alabama statewide math contest - round 3 division ii · 2020. 4. 16. · alabama statewide math...
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GeometryAlgebra II & Trig
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Alabama Statewide Math Contest - Round 3Division II
University of Alabama at Birmingham
April 14, 2018
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Scoring
Scoring0:00 - 0:30 10 points0:31 - 1:00 8 points1:01 - 1:30 6 points1:31 - 2:00 4 points
If the first person to answer is correct, they receive2 Bonus Points.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Rules
Rules1. Answers must be in answer box provided to be counted. Units
such as cm, in, etc. are not necessary.
2. Fractions must be reduced. Improper fractions are acceptable.
3. The numbers π and e must be left as such.
4. Complex numbers must be put into a+ bi form.
5. Answers with radicals must be simplified. Denominators mustbe rationalized.
6. Exponents should be positive.
7. Answers involving trigonometric functions should be simplifiedas much as possible.
8. log(x) means log10(x) and ln(x) means loge(x).
9. The time limit for all problems is 2 minutes.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
Comprehensive Part 1Comprehensive Part 2
Team
Rules
Rules
1. Answers must be in answer box provided to be counted. Unitssuch as cm, in, etc. are not necessary.
2. Fractions must be reduced. Improper fractions are acceptable.
3. The numbers π and e must be left as such.
4. Complex numbers must be put into a+ bi form.
5. Answers with radicals must be simplified. Denominators mustbe rationalized.
6. Exponents should be positive.
7. Answers involving trigonometric functions should be simplifiedas much as possible.
8. log(x) means log10(x) and ln(x) means loge(x).
9. The time limit for all problems is 2 minutes.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
![Page 5: Alabama Statewide Math Contest - Round 3 Division II · 2020. 4. 16. · Alabama Statewide Math Contest - Round 3 Division II University of Alabama at Birmingham April 14, ... Round](https://reader033.vdocuments.mx/reader033/viewer/2022051911/6000ba04a4504f543c0a7ad7/html5/thumbnails/5.jpg)
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Sample Problem # 1
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Sample Problem
RESET :
Solve for x in the equation
x2 − 6x− 3 = 0
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Sample Problem
Answer:
3 + 2√3, and 3− 2
√3.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Sample Problem
Answer: 3 + 2√3, and 3− 2
√3.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Question # 1Question # 2
Round 3
Geometry
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Question # 1Question # 2
Geometry Question # 1
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Question # 1Question # 2
Geometry Question # 1
RESET :A rhombus has sides of length 10, and its diagonals differ by 4.What is its area?
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 1Question # 2
Geometry Question # 1
Answer:
96
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 1Question # 2
Geometry Question # 1
Answer: 96
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Question # 1Question # 2
Geometry Question # 2
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 1Question # 2
Geometry Question # 2
RESET :In the figure below, AB = 6, m(∠ABC) = 75◦ andm(∠ACB) = 45◦. Find the length of side BC.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
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Question # 1Question # 2
Geometry Question # 2
Answer:
3√6
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 1Question # 2
Geometry Question # 2
Answer: 3√6
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 3Question # 4
Round 3
Algebra II & Trig
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Question # 3Question # 4
Algebra II & Trig Question # 3
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Question # 3Question # 4
Algebra II & Trig Question # 3
RESET :Find the median of the solution set to
2x3 − 5x2 − 4x+ 3 = 0
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 3Question # 4
Algebra II & Trig Question # 3
Answer:
1
2
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 3Question # 4
Algebra II & Trig Question # 3
Answer:1
2
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 3Question # 4
Algebra II & Trig Question # 4
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 3Question # 4
Algebra II & Trig Question # 4
RESET :Find the x-intercept of the line which passes through the point(1, 2) and is perpendicular to the line 3x+ 2y = 5.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 3Question # 4
Algebra II & Trig Question # 4
Answer:
−2
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 3Question # 4
Algebra II & Trig Question # 4
Answer: −2
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Question # 5Question # 6
Round 3
Comprehensive Part 1
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Comprehensive Part 1Question # 5
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Comprehensive Part 1 Question # 5
RESET :A class has an average of 8.5 on a quiz. One more person takes it,receives a 7, and the average drops to 8.25. How many peopleoriginally took the quiz?
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Question # 5Question # 6
Comprehensive Part 1 Question # 5
Answer:
5
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Comprehensive Part 1 Question # 5
Answer: 5
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Comprehensive Part 1Question # 6
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Question # 5Question # 6
Comprehensive Part 1 Question # 6
RESET :The product of the roots of a quadratic function is −4 and their
sum is −15
2. Find the absolute value of the difference of the roots.
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Question # 5Question # 6
Comprehensive Part 1 Question # 6
Answer:
17
2
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Question # 5Question # 6
Comprehensive Part 1 Question # 6
Answer:17
2
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Round 3
Comprehensive Part 2
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Comprehensive Part 2Question # 7
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Question # 7Question # 8
Comprehensive Part 2 Question # 7
RESET :If logb(x) = 2, find logb
(1
x5
).
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Question # 7Question # 8
Comprehensive Part 2 Question # 7
Answer:
−10
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Question # 7Question # 8
Comprehensive Part 2 Question # 7
Answer: −10
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Comprehensive Part 2Question # 8
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Question # 7Question # 8
Comprehensive Part 2 Question # 8
RESET :A fair coin is flipped five times. What is the probability that itshows exactly three heads?
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Question # 7Question # 8
Comprehensive Part 2 Question # 8
Answer:
5
16
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Question # 7Question # 8
Comprehensive Part 2 Question # 8
Answer:5
16
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Question # 9Question # 10
Round 3
Team
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Question # 9Question # 10
Team Question # 9
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Team Question # 9
RESET :In a certain basketball-type game, the only ways to score points arewith a three point basket or a five point basket. What is thelargest score that is not attainable?
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Question # 9Question # 10
Team Question # 9
Answer:
7
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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Question # 9Question # 10
Team Question # 9
Answer: 7
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
Comprehensive Part 1Comprehensive Part 2
Team
Question # 9Question # 10
Team Question # 10
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
Comprehensive Part 1Comprehensive Part 2
Team
Question # 9Question # 10
Team Question # 10
RESET :The function f(x) = x3 − 8 has three unique roots. Find the areaof the triangle formed by these three roots in the complex plane.
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
Comprehensive Part 1Comprehensive Part 2
Team
Question # 9Question # 10
Team Question # 10
Answer:
3√3
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
Comprehensive Part 1Comprehensive Part 2
Team
Question # 9Question # 10
Team Question # 10
Answer: 3√3
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II
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GeometryAlgebra II & Trig
Comprehensive Part 1Comprehensive Part 2
Team
Question # 9Question # 10
End of Round 3
University of Alabama at Birmingham Alabama Statewide Math Contest - Round 3 Division II