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The Lion

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The Lion Team Competition Welcome to the team competition. This is the event where using all your teammates to optimize your time will be essential. – PowerPoint PPT presentation

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Title: The Lion

1
The Lion

Team Competition

Welcome to the team competition. This is the
event where using all your teammates to optimize
your time will be essential.
Each question will have a different allotment of
time and each question varies in difficulty.
For each question you may score 2 points. One
point for a speed answer and a second point for
your final answer. (Note to get the speed
answer point it must be same correct answer as
your final answer.)
Lets do a practice question!

3
Practice question time

Speed answer 2 minutes
Final Answer 3 minutes

4
Practice question

In Circle Land, all rules of mathematics are the
same as we know them except numbers are shown in
the following way

Calculate the following expression and provide
the answer as they would in Circle Land?
5
Practice question

In Circle Land, all rules of mathematics are the
same as we know them except numbers are shown in
the following way

Calculate the following expression and provide
the answer as they would in Circle Land?
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Answers in!!!!!!
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Practice question answer
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Now for the real thing. Good luck.

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Question 1 time

Speed answer 3 minutes
Final Answer 4 minutes

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Question 1

In the diagram, ABCD is a square with area 25 cm2
. If PQCD is a rhombus with area 20 cm2.
What is the area of the shaded region?

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Question 1

In the diagram, ABCD is a square with area 25 cm2
. If PQCD is a rhombus with area 20 cm2.
What is the area of the shaded region?

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Answers in!!!!!!
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Question 2 time

Speed answer 4.5 minutes
Final Answer 6 minutes

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Question 2

A hat contains n slips of paper. The slips of
paper are numbered with consecutive even integers
from 2 to 2n. Consider the situation where there
are six slips of paper (n 6), in the hat, two
students, Tarang and Joon, will each choose three
slips from the hat and sum their total. In this
situation (when n6) it is impossible for them to
have the same total.
If more slips of paper are added to the hat, what
is the smallest value of n gt 6 so that Tarang and
Joon can each choose half of the slips and obtain
the same total?

15
Question 2

A hat contains n slips of paper. The slips of
paper are numbered with consecutive even integers
from 2 to 2n. Consider the situation where there
are six slips of paper (n 6), in the hat, two
students, Tarang and Joon, will each choose three
slips from the hat and sum their total. In this
situation (when n6) it is impossible for them to
have the same total.
If more slips of paper are added to the hat, what
is the smallest value of n gt 6 so that Tarang and
Joon can each choose half of the slips and obtain
the same total?

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Answers in!!!!!!
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Question 3 time

Speed answer 2 minutes
Final Answer 3 minutes

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Question 3

The Fryer Foundation is giving out four types of
prizes, valued at 5, 25, 125 and 625.
There are two ways in which the Foundation could
give away prizes totaling 880 while making sure
to give away at least one and at most six of each
prize. Determine the two ways this can be done.

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Question 3

The Fryer Foundation is giving out four types of
prizes, valued at 5, 25, 125 and 625.
There are two ways in which the Foundation could
give away prizes totaling 880 while making sure
to give away at least one and at most six of each
prize. Determine the two ways this can be done.

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Answers in!!!!!!
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Question 4 time

Speed answer 2 minutes
Final Answer 3 minutes

22
Question 4

A Nakamoto triangle is a right-angled triangle
with integer side lengths which are in the ratio
3 4 5. (For example, a triangle with side
lengths 9, 12 and 15 is a Nakamoto triangle.)
There are three Nakamoto triangles that have a
side length of 60. Find the combined area of
these three triangles.

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Question 4

A Nakamoto triangle is a right-angled triangle
with integer side lengths which are in the ratio
3 4 5. (For example, a triangle with side
lengths 9, 12 and 15 is a Nakamoto triangle.)
There are three Nakamoto triangles that have a
side length of 60. Find the combined area of
these three triangles.

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Answers in!!!!!!
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Question 5 time

Speed answer 3.5 minutes
Final Answer 5 minutes

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Question 5

Let s be the number of positive integers from 1
to 100, inclusive, that do not contain the digit
7.
Let t be the number of positive integers from
101 to 300, inclusive, that do not contain the
digit 2.
Let f be the number of positive integers from
3901 to 5000, inclusive, that do not contain the
digit 4.
Determine the value of stf.

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Question 5

Let s be the number of positive integers from 1
to 100, inclusive, that do not contain the digit
7.
Let t be the number of positive integers from
101 to 300, inclusive, that do not contain the
digit 2.
Let f be the number of positive integers from
3901 to 5000, inclusive, that do not contain the
digit 4.
Determine the value of stf.

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Answers in!!!!!!
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Question 6 time

Speed answer 3 minutes
Final Answer 4 minutes

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Question 6
Limits 98
Derivatives 80
Applications of Derivatives 87
Integration 85
Applications of Integration 64
Integration Techniques 96
Series 91
Parametrics ???
Polar ???

Amanda has the following grades on her Calculus
tests this past year. She cant remember her
grade on her Parametrics test but she does
remember that her worst test was Applications of
Integration. She took her Polar test today but
has no idea how she did on it. What is the
difference between her highest possible average
for the year and her lowest possible average?

31
Question 6
Limits 98
Derivatives 80
Applications of Derivatives 87
Integration 85
Applications of Integration 64
Integration Techniques 96
Series 91
Parametrics ???
Polar ???

Amanda has the following grades on her Calculus
tests this past year. She cant remember her
grade on her Parametrics test but she does
remember that her worst test was Applications of
Integration. She took her Polar test today but
has no idea how she did on it. What is the
difference between her highest possible average
for the year and her lowest possible average?

