Download Test #4

Name: ______________________
Test #4a – Spring 2003
Algebra
Instructions: Put your name on the top before beginning. You will have approximately one hour to
complete this exam. You may use a calculator. Please attach your note card to the back of the test when
finished. If you can’t complete a problem in the space allotted, please direct me to the place where you
have completed the work and label it clearly. A problem without work will not receive full credit under
any circumstances. Word problems must show the appropriate set up, equation, substitution and work to
receive full credit. Remember that improper fractions must be converted to mixed numbers for final
answers and all fractional answers must be in lowest terms. Show all work and box your final answer.
Good luck!
1.
Use the Pythagorean theorem to solve the following problem.
The hypotenuse of a right triangle is 15 inches. Leg "a" is 6 less than
twice leg b. Find the length of leg a. (You may use the quadratic formula, but a
hint is that one root is –21/5, and 5 is prime.)
2.
Johnny has $2200 invested in 2 accounts. Using a system of 2 equations and 2
unknowns, how much money does Johnny have in each account if he made $56
last year when the annual percentage rates were 3% and 2% on the accounts?
1
3.
The area of a rectangle is 32 inches2. If the length is two more than some number
and the width is 2 less than some number, find the length and the width.
4.
Simplify each of the following.
a)
2-2
5.
b)
3x0  x0
c)
(3x2y)(5x2y3)
d)
24x3y2
15xy3
e)
(2x2y -3)3
Simplify by adding or subtracting
a)
(2x2 + x  5) + (x2 + 7  3x)
b)
(x2  9)  (2x2 + 7x  10)
2
6.
Graph the following system to determine the solution. In the next problem you
will be asked to solve the same system as a check. This problem needs to show
work for graphing each line using a minimum of 2 points. Give your answer
here. _________
y = x + 1
y = -x + 3
y
x
3
7.
Use substitution to check the solution to the problem in 6. In other words, solve
the following system using substitution.
y = x + 1
y = -x + 3
8.
Use elimination to solve the following system.
2y = x + 2
2y = x  2
9.
Factor the following completely.
a)
(by grouping)
3x2  9x  9x + 27
b)
3x2  12x + 12
4
10.
Write the following in standard form.
a)
2.72 x 106
b)
11.
Write the following in correct scientific notation.
a)
1,051,000
b)
EC.
1.73 x 10 –3
0.00017
Solve the following quadratic equation by factoring.
[3(x + 2)(x  2)]  9x = 9x  39
5