Student:
Teacher
Due Date: August 10th, 2014
Algebra II Summer HW 4
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Non Extended Response (1.5 points each)
1) Factor the following perfect-square trinomials:
a) 𝑥 2 − 12𝑥 + 36
(x - 6)2
2) Continued from question 1.
In the following, choose k to create a perfect
square trinomial:
b) 𝑥 2 + 14𝑥 + 49
c) 𝑥 2 − 20𝑥 + 100
a) 𝑥 2 − 16𝑥 + 𝑘
b = 16
𝑏
=8
2
2
8 = 64
x2 – 16x +64
As suggested, these should all look like either(𝑥 −
𝑟)2 𝑜𝑟 (𝑥 + 𝑟)2 . State the important connection between
the coefficients of the given trinomials and the values
you found for r.
3) The point on segment AB that is equidistant
from A and B is called the midpoint of AB. For
each of the following, find coordinates for the
midpoint of AB:
𝐴 = (−1,5) 𝑎𝑛𝑑 𝐵 = (3, −7)
Midpoint Formula
(𝑥1 + 𝑥2 ) (𝑦1 + 𝑦2 )
,
2
2
b) 𝑥 2 + 10𝑥 + 𝑘
c) 𝑥 2 − 5𝑥 + 𝑘
4) ∆𝐴𝐵𝐶 is similar to ∆𝑋𝑌𝑍. 𝐴𝐵 is 5 inches long, 𝐵𝐶
is 8 inches long, and 𝐴𝐶 is 3 inches long. If the
longest side of ∆𝑋𝑌𝑍 is 20 inches long, what is
the perimeter, in inches, of ∆𝑋𝑌𝑍?
a.
b.
c.
d.
e.
16
28
40
64
88
First, draw ∆𝐴𝐵𝐶. Then, draw ∆𝑋𝑌𝑍.
You will have to set up two proportions to set up
the side lengths.
8
5
The first one starts with 20=𝑥
4
5) √27 + √48 = ?
a.
b.
c.
d.
e.
6) If the circumference of a circle is 3 𝜋 inches, how
long is the radius, in inches?
5√3
7√3
3√3 + 3√4
12√3
3 + 4√3
a.
3
4
b.
3
2
c.
2
3
d. √
e.
7) Apply the zero-product property (you may have
to look this up) to solve the following equations:
a) (𝑥 − 2)(𝑥 + 3) = 0
b) 𝑥(2𝑥 + 5) = 0
c) 5(𝑥 − 1)(𝑥 + 4)(2𝑥 − 3) = 0
The zero product property says that if any two
numbers multiplied together equals zero, then one
or both of those terms equal zero.
𝐶 = 𝜋2𝑟, solve for r
4
3
4√3
3
8) What is the value of the expression 2𝑥 3 − 𝑥 2 +
3𝑥 + 5 for 𝑥 = −2?
a.
b.
c.
d.
e.
-21
-13
8
11
21
If you use your calculator, make sure to use
parentheses: 2(−2)3…
Extended Response (4 points each)
1) According to the U.S. Census Bureau, the population of the USA has a net gain of 1 person every 14
seconds. How would you figure out how many additional persons this amounts to in one year?
The important part of this question is not the final answer, but your explanation of the process you
would use to solve it.
First, decide how many people it would be in a minute, hour, day, etc.
2) What are you most excited for going into Algebra II? What are you most apprehensive about?
The first change could be from work-word.