CLC Math Contest 2010 - Mr. Thell
CLC Math Championship 2014
Directions: This test is composed of 40 problems covering various mathematical concepts in the areas of algebra, geometry, and pre-calculus. There are also four free-response problems that will only be used in the event of a tie. You have 60 minutes to complete the test. Record all answers on the answer sheet provided. Please mark your answers as capital letters.
1. What happens to the area of a rectangle if both its length and width are increased by 10%?
A.) Increases by 10% B.) Increases by 15% C.) Increases by 20% D.) Increase by 21%
2. [pic]
A.) [pic] B.) [pic] C.) [pic] D.) [pic]
3. Let [pic]. Where is the center of this circle?
A.) (-3, 2) B.) (3, 2) C.) (6, 4) D.) ( 6, -4)
4. The solution to the system [pic] is an ordered triple of the form [pic] Find [pic]
A.) -2 B.) 0 C.) 3 D.) 5
5. What is the equation of the absolute value function?
A.) [pic]
B.) [pic]
C.) [pic]
D.)[pic]
6. Find “p” if [pic] is divisible by [pic].
A.) 0 B.) 2 C.) 4 D.) 6
7. If [pic] , find [pic].
A.) [pic] B.) [pic] C.) [pic] D.) [pic]
8. Simplify [pic]
A.) [pic] B.) [pic] C.) [pic] D.) [pic]
9. Suppose [pic] and [pic] Find “c”.
A.) -18 B.) 4 C.) -2 D.) 2
10. Simplify [pic]
A.) [pic] B.) [pic] C.) [pic] D.) [pic]
11. Solve for x: [pic]
A.) [pic] B.) [pic] C.) [pic] D.) [pic]
12. In the diagram below, the angles are represented as shown. Find the m[pic]DBC.
[pic]
A.) 25 ° B.) 125° C.) 155° D.) 158°
13. Which of the following are solutions of the equation 1 – 3/x = 6/(x2 + 2x) ?
A. x = -2 or x = 4
B. x = -3 or x = 0
C. x = -3 or [pic] = 4
D. x = -3
14. Which of the following represents a horizontal translation of 4 units to the right?
A. y = f(x) + 4
B. y = f(x) – 4
C. y = f(x + 4)
D. y = f(x – 4)
15. John stands 50 feet from the base of a building and then measures the angle of elevation from the ground to the top of the building at the point to be 58 degrees. About how tall is the building?
A.) 31 feet B.) 42 feet C.) 59 feet D.) 80 feet
16. If g(x) = x + 3 and h(x) = x2 + x – 1, find the value for g(h(-20)).
A.) 422 B.) 551 C.) 277 D.) 382
Simplify [pic]
17.
A.) [pic] B.) [pic] C.) m + 2 D.) 3(m - 2)
18. What is the solution to the equation log4 4x + 2log4 x = 4 ?
A.) 1 B.) 2 C.) 3 D.) 4
19. A region is defined by the following system:
y > -½x – 1
y > -x + 3
In which quadrant(s) of the coordinate plan is the region located?
A.) I and IV only B.) III only C.) I, II, and IV only D.) II and III only
20. If the graph of a line has a positive slope and a negative y-intercept, what happens to the x-intercept if the slope and the y-intercept are doubled?
A. The x-intercept becomes four times as great.
B. The x-intercept becomes twice as great.
C. The x-intercept becomes one-fourth as great.
D. The x-intercept remains the same.
21. A person 2 meters tall casts a shadow 3 meters long. At the same time, a telephone pole casts a shadow 12 meters long. How many meters tall is the pole?
A. 4 B.) 6 C.) 8 D.) 11
22. If a < -1, which of the following best describes a general relationship between [pic] and [pic]?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
23. If [pic], then n = ?
A. [pic]
B. - 1
C. [pic]
D. [pic]
24. If a marble is randomly chosen from a bag that contains exactly 8 red marbles, 6 blue marbles, and 6 white marbles, what is the probability that the marble will NOT be white?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
25. Kareem has 4 sweaters, 6 shirts, and 3 pairs of slacks. How many distinct outfits, each consisting of a sweater, a shirt, and a pair of slacks, can Kareem select?
A. 13
B. 36
C. 42
D. 72
26. If a rectangle measures 54 meters by 72 meters, what is the length, in meters, of the diagonal of the rectangle?
A. 48
B. 63
C. 90
D. 126
27. What is the x-coordinate of the point that in the standard (x, y) coordinate plane at which the two lines y = 2x +6 and y = 3x +4 intersect?
A. 1 B.) 2 C.) 4 D.) 6
28. If [pic], then [pic]?
A. -16 B.) -8 C.) 1 D.) 16
29. Members of the fire department lean a 30 foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?
A. 10 B.) 20 C.) 28 D.) 31
30. The ratio of the side lengths for a triangle is exactly 12:14:15. In a second triangle similar to the first, the shortest side is 8 inches long. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?
A. 11.0 B.) 10.0 C.) 9.3 D.) 6.4
31. A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 5 and tangent to the y-axis at 5. Which of the following is an equation of the circle?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
32. In the complex numbers, where [pic]
[pic]=?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
33. If [pic] and [pic], then [pic]
A. [pic]
B. [pic]
C. [pic]
D. [pic]
34. If [pic], then [pic]
A. [pic]
B. [pic]
C. [pic]
D. [pic]
35. If [pic] and [pic], which of the following expresses y in terms of x?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
36. The vertices of a regular pentagon, labeled in a counterclockwise are ABCDE. What is the angle measure of [pic]?
A.) 36 B.) 54 C.) 28 D.) cannot be found
37. A watermelon weighs 500 pounds, 99% of its weight being due to the water it contains. After it sat in a drying room for a while, it lost 250 pounds of water. What percent of its weight was then water?
A.) 50% B.)49.5% C.) 99% D.) 98%
38. Express as a multiple of [pic], the radian measure of an angle in the third quadrant that has a sine of –1/2.
A.) 7[pic]/6 B.) 4[pic]/3 C.) 5[pic]/4 D.) 5[pic]/6
39. A hand of 5 cards is drawn from a standard deck of 52 cards. Find the probability of getting exactly one ace. Give the answer accurate to six places to the right of the decimal.
A.) 0.076923 B.) 0.096154 C.) 0.299474 D.) 0.005917
40. If [pic], then [pic]
A.) 4x B.) 9x C.) x + 3 D.) x + 2
Free Response Tie-Breaker Problems
41. Simplify [pic]
42. [pic] has two zeros. What is the product of them?
43. What is the largest prime divisor of every 3-digit number with 3 identical
nonzero digits.
44. Solve for x: [pic]
Answer Sheet Name (print clearly): ______________________________
School: ____________________________Grade: ______
1. _____ 23. _____
2. _____ 24. _____
3. _____ 25. _____
4. _____ 26. _____
5. _____ 27. _____
6. _____ 28. _____
7. _____ 29. _____
8. _____ 30. _____
9. _____ 31. _____
10. _____ 32. _____
11. _____ 33. _____
12. _____ 34. _____
13. _____ 35. _____
14. _____ 36. _____
15. _____ 37. _____
16. _____ 38. _____
17. _____ 39. _____
18. _____ 40. _____
19. _____ 41. _______________________
20. _____ 42. _______________________
21. _____ 43. _______________________
22. _____ 44. _______________________
Number correct: ________
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