Muscle Shoals Middle School Math Tournament Algebra I Written Test January 24, 2009
1. Find the area of the triangle: 26
24 a. 60 b. 120 c. 240 d. 312
3 6(2) 6(4 10) 2 2. Simplify: 4 (6 8) 1 1 1 a. 4 b. 2 c. 7 d. 2 6 3 2
3. A trapezoid has an area of 117 square feet and a height of 3 yards. One base is four feet shorter than the other base. How long is the longer base?
a. 15 ft. b. 13 ft. c. 11 ft. d. 9 ft.
4. If x is a natural number, which of the following must be a factor of x6?
a. 2 b. 6 c. x5 d. x12
5. Find the geometric mean of x and y: 2x + y = 30 and 5x - 9y = 6.
a. 9 b. 7 c. 6 2 d. -3 3
6. {2, 4, 6, 8} { 21, 22 , 23, 24}
a. {6, 16} b. {2, 4, 8} c. {2, 4, 6, 8, 16} d.
7. Willy Wonka answered all 25 problems on the test and got an 85. Scores are computed by giving 4 points for each correct answer and subtracting 1 point for each wrong answer. How many problems did Willy Wonka get right and wrong?
a. 23 right and 2 wrong b. 24 right and 1 wrong c. 21 right and 4 wrong d. 22 right and 3 wrong 5 w 8. For the equation 2w 3 , solve for w. n n 5 8 3n 5 a. b. 3 c. d. 8 n 2n 1 2n 1 Muscle Shoals Middle School Math Tournament Algebra I Written Test January 24, 2009 x2 1 y2 9. Simplify: x2 2x 1 y2 y x y x y 1 x(x y) a. b. c. d. x y x y x y x y
10. Evaluate f(-3) – g(4), given that f(x) = 6x² - 50 and g(x) = 4 - 2x a. 8 b. 0 c. -4 d. -100
11. The solution in a 7-liter radiator system is 35% antifreeze. How much of the solution must be drained and replaced by a 95% antifreeze solution to obtain a 50% antifreeze solution?
a. 0.6 liters b. 1.75 liters c. 2.45 liters d. 3.5 liters
12. Change 1.215 to an improper fraction and find the sum of the numerator and denominator.
a. 1731 b. 2213 c. 731 d. Not a rational number
x2 4 4 13. Simplify x2 20 9x 7x x2 12
x3 3x2 8 x 5 a. b. (x 5)(x 4)(x 3) (x 5)(x 3) x 4 x2 5x 1 c. d. (x 5)(x 3) (x 5)(x 3)
14. What is the integer remainder of (6x3 3) (x 2) ?
a. 21 b. 27 c. 45 d. 51
15. Penny flew 80 km. She flew the first 4 minutes at full speed and the second 4 minutes at half speed. The full speed of the plane in km/hr is:
1 a. 13 b. 400 c. 600 d. 800 3
16. Four times a certain negative number is one less than its square. Find the number.
a. 2 5 b. 2 5 c. 3 5 d. 1 2
3 3 5 17. Simplify. (32 5 4 2 ) 4 Muscle Shoals Middle School Math Tournament Algebra I Written Test January 24, 2009
a. 31.5 b. 32 c. 45 d. 144
18. Solve. 4x 5 3x 1
4 4 a. x b. x 6 or x 7 7 4 c. x 6 d. x 6 or x 7 54 3 256x8 y12 19. Simplify. 18 3 16x2 y4 a. 12x3 y4 b. 4x3 y4 c. 6x2 3 2y d. 6x2 y2 3 2y2
3 2 20. Simplify: 6 1 3
3 6 5 a. 2 b. c. d. 2 2 2
21. Two birds start flying from the tops of two towers 50 feet apart; one tower is 30 feet high and the other 40 feet high. Starting at the same time and flying at the same rate, the birds reach a fountain between the bases of the towers at the same moment. How far is the fountain from the 40 foot high tower?
a. 32 feet b. 18 feet c. 50 feet d. 16 feet
22. A merchant doing business in Lucca doubled his money there and then spent 12 denarii. On leaving, he went to Florence, where he also doubled his money and spent 12 denarii. Returning home to Pisa, he there doubled his money and again spent 12 denarii, nothing remaining. How much did he have in the beginning?
a. 10.5 b. 84 c. 11 d. 16
23. The area of Square A is 4. The perimeter of Square B is three times the perimeter of Square A. The area of Square B is:
a. 12 b. 36 c. 48 d. 144
24. If x varies jointly as y and z and inversely as m squared and x = 10 when y = 2, z = 5, and m = 4, find x when y = 3, z = 9, and m = 6.
a. 12 b. 72 c. 3 d. 18 Muscle Shoals Middle School Math Tournament Algebra I Written Test January 24, 2009 25. A club received $217.20 from the sale of tickets to a musical program. If the price of the tickets was 35 cents for adults and 25 cents for children and the total number sold was 744, how many children tickets were sold?
a. 312 b. 288 c. 372 d. 432
TB1 Simplify: i 14 3 i 24
TB2: What is the distance between (6, -4) and (0, –12)?
TB3. Find the equation of the diagonal of a square with vertices at (-10,8), (-10,-5), (3,8) and (3,-5). List the diagonal with the positive slope and put the equation in standard form.