Honors Algebra II Midterm Exam Review
Part I: Essay/Short Answer
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Directions: Answer in writing each question below. Show all work.
1. Name the property used in each step of simplification:
3 ( 2x + y ) + 4x
Given
(6x + 3y) + 4x
_____________________________________
(3y + 6x) + 4x
_____________________________________
3y + (6x + 4x)
_____________________________________
3y + x ( 6 + 4 )
_____________________________________
3y + x ( 10)
_____________________________________
3y + 10 x
_____________________________________
2. Write three equations that are equal to x = 5.
_______________
_______________
_______________
3. What is the slope of a line and how is it found?
4. Without graphing, describe everything you know about the line x = 2.
5. Describe the relationship between the slopes of two lines if the lines are a. perpendicular and
b. parallel.
6. If you know a point on a line and you know the equation of a line perpendicular to this line,
explain how to write the line’s equation.
7. If a relation is represented by a set of ordered pairs, explain how to determine if a relationship
is a function.
Honors Algebra II Midterm Exam Review
Part I: Essay/Short Answer
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8. Explain how the vertical line test is used to determine whether a graph is a function.
9. What is a quadratic equation?
10. Explain how to solve x2 + 6x + 8 = 0 using factoring and the zero-product property.
11. Explain how to solve x2 + 6x + 8 = 0 by completing the square.
12. What is the discriminant and what information does it provide about a quadratic equation?
13. Name the various methods used to solve quadratic equations. If you are given a quadratic
equation, how do you determine which of these methods to use to solve it?
ESSAY
14. Tasty Baker sells three kinds of muffins: chocolate chip muffins for $ 0.65 each, oatmeal
muffins for $0.70 each, and blueberry muffins for $0.75 each. Charles buys some of each kind
and chooses three more chocolate chip muffins than blueberry muffins. If he spends $6.85 on 10
muffins, how many of each muffin does he buy? Write and solve a linear system in three
variables. Be sure to define your variables and show all work.
Honors Algebra II Midterm Exam Review
Part I: Essay/Short Answer
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15. Art N. Craft is making two kinds of bracelets to sell at a craft fair. For each thin bracelet he
sells, he will make $2. For each thick bracelet he sells, he will make $3. He wants to have a
profit of at least $30. He knows that he cannot make more than 20 bracelets before the fair.
Let x = number of thin bracelets and y = number of thick bracelets.
a. Write an inequality using the cost for each type of bracelet and the least amount of profit
Art wants. Then write an inequality using the fact he cannot make more than 20
bracelets before the fair. Explain what each section of the inequality represents.
b. Graph both inequalities on the graph below.
y
x
c.
The solution to a system of linear inequalities is where the shaded areas overlap.
Choose two points from the solution of this system. Explain how the points relate to the
number of thick and thin bracelets in the problem.
Honors Algebra II Midterm Exam Review
Part I: Essay/Short Answer
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16. The height of a ball at any given time, t, is given by the quadratic equation below:
h (t) = - 16t2 + 50 t + 4
a. Create a table of values that would satisfy the quadratic equation. Include at least 7
points with both positive and negative values for t.
t
h
b. Use the points created in part a to graph the equation on the coordinate plane below.
Circle the section of the graph that relates to the problem.
y
x
c.
Use the algebraic equation to find the height of the ball at 2.5 seconds. Show all your
work. Explain how your answer relates to the graph.
Honors Algebra II Midterm Exam Review
Part I: Essay/Short Answer
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