Practice Problems for Test #3 – Spring 2006
1. Solve, give in interval notation and graph
a)3x 7(x + 1) 5x + 2
b)-4 2x 2 ≤ 6
c)5 ≤ 5(2 x) < 10
d)3(x + 2) 6 14 2(x 3)
e)1 -4x + 5 9
2. Solve the following by clearing the equation of fractions
a)4v + 2/3 = 5v 5/6
b)2/3x + 1/3(x ½) = 1/15 2/5x
3.On an architect’s blueprint, 1 inch corresponds to 4 feet. Find the length of a wall
represented by a line that is 3 7/8 inches long on the blueprint, using a proportion
set up.
4.For the following decimals, give an equivalent fraction.
a)0.666666666b)0.6c)0.5
d)0.3333333333e)0.4444444444f)0.875
g)0.75
5.Setup, give an equation and solve (You must know how to use ALGEBRA to get
your answer.)
a) The quotient of a number and three is the same as the difference of the number
and two. Find the number.
b)Find three consecutive even integers whose sum is negative 114.
c) How long will it take a sports car traveling at 60 mph to overtake a passenger
car traveling at 40 mph if the passenger car had a 1.5 hour head start?
d) Ned and Less are 12 miles apart and hiking toward one another. How long
will it take them to meet if Ned walks at 3 mph and Less walks 1 mph faster?
e) By buying in bulk, a family was able to decrease their weekly food bill from
$150 to $130. Find the percent decrease.
f) Iceberg lettuce is grown and shipped to stores for 40 cents per head, and
consumers purchase it for 70 cents a head. Find the percent increase.
g) Los Molinos, is about 150 miles from Stockton. If Dennis Owen leaves
Los Molinos at 4 am and averages 45 mph, at what time should he arrive in
Stockton?
h) Charles Pecot can afford enough fencing to enclose a rectangular garden with
a perimeter of 140 feet. If the width of his garden is to be 30 feet, find the
length.
i) Rajiv invested part of his $20,000 inheritance in a mutual fund that pays 7%
simple interest yearly and the rest in a CD that pays 9%. At the end of one
year, Rajiv’s investments earned $1550. Find the amount that he invested at
each rate.
j) A chemist needs 12 liters of a 50% acid solution for a lab experiment. He has
only 40% and 70% solutions. How much of each solution should be mixed
together to form 12 liters of a 50% solution?
6. Solve for a:3b + 2a = 7
7.Graph the following ordered pairs:
a)(0, 5)b)(-2, 5)c)(-1, -5)d)(3, 0)
e)(4, -2)f)(-4, 0)g)(0, -1)
8.Which of the parts in #7 are x-intercepts? How can you tell?
9.Which of the parts in #8 are y-intercepts? How can you tell?
10.Label the points plotted below with their ordered pairs.
11.Find the slope of the line on the graph above using rise over run.
12.Find the slope of the lines through the following sets of ordered pairs.
a)(0,2);(5, 7)b)(12, 2);(5, 2)c)(-1, ½);(-1, 3/2)
13.Find the slope of the following lines: (Don’t work too hard)
a)2x 3y = 9b)2y = -3x 9
14.Find 3 solutions to the following line and give them as ordered pairs.
2x 3y = 9