2007 vanderbilt high school mathematics competition

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2007 Vanderbilt High School Mathematics Competition Junior Varsity Ciphering Please send your first round cipherer to the front at this time

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2007 Vanderbilt High School Mathematics Competition. Junior Varsity Ciphering Please send your first round cipherer to the front at this time. 2007 Vanderbilt High School Mathematics Competition. Ciphering Guidelines Separate and completely fill out answer sheets - PowerPoint PPT Presentation

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Page 1: 2007 Vanderbilt High School Mathematics Competition

2007 Vanderbilt High School Mathematics Competition

Junior Varsity Ciphering

Please send your first round cipherer to the front at this time

Page 2: 2007 Vanderbilt High School Mathematics Competition

2007 Vanderbilt High School Mathematics Competition

Ciphering Guidelines•Separate and completely fill out answer sheets•Only answers written in the answer blank provided will be graded•There will be two one-minute time frames; a correct answer in the first minute is worth 10 points and a correct answer in the second minute is worth 5 points.•A 5-second warning will be announced before the end of each time frame. Please fold your answer sheet and hold it in the air during this warning to turn in your answer.

Page 3: 2007 Vanderbilt High School Mathematics Competition

2007 Vanderbilt High School Mathematics Competition

Ciphering Guidelines (cont.)•Answer sheets will only be accepted during the 5-second interval, and answer sheets raised after the end of the time frame will not be accepted .•A student may not take his answer sheet back after a runner has taken it. You may submit only one answer sheet per question.•As always, calculators and other forms of aid are prohibited and using them will result in immediate disqualification.

Page 4: 2007 Vanderbilt High School Mathematics Competition

2007 Vanderbilt High School Mathematics Competition

Ciphering Guidelines (cont.)•Do not approximate radicals or other irrational numbers such as Φ, π, and e unless specifically instructed otherwise in the problem.•Fractions may be left in mixed (ex. 3 ½), improper

(ex. 7/2), or decimal (ex. 3.5) form as long as they are fully reduced. For example, 14/4 would not be an acceptable answer.

Page 5: 2007 Vanderbilt High School Mathematics Competition

Round 1

Practice Question

Page 6: 2007 Vanderbilt High School Mathematics Competition

Practice Question

What is a billion plus two?

Page 7: 2007 Vanderbilt High School Mathematics Competition

Round 1

Question 1

Page 8: 2007 Vanderbilt High School Mathematics Competition

Question 1.1

Find ...333

Page 9: 2007 Vanderbilt High School Mathematics Competition

Round 1

Question 2

Page 10: 2007 Vanderbilt High School Mathematics Competition

Question 1.2

A circle is inscribed inside a triangle with sides of lengths 4, 6, and 8. Find the square root of the ratio of the area of the triangle to the radius of the

circle.

Page 11: 2007 Vanderbilt High School Mathematics Competition

Round 1

Question 3

Page 12: 2007 Vanderbilt High School Mathematics Competition

Question 1.3

If 35° is added to an angle, the resulting angle is equal to the

supplement of the original angle. Find the complement of

the original angle.

Page 13: 2007 Vanderbilt High School Mathematics Competition

Round 1

Question 4

Page 14: 2007 Vanderbilt High School Mathematics Competition

Question 1.4

Find the number of diagonals that can be drawn in a

regular polygon having 37 sides.

Page 15: 2007 Vanderbilt High School Mathematics Competition

End of Round 1

Please send your next cipherer forward at this time

Page 16: 2007 Vanderbilt High School Mathematics Competition

Round 2

Question 1

Page 17: 2007 Vanderbilt High School Mathematics Competition

Question 2.1

A locomotive is pulling 10 supply cars. 5 of the cars are carrying coal, 3 of the cars are carrying lumber, and the rest of the supply cars are carrying oil. How many distinct ways can you arrange all the cars behind the locomotive if there is also a caboose and 2 identical passenger cars that must be connected behind the last supply car? (note: the caboose does not necessarily have to be the last car on the train)

Page 18: 2007 Vanderbilt High School Mathematics Competition

Round 2

Question 2

Page 19: 2007 Vanderbilt High School Mathematics Competition

Question 2.2

Given the figure below, find xy. Assume all angles that look like right angles are right.

xz

5

1

1

3

3y8

8

Page 20: 2007 Vanderbilt High School Mathematics Competition

Round 2

Question 3

Page 21: 2007 Vanderbilt High School Mathematics Competition

Question 2.3

f(x) = 4x + 5

g(x) = x2 – 2

Find f(g(3x + 6))

Page 22: 2007 Vanderbilt High School Mathematics Competition

Round 2

Question 4

Page 23: 2007 Vanderbilt High School Mathematics Competition

Question 2.4

Find the remainder when

4x3 – x4 + x2 + 3x4 - 2

is divided by x-3.

Page 24: 2007 Vanderbilt High School Mathematics Competition

End of Round 2

Please send your next cipherer forward at this time

Page 25: 2007 Vanderbilt High School Mathematics Competition

Round 3

Question 1

Page 26: 2007 Vanderbilt High School Mathematics Competition

Question 3.1

Find (log69)(log912)(log1215)…(log77737776)

Page 27: 2007 Vanderbilt High School Mathematics Competition

Round 3

Question 2

Page 28: 2007 Vanderbilt High School Mathematics Competition

Question 3.2

How many consecutive zeros does

have at the end?

1912952

!132

Page 29: 2007 Vanderbilt High School Mathematics Competition

Round 3

Question 3

Page 30: 2007 Vanderbilt High School Mathematics Competition

Question 3.3

Write (1 + i)-4 in a + bi form.

Page 31: 2007 Vanderbilt High School Mathematics Competition

Round 3

Question 4

Page 32: 2007 Vanderbilt High School Mathematics Competition

Question 3.4

Find the units digit of 617 + 428 + 639 + 373

Page 33: 2007 Vanderbilt High School Mathematics Competition

End of Round 3

Please send your next cipherer forward at this time

Page 34: 2007 Vanderbilt High School Mathematics Competition

Round 4

Question 1

Page 35: 2007 Vanderbilt High School Mathematics Competition

Question 4.1

Find the sum of the integral divisors of 144.

Page 36: 2007 Vanderbilt High School Mathematics Competition

Round 4

Question 2

Page 37: 2007 Vanderbilt High School Mathematics Competition

Question 4.2

Find the square of the length of the apothem of a regular hexagon with perimeter 60

Page 38: 2007 Vanderbilt High School Mathematics Competition

Round 4

Question 3

Page 39: 2007 Vanderbilt High School Mathematics Competition

Question 4.3

If A =

find the determinant of A2 – 4A

63

41

Page 40: 2007 Vanderbilt High School Mathematics Competition

Round 4

Question 4

Page 41: 2007 Vanderbilt High School Mathematics Competition

Question 4.4

The 3rd term of a geometric progression is 8/3. The 5th term is 1/6. Find the sum of

the first 4 terms.

Page 42: 2007 Vanderbilt High School Mathematics Competition

End of Ciphering

Page 43: 2007 Vanderbilt High School Mathematics Competition

Extra Question #1

Page 44: 2007 Vanderbilt High School Mathematics Competition

Question E.1

What is the probability that two integers from [1,10] selected

randomly with replacement can be the numerator and

denominator, respectively, of a proper fraction in lowest terms?

Page 45: 2007 Vanderbilt High School Mathematics Competition

Extra Question # 2

Page 46: 2007 Vanderbilt High School Mathematics Competition

Question E.2

7A = 2B 3B = 8C C = 15D 2D = 5E

Find A/E