove it. They knew that in a
right or 90° triangle the sum of the squares of the lengths of the
two shorter sides or legs (a²+b²) equals the square of the length of
the hypotenuse c².
Your Mission:
Show your skill by picking up where the Babylonians left off.
Prove the Pythagorean Theorem.
Mission Accomplished
Given: Right triangle ABC with right angle at C
Prove: a² + b² = c²
Proof: Draw the altitude from C to AB. Let AB = c, AC=b, BC=a, AD=x, DB=y, and CD=h.
Two geometric means now exist: c/a = a/y and c/b = b/x
a²=cy
b²= cx
Add the equations:
a² + b² = cy + cx
a² + b² = c(y+x)
a² + b² = c²
A
C
b
a
h
B
x
D
c
y
FYI: This was an actual problem from the
A’hmose Papyrus.
It is considered the antecedent to the famous
Mother Goose rhyme .
As I was going to Saint Ives.
I met a man with 7 wives.
Each wife had 7 sacks;
Every sack had seven cats;
Every cat had seven kits;
Kits, cats, sacks, and wives,
How many were going to Saint Ives
Mission Accomplished
7*7*7*7=7^4=2401
There were 2,401 going to Saint Ives.
FYI: In 2000 BC, Egyptians used a loop of rope knotted at 12 equal
intervals to determine the boundaries of their properties each year
after the Nile flooded! They stretched the rope around three steaks
so that the measures of the sides of the triangle we 3,4, and 5. This
right triangle was used to establish the corners of their fields.
The 3,4,5 right triangle is called a Pythagorean triple. Pretend you lived
back during the days of the Egyptians and you owned 4 pieces of
property, all of which had to be bounded by right triangles.
Your Mission:
Find 4 other triples that you can use to tie off your
property.
Mission Accomplished
The Berlin Papyrus
FYI: The Berlin Papyrus was created from
fragments of early Egyptian tablets dating back
prior to 1850 B.C. It solved simultaneous
equations in verbal form.
*Your mission today is to solve 2 of the
actual problems found on the Berlin
Papyrus.
x²+y²=100
x²+y²=400
4x-3y=0
4x-3y=0
Mission Accomplished
X²+y²=100
4x - 3y = 0
4x = 3y ,
4
4
x²+y²=400
4x - 3y = 0
x = (3/4)y
x = (3/4)y ,
(3/4 y)² + y² =100
(9/16)y² + (16/16)y² = 100
y²/16) = 
(5/4)y = 10
5y = 40
y=8
X = (3/4)(8)
X=6
(3/4 y)² + y² = 400
(9/16)y + 16/16)y² = 400
16 [ (25/16)y² = 400 ]
2y²) =
5y = 80
y = 16
x = (3/4)(16)
x = 12
FYI: The Greek mathematician Thales
was the first to measure the height of a
pyramid by using geometry. He showed
that the ratio of a pyramid to a staff was
equal to the ratio of one shadow to the
other.
Given:
The height of a staff EF is 5 feet and
the length of its shadow FD is 6 feet.
Your mission today:
Find the height of a pyramid if the
shadow of the pyramid BC is 576 feet,
using similar triangles.
Mission Accomplished
x/576 = 5/6
6x = 5(576)
6
6
x = 480 feet, the height of the pyramid
FYI:
The Noks were one of Africa’s earliest
civilizations, dating back to 500 B.C.
Your mission today is to determine a
valid conclusion can be reached
from the two true statements. If it is
a Nok sculpture, then it has hallowed
out eyes and mouth and if a
sculpture has hallowed out eyes and
mouth, then it has air vents that
prevent cracking.
Mission Accomplished
Let p,q and r represent the parts of the
statements.
P: it is a Nok sculpture
Q: it has hallowed out eyes and mouth
R: it has air vents that prevent cracking
*Using these letters, the given
statements can be represented as pq and q-r. Since the given
statements are true, we can use the
Law of Syllogism to conclude p-r.
That is , if it is a Nok sculpture, then
it has air vents that prevent cracking.
FYI:
Early Africans had technology for making steel
tools as early as 100 B.C.
The gold disk once belonged to the
high rulers of the West African
kingdom of Ghana, which was
founded about A.D. 200.
If m<1=40 ,m<1= m<2, and m<2 =
m<3, find m <3.
Mission Accomplished
1
2
Since congruence of
angles is transitive,
m<1= m<3.
Therefore, m <3=40.
3
FYI: The early Egyptians used to make triangles by
using a rope with knots tied at equal intervals. Each
vertex of the triangle had to occur at a knot.
Suppose you had a rope with exactly 13
knots.
Your Mission:
Find out how many different triangles you can
make
MISSION ACCOMPLISHED
The 13 knots divide the rope into 12 sections of equal length. Thus, the perimeter of
each rectangle that can be formed will be 12 units. If x, y, and z represent the lengths
of the 3 sides then x + y + z= 12. We also know that x + y > z, x + z > y, and y + z > x
by the Triangle Inequality theorem.
X
1
1
1
1
1
2
2
2
2
3
3
4
Y
1
2
3
4
5
2
3
4
5
3
4
4
X
10
9
8
7
6
8
7
6
5
6
5
4
Triangle
no
no
no
no
no
no
no
no
yes
no
yes
yes
There are 3 possible triangles.
FYI: Problems 24 through 27 of the A’hmose Papyrus
give the oldest and most universal method of solving linear
equations with one unknown.
Problem 26 states:
“A quantity whose fourth part is
added to it becomes 15.”
Your Mission:
Find the quantity.
Mission Accomplished
x + (x/4) = 15
4[x+x/4 = 15]
4x+x = 60
5x = 60
x=12
Check: 12 + 12(1/4) = 12 + 3 = 15
FYI: In 1942, the United States Army established its first
and only training facility for African American pilots in
Tuskegee, Alabama. In addition to flying skills, pilots at the
Tuskegee Institute were taught to plot a course.
Since distances are relative to the same airport the
airport can be represented by the origin.
An airplane at an elevation of 2 miles is 50 miles
east and 100 miles north of an airport. Another
airplane at an elevation of 2.5 miles is 240 miles
west and 140 miles north of the airport.
Your mission today is to find the distance between
the two planes.
MISSION ACCOMPLISHED
Use the distance between the airplanes given 3 points in
space (x, y, z). The distance between A and B is
AB 
x2  x1 
2
  y2  y1   x2  x1 
2
2
50   2402  100 1402  2  2.5
2
2
2902   40   0.5 
2

