Download Algebra 2 Midterm Exam Algebra II Midterm Exam Name: Score

Algebra 2 Midterm Exam
Algebra II Midterm Exam
Name: _________________________
Score: ______ / ______
Answer the questions below. Make sure to show your work and justify all of your answers
1.
Simplify:
Show your work.
= 4.472/1.495
=3
4. For the given quadratic equation convert into vertex form, find the vertex, and find
the value for x = 6. Show your work.
Y = -2x2 + 2x +2
=-2x^2 + 4x-2x + 2
=-2x(x-2) -2(x-2)
=(-2x-2)=0 (x-2)=0
=x=2, x=1
3. A manufacturer of shipping boxes has a box shaped like a cube. The side length is
(5a + 4b). What is the volume of the box in terms of a and b? Show your work.
(5a + 4b)^3
Algebra 2 Midterm Exam
=(25a^2 + 40ab + 16b^2) (5a + 4b).
4. If a function, f(x) is shifted to the left four units, what will the transformed function
look like?
The transformation would be f (-4x)
5. Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a
fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an
equation to find how many T-shirts the club needs to make and sell in order to profit at
least $100. Show your work.
=12t -100 = 28t
=-100 =16t
6. The velocity of sound in air is given by the equation
, where v is the
velocity in meters per second and t is the temperature in degrees Celsius. Find the
temperature when the velocity is 329 meters per second by graphing the equation. Round
the answer to the nearest degree. Show your work.
=root 20 (273+329)
=root 20 (602)
=1.377
7. The volume in cubic feet of a box can be expressed as
, or as the
product of three linear factors with integer coefficients. The width of the box is x-2.
Factor the polynomial to find linear expressions for the height and the length. Show your
work.
Algebra 2 Midterm Exam
8. What is the solution to the equation
. Show your work.
2x + 8 =100
2x=92
X=46
9. Solve the equation. Check for extraneous solutions. Type your answers in the blanks.
Show your work.
Algebra 2 Midterm Exam
x = ___3__ or ___2__
10. Write an expression for the volume of a cylinder with a height 7in. greater than the
radius.
V = pi*r^2*h
11. What is the value of log81 3? Show your work.
=3 ^n=81
3^n=3^4
Therefore n=4
12. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures
and then warmed again.
Time (hours)
0
1
2
3
4
5
6
Population (1000s)
5.1 3.03 1.72 1.17 1.38 2.35 4.08
Find a quadratic model for the data in the table. Type your answer below. Show your work.
When t = 1, P= 3.03.
When t = 2, P = 1.72.
When t = 3, P = 1.17.
Substitute into the equation to obtain these the simultaneous equations below;
a + b + c = 3.03
4a + 2b + c = 1.72
9a + 3b = c = 1.17
Algebra 2 Midterm Exam
13. Use the model from problem 12 to estimate the population of bacteria at 9 hours.
Type your answer below. Show your work.
When t = 1, P= 3.03.
When t = 2, P = 1.72.
When t = 3, P = 1.17.
Substitute into the equation to obtain these the simultaneous equations below;
a + b + c = 3.03
4a + 2b + c = 1.72
9a + 3b = c = 1.17
Solving gives: a = 0.38, b = -2.45, c = 5.1.
The equation is therefore, P = 0.38t^2 - 2.45t + 5.1
Testing with t = 0 to 6 gives the values of the population as provided,
so it is a valid model.
At t = 9 hrs, P = 0.38*9^2 - 2.45*9 + 5.1 = 13.83.
14. Evaluate the expression for the given value of the variable(s). Show your work.
= {4 (-12)}/-1 = 48
15. Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your
work.
A quadratic function:
First, take the point (0,-4) and plug the values (x,y) into the equation:
Algebra 2 Midterm Exam
So the equation is
.
Now plug the values of the other two points into the equation and set up a system of equation:
16. Simplify the expression. Type your answer in the blank.
-
=-13
17. Suppose you cut a small square from a square of fabric as shown in the diagram. Write
an expression for the remaining shaded area. Factor the expression. Type your answer
below.
Algebra 2 Midterm Exam
The area of our original piece of fabric is x². However, the area of the cut out circle is 3²=9. Therefore, the
remaining area is x² - 9
18. Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your
answer below.
To confirm, we check to see if there are repeating numbers. In our case, the first numbers are
{3,−4,−5,1,4} but with no repeats so it qualifies to be a function
19. Evaluate
Show your work.
=4th root of 7x^2 -14th root of 49x
4√(7x2) - 14√(49x)
4√(7x2) - 14√(72x)
20. Consider the leading term of the polynomial function. What is the end behavior of the
graph? Describe the end behavior and provide the leading term.
-3x5 + 9x4 + 5x3 + 3
The leading term is -3x5. Because n is odd and a is negative then the end behavior is up
and down
Algebra 2 Midterm Exam