Exam 2: Review 1.1-2.4
College Algebra: Math1005,N. Pollesch
1) Solve for x:
a.
b.
1. How many gallons of hydrochloric acid must be added to 12 gallons of a 30% solution to obtain a
40% solution?
1. Find a number so that 6 more than one-half the number is two-thirds the number.
2. Jesse B. Davis wants to have a rectangular pool put in the backyard of his home. He wants it to be
24 meters long, and he insists that it have at least as much area as neighbor's pool, which is a
square 12 meters on a side. Find the dimensions of the smallest pool that meets these criteria.
3. Rewrite in inequality notation and graph on a real number line:
a.
b.
c.
d.
e.
4. Rewrite in interval notation and graph on a real number line (if possible):
a.
b.
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a.
b.
c.
d.
e.
f.
1. Solve and graph:
a.
b.
c.
For the absolute values problems below, solve and report answers in interval notation:
2.
a.
b.
a.
a.
1.
2.
1. Complete the following statements based on the definitions for operating on complex numbers
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1. Complete the following statements based on the definitions for operating on complex numbers
a. Equality:
if and only if ___ = and ___ =
-Another way to say this is as follows: Two complex numbers are equal if the _______ parts
are equal and the ______ parts are equal.
b. Addition:
(___+___) + (___+___)
2. Complete the following operations:
a.
b.
a.
a.
a. These two numbers are ___________ of each other.
1. Solve for
a.
and :
a. What property of complex numbers did you use to solve the above problem?
1. Solve for :
Recall that for this problem you want to
a) Separate terms that include and do not include z .
b) Use complex division to isolate z.
c) Make sure to report your answer in standard form.
1. Solve the following quadratic equations by any method (remember now you can solve any of
these regardless if they have complex solutions or not)
2.
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1.
1.
1.
1.
for
1. Find two consecutive positive integers whose product is 168.
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1. Solve for t:
Make sure to check your answers, these problem types can generate
extraneous solutions. (See page 98 if you need an example)
1. Test for symmetry, do not graph:
a.
a.
1. Graph the following functions, if you want, use symmetry as an aid. (Even if you do not formally
test for symmetry, it is useful to keep it in mind as you graph)
1. Find the distance and the midpoint of the following sets of points:
a.
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1. Find the distance and the midpoint of the following sets of points:
a.
b.
a.
1. Find the center and radius of the following circles:
a.
b.
a.
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1. Complete the following table involving lines:
Standard form
___________
A and B both not ___
Slope-intercept form
___________
Slope: __, y-intercept:__
Point-slope form
___________
Slope: m, for Point (__,__)
Horizontal line
Slope: ___
Vertical line
Slope: ___
2. Find an equation for the line with the given information, report in slope-intercept form:
a. (1,2), m=-1
b. (0,4), m=2/3
a. (-3,4) , (2,1)
b. x-intercept: -4, y-intercept: 3
a. Parallel to the line:
a. Perpendicular to the line:
, through the point (1,1)
, through the point (-2,3)
1. Hooke's law states that the relationship between the stretch of a spring and the weight
causing the stretch is linear. For a particular spring, a 5-pound weight causes a stretch of 2 inches,
while with no weight the stretch of the spring is . (From 2.3 pg 146)
2. Find a linear equation that expresses in terms of
3. What is the stretch for a weight of 20lbs?
4. What weight will cause a stretch of 3.6 inches
5. The speed of sounds through the air near sea level is linearly related to the temperature of the air.
If sound travels at 741mph at 32 F and at 771 mph at 72 F, construct a linear model relating the
speed of sound ( ) to the air temperature ( ). Interpret the slope of this model. (From 2.4 pg 155)
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If sound travels at 741mph at 32 F and at 771 mph at 72 F, construct a linear model relating the
speed of sound ( ) to the air temperature ( ). Interpret the slope of this model. (From 2.4 pg 155)
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