85,700.25
 292.75
The airplanes are about 292.75 miles apart.
FYI: Benjamin Oliver Davis, Jr. was the first African
American to become an Air Force general and command
an air base.
A plane P is 3 miles above an air base.
The pilot sights the airport A at an
angle of depression of 15 degrees.
He sights his house H at an angle of
depression of 32 degrees.
Your Mission:
Find the ground distance d between
the pilots house and the airport?
MISSION ACCOMPLISHED
(sin 15°)/5.66 = (sin 17°)/a
 a = (sin 17° * 5.66)/sin 15°
 a = 6.4


The distance between the pilots
house and the airport is about 6.4
miles.
FYI:
Most of our knowledge of the order of
mathematics in Egypt is derived from two papyri- The
Rhind Papyrus and the Golenischev Papyrus. The Rhind
Papyrus was purchased in Luxor Egypt in 1858 by
Scotman A. Henry Rhind.
The Luxor Hotel in Las Vegas, Nevada, is
shaped like a gigantic black glass pyramid.
The base of the pyramid is a square with
edges 646 feet long. The hotel is 350 feet tall.
Your mission:
Find the area of the glass on the Luxor.
*The area of the glass is the lateral area of the
pyramid.
MISSION ACCOMPLISHED




Use the Pythagorean theorem to find the slant height:
l²=250² + (.5 * 646)²
l²=226,829
l²=√226,829≈476.3
 L=½Pl
 =½(4*646)(476.3)
 ≈615,379.6
 The area of the glass on the Luxor is about 615,380ft²
FYI: In 1996, Allen Johnson ran the 110-meter hurdles in 12.92 seconds making him
the fourth athlete to run this event in less than 13 seconds. To help him improve his
performance, Johnson used a computer model.
The distance from his take off point to his
landing point was 19.7 feet. The distance
from the top of the hurdle to his landing
point was 8.8 feet.
Your mission is to find the measure of the
angle formed by his takeoff point to the
top of the hurdle and the top of the hurdle
to his landing point.
MISSION ACCOMPLISHED
t 2  s2  t 2  2st cosT
19.7 2  8.8 2 12.12  28.812.1cosT
19.7 2  8.8 2 12.12
 cosT
28.812.1
0.7712 cosT
140.5  T

