Chapter 10 Review Algebra
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Date:__________________Per:__________
1. Graph y = 4(3x). How does this graph compare to the graph of y  4  13  ? Explain completely.
x
[ See graph at right. The second would be a decreasing exponential
function. ]
2. Ms. Hookman gave a math test that was calculator-optional. She created a two-way table that
categorized students by calculator use and grade earned on the test.
a.
b.
If you were to choose one of the 160 students at random, what it the probability that they
earned an “A” and used a calculator?
If you were to choose one of the 160 students at random, what it the probability that they
earned an “other” or used a calculator?
d.
Is there an association between using a calculator and the grade earned? Show your
evidence clearly.
[ a: P(A&Calc) = 25/160 = 0.156; b: P(Other or Calc) = P(Other) + P(Calc) –
P(Other&Calc) = 30/160 + 130/160 – 24/160 = 0.85; d: Using Grades as the independent
variable the relative frequencies are:
There does not seem to be much of a difference between the columns of relative
frequencies. For example: Of the students who earned a “B”, 80% used a calculator, and
of those earning an “other”, again 80% used a calculator. Comparing relative frequencies
across the rows one finds little difference. There seems to be little or no association
between these exam grades and calculator use.
OR
Using calculator use as the independent variable, the relative frequencies are:
There does not seem to be much of a difference between the columns of relative
frequencies. For example: Of the students who used a calculator 25.4% earned a “C”, and
of those not using a calculator 23.3% earned a “C”. Comparing relative frequencies across
the rows one finds little difference. There seems to be little or no association between these
exam grades and calculator use. ]
3. Consider the quadratic inequality x2 + 4x + 4 > 0. .
a.
Solve for the boundary point(s). How many boundary points are there?
b.
Place the boundary point(s) on a number line. How many regions do you need to test?
c.
Test each region and determine which one(s) make the inequality true. Identify the
solution algebraically and on the number line.
[ a: x = 2, –2, two of them; b: Three regions; c: x < –2 and x > 2 ]
4. Solve the inequality: |7 – 2x| ≥ 15.
[ –4 ≤ x ≤ 11 ]
5. Consider the equation 4x + 3 = –2x – 9.
a.
Solve for x. How do you know your solution is correct? Explain completely.
b.
Graph the following system:
y = 4x + 3
y = –2x – 9
c.
How do parts (a) and (b) relate? Explain completely.
[ a: x = –2; b: Two lines crossing at x = –2, y = –5; c: If we were two solve the system in
part (b), we would use the equal values method and get the equation in part (a), so they are
solving for the same thing. ]