Download Test - Mu Alpha Theta

Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 1
Round 1 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
1.
What is the number of sides on a regular polygon with interior angles measuring 156 ?
2. How many centimeters are there in one foot, to the nearest tenth?
3. Find the measure, in degrees, of arc GDE in the figure below.
4.
If the 6th term of an arithmetic sequence is -27 and the 14th term is -43, what is the 21st term?
Round 2 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 2
Round 3 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
5.
What are the equations of the asymptotes of
y2
 ( x  2) 2  1 , written in the
9
form y  ax  b ?
6.
The distance required to stop a car varies directly as the square of its speed. If 200 ft are
required to stop a car traveling at 60 mph, how many feet are required to stop a car traveling
at 90 mph?
7.
What is the value of ( (4*3) # 7 ) * (-2 # 1) if x * y = xy + 1 and x # y = |2x-y| ?
8.
You have 3 double-headed coins, 1 double-tailed coin, and 5 fair coins. You select a coin at
random and flip it. What is the probability that it shows a head?
Round 4 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 3
Round 5 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
9.
 2  3
1 8 
Let A equal 
and B equal 

 . Evaluate A  B  A  B .
5
7
 2  9
10. Let A equal 6 P2 - 6 C 2 .
Let B equal P(3 heads in 5 flips of a fair coin).
A
Evaluate: 8 B 
2
11. If 3 woozles equal 2 floobes, 5 floobes equal 4 widgets, and 10 minnos equal 4 woozles,
how many widgets do I have if I have 300 minnos?
12. In a special giveaway pencil box of 24, some pencils are orange and the rest are green. The
ratio of orange to green pencils is 5:3. What is the number of green pencils in the box?
Round 6 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 4
Round 7 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
13. In a recent survey of 77 test-writers, 64 said they knew Tom and 8 said they knew Kathy. If
11 said they knew neither of the two, how many said they knew both?
14. Let A equal the sum of the 60 smallest odd natural numbers.
Let B equal the sum of the geometric series
9 27 81


 ...
4 16 64
Let C equal the real number y, the solution to the equation: 9
A
Evaluate
.
BC
log y
3  64 .
15. What is the product of all real solutions to the equation log( 2 x  1)  log( 4 x  3)  log( x) ?
16. What is the area, in square centimeters, of a circle with circumference of 12 cm?
Round 8 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 5
Round 9 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
17. How many ways can a President, Vice-president, and two Representatives be chosen from a
group of 11?
18. Let A equal the number of square centimeters in the surface area of a sphere with a radius of
6 cm. Let B equal the number of cubic centimeters in the volume of a cone with a radius of
6 cm and a height of 7. Evaluate: A-B
19. Solve the following system and express your answer in the form (x,y,z).
x  z  11
2 x  y  z  10
 2y 
1
z  13
3
20. Find length m in the circle below.
Round 10 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 6
Round 11 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
21. The statements below have been assigned point values, given in parenthesis before each
statement. Find the sum of the point values of all statements that are true about the
polynomial function f(x) = x3  5 x 2  x  5 .
(5) The degree of f(x) is even.
(8) The only unique zeros are -1 and 5.
(7) The greatest multiplicity of the factors is 1.
(10) The function is symmetric about the origin.
(3) There is a y-intercept at (0,5).
22. Find the number of positive integral factors of 1200.
23. The following expression can be written as one term of the form a b , where a and b are
1
45  125 .
integers and a b is in simplest radical form: 2 20  80 
3
a 
Evaluate:  
b
24. A trapezoid has a median of length 19 and an altitude of length 8. The two bases measure
4x  3 and 7 x  2 .
Let A equal x.
Let B equal the area of the trapezoid.
Evaluate: |A-B|
Round 12 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 7
Round 13 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
25. If A equals 1, B equals 2, C equals 3, etc, find the sum of the letters that spell the answer to
the following question: The function symbol f(x) was first used by him in 1734; he also
discovered this identity: e ix  cos( x)  i sin( x) , which is named after him. What is this
mathematician’s surname?
26. For what values of k does 6 x 2  kx  1 have real roots?
27. If the area of the shaded regions can be expressed as A  B , where A and B are integers,
find A+B.
28. One card is drawn randomly from a standard deck of 52 cards.
Let A equal{x : x is a jack, queen, or king}.
Let B equal{x : x is a 9, 10, or jack and the suit color of x is red}.
Find P( A  B ) + P( A  B ).
Round 14 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 8
Round 15 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
29. What is the distance between the foci of the graph of the equation 16( x  1) 2  25 y 2  400 ?
30. The positive difference of two positive numbers is 1. The product of these same two
numbers is also 1. What is the difference of the cubes of these two numbers?
.
31. Let r  4  3i and s  1  2i , where i  1 . What is s 2  (r  s ) in the form a  bi ?
32. Let A equal
9  32 x  27  3 2 x 1
. Evaluate: A  3 2
3  3 2 x 1
Round 16 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 9
Round 17 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
33. The number 3 appears on each of two balls in a hat and the number 9 on a third ball in the
hat. Tom draws one ball at random from the hat and receives either $3 or $9, depending on
the number on the ball (3→$3 and 9→$9), and then returns the ball back to the hat. If Tom
plays this game for a very long time, how many dollars can he expect to receive on the
average per play if we assume each ball is equally likely to be drawn?
34. For a linear function f, f(0) equals 3 and f(f(0)) equals -12. Find the equation of the line
perpendicular to y = f(x) through (1,2) in slope-intercept form.
3
 12  8 3
= A  B C , where A, B, and C are integers and B C is in simplest
2 3
32 3
radical form, evaluate A+B.
35. If

36. If x varies directly with y 2 and inversely with z so that x equals 2 when y and z both equal 4,
what is the value of x when y equals 3 and z equals 5?
Round 18 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
Round 10
Round 19 of 20
Mu Alpha Theta National Convention: Hawaii, 2005
State Bowl – Theta Division
37. A man at his house needs to get to his new job. He is not sure how to get there so he drives
as follows: he drives 5 miles south from his house, then 16 miles east, 15 miles south, 3
miles west, 4 miles north, 8 miles west, and 4 miles north to finally arrive at work. How
many miles is work from his house (straight-line distance)?
38. Find the radius of the circle given by the equation x 2  y 2  6 x  8 y  96 .
39. How many ways can you make $1 with exactly 21 coins using pennies, nickels, and dimes,
but no quarters?
40. A right rectangular prism has edge lengths 3, 5, and 6. The ratio of its total surface area to
c
its volume can be expressed as a fraction , where c and d are relatively prime. Find
d
LCM(c,d).
Round 20 of 20