FYI:
Bernard A. Harris Jr., MD is the 1st African
American astronaut to walk in space. In 1993, he logged
4,164,183 miles in space on a mission aboard the STS-55.
If the orbit was 250 miles above Earth
and the diameter of Earth is about 8000
miles, your mission today is to find how
many orbits around Earth Dr. Harris made
on that mission.
Mission Accomplished
C  d, d  8000 500
4164,183 8500x

8500
8500
x  155.94
Dr. Harris made about 156 orbits around Earth.

FYI: In the Old Babylonian period (1800-1600B.C.) the
circumference of a circle was found by taking three times its
diameter. Putting this equal to πd, we see that their calculation is
equivalent to using 3 for the value of π.
In 1996, inspectors checked the accuracy of the
Olympic marathon course by using the “calibrated
bicycle method.” The inspectors rode bicycles
equipped with counters that tracked the turns of the
wheels. If the radius of a bicycle wheel is 13 inches
and the counter shows 20,300 revolutions at the
end of a course, your mission is to find the length of
the course using the Old Babylonian value of pi and
the present day value of pi.
MISSION ACCOMPLISHED
Present day π
Old Babylonian π
20,300 (2πr)
527,800(3)inches
=20,300(2π)(13)
63,360 in/mi
=527,800 π inches
=24.99 miles
For miles 12” = 5280 ft/mi or 63,360 in/mi
527,800π inches/63,360 inches/mi
=26.17 miles
FYI: The Great Pyramid of Cheops in Egypt is considered to be
one of the Seven Wonders of the World. It is also the largest pyramid in
the world. The area of the its base is 4050 square meters.
The volume of any pyramid is onethird the product of the area of the
base B and its height h.
FYI continued
Pyramid
Height ( meters)
Great Pyramid of Cheops
147
Bent Pyramid in Egypt
101
Inca Pyramid in Peru
75
Pyramid of the Sun in Mexico
60
Step Pyramid of Djoser in Egypt 60
Pyramid of the Sun in Peru
50
a) Write an expression that represents the
volume of a pyramid.
b) Find the volume of the Great Pyramid of
Cheops
MISSION ACCMPLISHED
a) V=1/3 Bh
b) V=4050(147)
3
V=198,450 cu. ft.
FYI: In 1995, Sheila Hudson Strudwick set the U.S.
women’s triple jump record.
Suppose her first jump was 46 feet 9 inches and her next
jump was 1 ¾ inches longer. Her record-setting jump
was 1 foot 2.5 inches longer than her second jump.
Your mission: Find the length of her record setting jump.
MISSION ACCOMPLISHED
1st jump – 46ft 9in
2nd jump – 46ft 9in + 1 ¾ = 46ft 10 ¾in
3rd jump – 46ft 10 ¾in + 1ft ½ in =
46ft 10 ¾ in
+ 1ft 2 ½ in
47 ft 12 5/4in
Her record setting jump was
48ft 1 ¼in
FYI: The largest loaf of bread ever baked was 2132
feet 2 ½in.
If this loaf were cut into ½” slices, your
mission is to find out how many slices of
bread would there have been?
MISSION ACCOMPLISHED
1st change 2132ft 2 ½” to inches
2132*12 = 25584
+
2 ½”
25,586.5”
Then divide by ½:
25,586.5/.5=51,173
*There would have been 51,173 slices of bread.
FYI: Truncated square pyramids, which are shaped like
cornerstones with sloping sides required great accuracy in
constructing the early pyramids. Egyptian scribal
mathematicians had found at least one specific case of the
correct volume formula :
V=(h/3) (a^2+ab+b^2)
Your Mission:
Find the volume of a truncated square
pyramid (or frustum) with altitude 6,
base side 4, and top side 2.
Mission Accomplished
V=(h/3)(a^2+ab+b^2)
V=(6/3)(2^2+2(4)+4^2)
V=2(4+8+16)
V=2(28)
V=56