1. Grissom High School Math Tournament 2007
Algebra II / Comprehensive Ciphering
Algebra II questions will be on top
Comprehensive questions will be on bottom
Algebra II
please sit on the left side of the auditorium, facing the stage
Comprehensive please sit on the right side of the auditorium, facing the stage

2. Ciphering Rules Scoring: First Time Frame (30 sec) 5 Points
Second Time Frame (30 sec) 3 Points
Third Time Frame (30 sec) 1 Point
** There will be a sliding scale on scoring.
A five second warning will be given before the end of each time frame. Checkers will not take your answer sheets until they are folded and raised in the air.
Place your answers in the answer box provided on the ciphering sheet or your answer will not receive any points.
Answers must be given in exact, reduced, and simplified form. Simplification includes, but is not limited to, the following:
All fractions should be written in lowest terms with denominators rationalized. When appropriate, leave answers as simplified improper fractions.
Leave answers in terms of ,e, or i.

3. Sample: Find the coordinates of the y-intercept:
Algebra II Ciphering
Sample:
Find the coordinates of the y-intercept:
Comprehensive Ciphering
Sample:
Find the focal width of the parabola:
y = 2(x -1)2 + 3

4. Question 1

5. Comprehensive Ciphering
Algebra II Ciphering
1. Evaluate:
Comprehensive Ciphering
1. Given that a>0, write the following in
simplest radical form:

6. Question 2

7. Comprehensive Ciphering
Algebra II Ciphering
2. Find the product of the real roots of the
equation: x2(x – 5) – 24 = 6(x – 4).
Comprehensive Ciphering
2. Evaluate the following determinant:

8. Question 3

9. 3. Find the maximum value of the function f(x) = -3x2 – 42x + 11.
Algebra II Ciphering
3. Find the maximum value of the function
f(x) = -3x2 – 42x + 11.
Comprehensive Ciphering
3. Find the maximum integral value of x in
the domain of the function:

10. Question 4

11. 4. If [x] = the greatest integer < x, then evaluate:
Algebra II Ciphering
4. If [x] = the greatest integer < x, then
evaluate:
Comprehensive Ciphering
4. Find the sum of the values of x on the
interval such that

12. Question 5

13. 5. How many multiples of 7 lie between 1007 and 2007?
Algebra II Ciphering
5. How many multiples of 7 lie between
1007 and 2007?
Comprehensive Ciphering
5. Describe the shape of the curve
described by the given set of parametric
equations:

14. Round 2 Please send up your next team member.
Algebra II Ciphering
Round 2
Please send up your next team member.
Comprehensive Ciphering
Round 2
Please send up your next team member.

15. 6. Solve the following for x:
Algebra II Ciphering
6. Solve the following for x:
Comprehensive Ciphering
6. Find the sum of the first four terms of the
geometric sequence with second term =
2007 and common ratio =

16. Question 7

17. Comprehensive Ciphering
Algebra II Ciphering
7. Given , and
, find
Comprehensive Ciphering
7. Solve the following for x:

18. Question 8

19. 8. Find the larger value of t that is a solution to the equation: .
Algebra II Ciphering
8. Find the larger value of t that is a solution
to the equation: .
Comprehensive Ciphering
8. Find the length of the minor axis of
7x2 + 16y2 – 14x – 105 = 0.

20. Question 9

21. Comprehensive Ciphering
Algebra II Ciphering
9. Solve the following over the complex
numbers: 2x3 – 3x2 + 18x – 27 = 0
Comprehensive Ciphering
9. Lumpy is wandering along the graph of
and reaches a hole.
Find the coordinates of the hole he needs
to patch to make his path continuous.

22. Question 10

23. Comprehensive Ciphering
Algebra II Ciphering
10. If A = and B = , find the
element in the second row, third column of AB.
Comprehensive Ciphering
10. How many integral values of x are solutions to the inequality: ?

24. Round 3 Please send up your next team member.
Algebra II Ciphering
Round 3
Please send up your next team member.
Comprehensive Ciphering
Round 3
Please send up your next team member.

25. 11. Find the slope of the line perpendicular to the line 4x = 5y -17.
Algebra II Ciphering
11. Find the slope of the line perpendicular to
the line 4x = 5y -17.
Comprehensive Ciphering
11. Write in a + bi form: (1 – i)7.

26. Question 12

27. 12. Solve the following for x:
Algebra II Ciphering
12. Solve the following for x:
Comprehensive Ciphering
12. If , and cos x > 0, find the
value of tan 2x.

28. Question 13

29. Comprehensive Ciphering
Algebra II Ciphering
13. If , find .
Comprehensive Ciphering
13. James and John are playing catch.
James is standing at the point with polar
coordinates (4, 220°) while John is at the
point (8, 280°). How far apart are they?

30. Question 14

31. Comprehensive Ciphering
Algebra II Ciphering
14. If A, B, and C are single digit numbers
and 29A86BC is divisible by 720,
find 2A + B – C.
Comprehensive Ciphering
14. Brownie the puppy has a new carpet for
his home, and its shape is described by
. Find the area of
his new carpet.

32. Question 15

33. Comprehensive Ciphering
Algebra II Ciphering
15. If , and , find
Comprehensive Ciphering
15. How many pairs of positive integers
(x, y) are solutions to the equation:
9x + 15y = 2007?

34. Round 4 Please send up your next team member.
Algebra II Ciphering
Round 4
Please send up your next team member.
Comprehensive Ciphering
Round 4
Please send up your next team member.

35. Comprehensive Ciphering
Algebra II Ciphering
16. Simplify:
Comprehensive Ciphering
16. Find the value of:

36. Question 17

37. Comprehensive Ciphering
Algebra II Ciphering
17. Tom defined a new function
a☼b = Find the smaller
value of a for which a☼2 =a.
Comprehensive Ciphering
17. Find the slope of the line tangent to the
circle with equation x2 + y2 = 4 at the
point

38. Question 18

39. Comprehensive Ciphering
Algebra II Ciphering
18. If three cards are drawn at random without replacement, what is the probability they are all the same suit?
Comprehensive Ciphering
18. If the graph of f(x) = |x3 – 1| is
increasing on the interval (a, b),
find the value of a.

40. Question 19

41. Comprehensive Ciphering
Algebra II Ciphering
19. If the solution to the system
of equations given is (a, b),
find the value of 3ab.
Comprehensive Ciphering
19. Find the sum of the real solutions
to the equation:

42. Question 20

43. Comprehensive Ciphering
Algebra II Ciphering
20. Write the range of the graph of
y = |x + 1| + | x – 2| in interval form.
Comprehensive Ciphering
20. Given three points in space G (2, 3, 7),
H (1, -2, a), and S (-3, -1, 5), find the
value(s) of a that make

44. This concludes ciphering
Algebra II Ciphering
Comprehensive Ciphering
This concludes ciphering

45. X1. Solve the following for x:
Algebra II Ciphering
X1. Solve the following for x:
Comprehensive Ciphering
X1. Find the smallest positive value of θ
such that

46. Extra Question 2

47. Comprehensive Ciphering
Algebra II Ciphering
X2. Find the probability of rolling at least one
odd number in two throws of a standard
six-sided die.
Comprehensive Ciphering
X2. If 1+i is one of the solutions to the
equation x3 – 6x2 + 14x – 24 = 0, find
the value of the real solution to the
equation.

48. Comprehensive Ciphering
Algebra II Ciphering
X3. Solve for x:
Comprehensive Ciphering
X3. Write the following in terms of a single
trig function: (sin θ – 1)(tan θ + sec θ).