1. In a survey of 500 students of a college, it was found that 49% liked watching football, 53% liked watching hockey and 62% liked watching basketball. Also, 27% liked watching football and hockey both, 29% liked watching basketball and hockey both and 28% liked watching football and basketball both. 5% liked watching none of these games. (Four answers - total 12 points.) How many students like watching all the three games?

Find the ratio of number of students who like watching only football to those who like watching only hockey.

Find the number of students who like watching only one of the three given games.

Find the number of students who like watching at least two of the given games.

2. Simplify the following expression: (10 + 3 8) - 32 + (8 4 2)

3. Simplify this statement (5ab)(3ab) A. 15a6b B. 15ab C. -15a6b D. 15a1b4

4. Solve |x + 4| = 3 graphically.

5. (2xy2 - 3x2y) - (2x2y2 - 4x2y) =

A) 2x2y2 B) -2x2y2 -7x2y - 2x2y2 C) -2x2y2 + x2y - 2x2y2 D) 2x2y2 + x2y - 2x2y2 E) -2x2y2 + x2y + 2xy

6. The sum of 2z2 + z + 5 and 4z2 + 3z + 1 is

7. Let f(x) = -x - 3x + 4, then f(-2) = a) 2 b) 6 c) 16 d) 14 e) -6

8. The area A enclosed by a circle, in square meters, is a function of its radius r, when measured in meters. This relation is expressed by the formula A(r) = r2 for r > 0. Find A(2) and solve A(r) = 16. (Two answers - total 8 points)

9. Determine analytically if the following functions are even, odd or neither. f(x) = x 2 x - 6 Even Odd Neither

10. What is the slope of the line through the points P(-5, -6) and Q(-12, 5)? A) -11/7

B) 17/11

C) - 11/17

D) 11/17

11. What is the graph of y = |3x + 6|? A) B) C) D) Answer is ___________

12. Regression analysis problem: Determine the correlation coefficient and coefficient of determination for the following data. Interpret the relationship between X and Y. (3 answers - 12 points)

X 5 3 6 3 4 4 6 8 Y 13 15 7 12 13 11 9 5

Correlation coefficient is _______________?

Coefficient of determination is _______________?

Interpretation:

13. In triangle ABC, angle B is five times as large as angle A. The measure of angle C is 2 less than that of angle A. Find the measures of the three angles.

14. The sum of 3__ + __2__ x + 2 x2 - 4

15. If f(x) and g(x) are two functions defined by f(x) = (x + 1) g(x) = | x - 1 |, then what is the value of f(g(9))?

A) 810 B) | 10 - 1 | C) 310 D) -3 E) 3

16. Find inverse f(x)= 24x+5/ (x-120) and x 4

17. Use the properties of logarithms to simplify log4 (4x2) for x > 0 A) 1 + 2 log4x B) 2(log4 4)(log4 x) C) 2 (log4 4x) D) log4 x2 E) none of these 18. The US annual per capita consumption of coffee was 33.4 gallons in 1970. By 2007, the amount had decreased to 24.6 gallons. Find the average rate of change in coffee consumption per capita from 1970 to 2007. Answer is ___________________

19. Determine the domain of the function. f(x) = 3x - 4 3x + 15

20. Multiple and simplify if possible.

x2 + 2x - 35 9x3 - 4x 3x3 - 2x2 7x + 49

21. Solve: log49 7

22. Solve:

2/(x + 5) + 1/(x - 5) = 16/(x2 - 25)

23. A chemistry formula for gasses. Solve for T1

P1V1 P2V2 T1 T2

24. A man wants to measure the distance across a large pond, but he does not have a boat. He is able to measure the length and width of the pond. He is also able to construct a right triangle. The length of the pond from point A to point C is 47 yards. The width of the pond, from point C to B, is 25 yards. What is the distance between points A and B (the hypotenuse)?

25. Graph the function and determine whether the function is one-to-one.

f(x) = -4/5