Answers to the Sample Problems for the June 2004 UMSL Math Placement Test.

1) 1/6

2) 5/16

3) –17/60

4)

5) hence x=

6) , hence

7) , so and x=-2.

8) 40% are not Cardinal fans, which is people.

9)

10)

11) . Hence . Thus .

12) . Hence .

13) , hence , hence . Thus or .

14) so , hence

15) so hence .

16)

17) Draw the graph as follows. When x=0, y=-3. When y=0, x=9/2. Hence plot the points (0,-3) and (9/2,0) and join them by a straight line.

18) .

19) .

20) Hence one of the factors is

21) . The solutions, obtained by setting each factor equal to zero, are: .

22) Hence . Factoring this, Hence

23)

24)

25) For the fraction to equal 0, the numerator must equal zero. The numerator factors as . Hence

26)

27)

28)

29)

30) hence Hence Factoring this as , we get x = 4 or 2. But 4 is not a solution in the original equation. So the only solution is x = 2.

31) (Note: )

32)

33)