Student:
Teacher
Due Date: August 11th, 2013
1) Factor the following perfect-square
trinomials:
a) 𝑥 2 − 12𝑥 + 36
(x - 6)2
b) 𝑥 2 + 14𝑥 + 49
c) 𝑥 2 − 20𝑥 + 100
College:
Algebra II Summer HW 4 FORM-A
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https://docs.google.com/forms/d/1Pq1SwDUFRH
ACT:
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ciJem1DaQYpPKH7NlK6yyc4uawaFWBHp0/vie
wform
2) Continued from question 1.
In the following, choose k to create a perfect
square trinomial:
a) 𝑥 2 − 16𝑥 + 𝑘
b = 16
𝑏
=8
2
2
8 = 64
x2 – 16x +64
b) 𝑥 2 + 10𝑥 + 𝑘
c) 𝑥 2 − 5𝑥 + 𝑘
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) 𝐴 = (−1,5) 𝑎𝑛𝑑 𝐵 = (3, −7)
b) 𝐴 = (𝑚, 𝑛)𝑎𝑛𝑑 𝐵 = (𝑘, 𝑙)
Distance Formula
(𝑥1 + 𝑥2 ) (𝑦1 + 𝑦2 )
,
2
2
5) √27 + √48 = ?
a.
b.
c.
d.
e.
5√3
7√3
3√3 + 3√4
12√3
3 + 4√3
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
6) Evaluate each of the following expressions
by substituting s=30 and t=-4.
a.
b.
c.
d.
𝑡 2 + 5𝑡 + 𝑠
2𝑡 2 𝑠
FORM-A (write this for your answer)
FORM-A (write this for your answer)
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.
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…
http://www.mathsisfun.com/algebra/zero-productproperty.html
4
9) If the circumference of a circle is 3 𝜋 inches,
how long is the radius, in inches?
a.
b.
c.
3
4
10)Catelyn and Stannis are having an algebra
argument. Catelyn is sure that −𝑥 2 is
equivalent to (−𝑥)2, but Stannis thinks
otherwise. Who do you agree with? Why?
What evidence does your calculator offer?
3
2
2
3
4
d. √
3
e.
4√3
3
𝐶 = 𝜋2𝑟, solve for r
Choose a number to substitute in for x and try both
Catelyn’s and Stannis’ method.
Extended Response (Turnitin.com class ID: 6545465, Enrollment Password: MathMathMath)
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) As the ancient wizards hoped, it is possible to turn lead into gold. You change one letter at a
time, always spelling real words: lead-load-toad-told-gold. Using the same technique, show
how you would turn work into play.
The first change could be from work-word.