Answer each of the questions below by putting only your final
answer in the space provided. Do all calculations on the scratch paper provided and throw it away
at the end of the exam. Read each question carefully. All questions can be answered.
Time limit: 90 minutes. You may not use calculators
on this test.
| 1. |
3/4 is 1/4 of 5/6 of 1/2 of a certain number.
What is the number? |
(1)___________________ |
| 2. |
 |
(2)___________________ |
| 3. |
 |
(3)___________________ |
| 4. |
One liter is 1000 cubic centimeters. How
many liters is one cubic meter? |
(4)___________________ |
| 5. |
Calculate the volume in cubic feet of a
rectangular tank 8 inches by 15 inches by 10 feet. |
(5)___________________ |
| 6. |
Factor: 2x2 + 3x
- 5 |
(6)___________________ |
| 7. |
Solve for b : 6ac - 3bc
+ 2ad - bd = 1. |
(7)___________________ |
| 8. |
Find the simplest expression for Mt,
given 2Mt = M0
+ 3M0
+ M0(1 - ). |
(8)___________________ |
| 9. |
What is the value of m if 6m
= 5w - 2m + 22 and 2m = 3w
+ 2? |
(9)___________________ |
| 10. |
The spread of rumor among 100 people can
be approximated by the equation log10(x)
- log10(100 - x) = (.1)t
- log10(90), where x is the number
of people who have heard the rumor after t days.
How many people have heard the rumor after 10 days? |
(10)__________________ |
| 11. |
Solve for x : 103x+5
= 29. |
(11)__________________ |
| 12. |
 |
(12)__________________ |
| 13. |
An open box is made from a rectangular
piece of cardboard having dimensions 20 inches x 30 inches
by cutting out identical squares of area x2
from each corner and turning up the resulting sides. Express
the volume of the box as a function of x. |
(13)__________________ |
| 14. |
Under certain conditions, the effective
wavelength ( )
of a beam of charged particles is inversely proportional
to the square root of the product of the electric potential
(E) through which the particles have been accelerated
and the charge (q) on the particles. Write an
equation, using the symbols ,
E, and q and a proportionality constant
k, that expresses the statement in the previous
sentence. |
(14)__________________ |
| 15. |
A light beam of intensity I0
enters a chemical solution and is partially absorbed.
If the intensity remaining after the light has traversed
the solution is I, then the quantity log
is termed the absorbance of the solution. Absorbance is
proportional to the concentration (c) and to the thickness
(d) of the solution. Use the symbols given here along
with a proportionality constant k to write an
equation that expresses the relationship between the absorbance
and the other variables. |
(15)__________________ |
| 16. |
Find an equation for the line which goes
through the points (1975,4900) and (1967,2500). |
(16)__________________ |
| 17. |
How many pounds of potatoes at x
cents per pound can be bought with the amount of money
that will buy d dozen eggs at y cents
per dozen? |
(17)__________________ |
| 18. |
A jeweler has two bars of gold alloy in
stock, one 12-carat and the other 18-carat (24-carat gold
is pure gold, 12-carat gold is 
pure, 18-carat gold is  pure, and so on). How many
grams of each alloy must be mixed to obtain 10 grams of
14-carat gold? |
(18)__________________ |
| 19. |
What is the fractional increase in area
obtained by changing a circle of radius 10 cm to a circle
of radius 11 cm? |
(19)__________________ |
| 20. |
If the weight of a box containing n
apples is W, and the weight of the empty box
is B, what is the weight of six apples? |
(20)__________________ |
| 21. |
Polluted water is passed through a filter
which removes 90% of impurities in the water. Initially
the untreated water contains impurities at a level of
420 parts per million. What is the level of impurities
in the water after it has passed through the filter? |
(21)__________________ |
| 22. |
What percent of $12.50 is .75 cents? |
(22)__________________ |
| 23. |
6 tile-setters laid 600 tiles in 6 hours.
At this rate, how long would it take 12 tile-setters to
set 400 tiles? |
(23)__________________ |
| 24. |
Suppose a one-celled animal is in a petri
dish and reproduces (by division) once every minute as
do its offspring. In one hour the dish is full. At what
time was the dish 1/4 full? |
(24)__________________ |
| 25. |
The hot water faucet fills a tub in 40 minutes.
The cold water faucet fills the tub in 30 minutes. The
tub can be drained in 20 minutes. If both faucets are
turned on completely while the drain is open, how soon
will the tub fill? |
(25)__________________ |
| 26. |
Two men run around a 1 mile oval track in
opposite directions, starting simultaneously from the
same point. The first man can run a mile in 4 minutes
and the second man can do it in 5 minutes. How far has
the first man run when they pass each other? |
(26)__________________ |
