1.Solve for
x in the equation
(A)
x = –3
(B)
x = 0
(C)
x = 6
(D)
x = 12
(E)
x = 24
2.Solve for
x in the following inequality:
> 3
(A)
x < –13
(B)
x ≥ –13
(C)
x ≤ –5
(D)
x < –5
(E)
x > –5
3.Solve for
x in the following equation: 3 + |2
x – 7| =
x + 2
(A)
x = –6
(B)
x = 8
(C)
x = {
, 8}
(D)
x = {6, 8}
(E)
x = {
, 6}
4.If
x = 2
y – 4 and
y = 7
s + 1, what is the value of
s in terms of
x?
(A)
s =
(B)
s =
(C)
s =
(D)
s =
+ 2 +
(E)
s =
5.Jim and Ryan run laps around a track which is 1 /4 of a mile long. If Jim runs
hlapsper hour, Ryan runs half as fast as Jim, and Jim starts runninghalf anhour before Ryan, how many miles farther than Ryan has Jim runtwo hoursafter Jim starts?
(A)
(B)
(C)
(D)
(E)
6. Ken buys a shirt on a 30% sale from itsoriginal price of 10 dollars. Hethen resells it at a 60% increase fromthe price at which he bought it.How much does Ken sell the shirt for?
(A) $4.20
(B) $11.20
(C) $13.00
(D) $13.30
(E) $14.20
7.A train leaves the station traveling dueeast at a rate of 45 miles perhour. A second train leaves a differentstation an hour later, travelingdue west on the same track, going 60miles per hour. If the stations are255 miles apart, how many milesfrom the halfway point between thestations will the trains collide?
(A) 0
(B) 5
(C) 7.5
(D) 12.5
(E) 25
8. A snowman weighing 250 pounds begins tomelt in the spring. It loses 4%of its weight every day. How many fulldays will pass before it weighsless than 100 pounds?
(A) 17
(B) 22
(C) 23
(D) 27
(E) 45
9.What is (
a +
b + 3
c)(2
a + 3
b + 4
c)?
(A) 3
a + 4
b + 7
c
(B) 2
a2 + 3
b2 + 12
c2
(C) 2
a2 + 10
ac + 12
c2
(D) 2
a2 + 3
ab + 10
ac + 9
bc + 12
c2
(E) 2
a2 + 3
b2 + 12
c2 + 5
ab + 10
ac + 13
bc
10.Solve for
x in the following equations: 3
x2 + 24
x – 27 = 0
(A)
x = 1
(B)
x = –9
(C)
x = {1, –9}
(D)
x = {–1, 9}
(E)
x = {3, 27}
Explanations
D
To solve this problem, just isolate the variable:
D
Solvingfor a variable in an inequality is similar to solving for a variable ina normal equation, with one big difference: you isolate the variable.But remember that if you multiply or divide an inequality by a negativenumber, you must reverse the direction of the inequality symbol:
E
First, isolate the expression within the absolute value brackets:
Then divide the equation into two equations. In this first case, the expression within absolute value brackets is positive:
Next, let the expression within absolute value brackets be negative:
The two solutions are
x = {8⁄3, 6}.
B
First, solve for
s in terms of
y:
Next, solve for
y in terms of
x:
Finally, substitute this value for
y in the equation with
s:
A
This is a ratequestion, and we are given the input and rate in order to find theoutput. So, we can plug the known values into the rate formula:
D eJim runs
h laps per hour for 2 hours, so his total distance traveled is 2
h laps, which equals 2
h⁄4 miles. Ryan runs .5
h laps per hour for 1.5 hours, so in total he runs 0.75
h laps. This is equal to .75
h⁄4 miles. The difference between the distance traveled by Jim and the distance traveled by Ryan is 2
h⁄4 – .75
h⁄4 = 1.25
h⁄4 miles.
B
This is a doublepercent-change problem, and so we perform each percent change one byone. First, Ken bought the shirt at a discount of 30%. The price atwhich he paid was:
1PM/fGHq
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本帖最后由 端木·宇 于 2008-6-18 19:55 编辑 ]