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Answers in!!!!!!
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Question 7 time

Speed answer 4.5 minutes
Final Answer 6 minutes

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Question 7

The odd positive integers are arranged in rows in
the triangular pattern, as shown. Determine the
row where the number 1001 occurs.

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Question 7

The odd positive integers are arranged in rows in
the triangular pattern, as shown. Determine the
row where the number 1001 occurs.

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Answers in!!!!!!
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Question 8 time

Speed answer 2 minutes
Final Answer 3 minutes

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Question 8

Dmitri has a collection of identical cubes. Each
cube is labeled with the integers 1 to 6 as shown
in the following net (This net can be folded to
make a cube.)
He forms a pyramid by stacking layers of the
cubes on a table, as shown, with the bottom layer
being a 7 by 7 square of cubes.
Let a be the total number of blocks used.
When all the visible numbers are added up, let b
be the smallest possible total.
When all the visible numbers are added from a
birds eye view, let c be the largest possible
sum.
Determine the value of abc.

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Question 8

Dmitri has a collection of identical cubes. Each
cube is labeled with the integers 1 to 6 as shown
in the following net (This net can be folded to
make a cube.)
He forms a pyramid by stacking layers of the
cubes on a table, as shown, with the bottom layer
being a 7 by 7 square of cubes.
Let a be the total number of blocks used.
When all the visible numbers are added up, let b
be the smallest possible total.
When all the visible numbers are added from a
birds eye view, let c be the largest possible
sum.
Determine the value of abc.

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Answers in!!!!!!
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Question 9 time

Speed answer 3 minutes
Final Answer 4 minutes

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Question 9

A number is Beprisque if it is the only natural
number between a prime number and a perfect
square (e.g. 10 is Beprisque but 12 is not). Find
the sum of the first five Beprisque numbers
(including 10).

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Question 9

A number is Beprisque if it is the only natural
number between a prime number and a perfect
square (e.g. 10 is Beprisque but 12 is not). Find
the sum of the first five Beprisque numbers
(including 10).

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Answers in!!!!!!
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Question 10 time

Speed answer 4 minutes
Final Answer 6 minutes

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Question 10

Felix the cat, wants to give fresh fish to his
girlfriend Kitty, as her birthday present. To do
this Felix has to walk to the Lumba River, catch
a bucket of fish and walk to Kittys house. The
Lumba River is located 105m north of Felixs
house, and runs straight east and west. Kittys
house is located 195m south of the Lumba River.
If the distance between Felixs house and Kittys
house is 410m, what is the shortest route that
Felix can take from his house to the river and
finally to Kittys house?

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Question 10

Felix the cat, wants to give fresh fish to his
girlfriend Kitty, as her birthday present. To do
this Felix has to walk to the Lumba River, catch
a bucket of fish and walk to Kittys house. The
Lumba River is located 105m north of Felixs
house, and runs straight east and west. Kittys
house is located 195m south of the Lumba River.
If the distance between Felixs house and Kittys
house is 410m, what is the shortest route that
Felix can take from his house to the river and
finally to Kittys house?

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Answers in!!!!!!
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Question 11 time

Speed answer 3 minutes
Final Answer 4 minutes

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Question 11

In a large grassy field there is a rectangular
barn of dimensions 11m x 5m. There are 2 horses
and a llama tied to ropes, the ropes are attached
to the barn at points A, B and C. The rope at
point A is 7 m long, the rope at point B is 4 m
long and the rope at point C is 5 m long. Based
upon the length of the rope, in terms of p,
determine the area of grass that the animals will
be able to reach.

BARN
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Question 11

In a large grassy field there is a rectangular
barn of dimensions 11m x 5m. There are 2 horses
and a llama tied to ropes, the ropes are attached
to the barn at points A, B and C. The rope at
point A is 7 m long, the rope at point B is 4 m
long and the rope at point C is 5 m long. Based
upon the length of the rope, in terms of p,
determine the area of grass that the animals will
be able to reach.

BARN
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Answers in!!!!!!
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Question 12 time

Speed answer 3.5 minutes
Final Answer 5 minutes

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Question 12

A palindrome is a positive integer whose digits
are the same when read forwards or backwards. For
example, 2882 is a four-digit palindrome and
49194 is a five-digit palindrome. There are pairs
of four digit palindromes whose sum is a
five-digit palindrome. One such pair is 2882 and
9339. How many such pairs are there?

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Question 12

A palindrome is a positive integer whose digits
are the same when read forwards or backwards. For
example, 2882 is a four-digit palindrome and
49194 is a five-digit palindrome. There are pairs
of four digit palindromes whose sum is a
five-digit palindrome. One such pair is 2882 and
9339. How many such pairs are there?

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Answers in!!!!!!
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Question 13 time

Speed answer 3.5 minutes
Final Answer 5 minutes

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Question 13

A double-single number is a three-digit number
made up of two identical digits followed by a
different digit. For example, 553 is a
double-single number. Let d be the number of
double-single numbers between 100 and 1000?
Let s be the sum of the digits of the integer
equal to 777 777 777 777 7772 - 222 222 222 222
2232
Determine the difference between d and s.

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Question 13

A double-single number is a three-digit number
made up of two identical digits followed by a
different digit. For example, 553 is a
double-single number. Let d be the number of
double-single numbers between 100 and 1000?
Let s be the sum of the digits of the integer
equal to 777 777 777 777 7772 - 222 222 222 222
2232
Determine the difference between d and s.