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Demonstrate your knowledge by giving clear, concise solutions to each problem. Be sure to include all
relevant drawings and justify your answers (show all your work). You may show your solution in more
than one way to investigate beyond the requirements of the problem.Lesson 1-8
Logical Reasoning and Counterexamples
1.
Which values are a counterexample to the given statement?
If x + y = an even number, then x is even and y is even.
2.
A.
x = 21, y = 3
B.
x = 12, y = 6
C.
x = 7, y = 12
D.
x = 10, y = 9
Identify the conclusion in the following algebraic statement:
If a = 3, then 2a + 1 = 7.
3.
A.
a=3
B.
C.
2a + 1 D.
2a
2a + 1 = 7
Which values are a counterexample to the given statement?
If x · y = a decimal, then neither x nor y is a whole number.
4.
5.
A.
x = 7.1, y = 2.2 B.
x = 1, y = 0.5
C.
x = 1.75, y = 0.9 D.
x = 0.3, y = 0.2
Identify the conclusion in the following statement: If 13b + 12 = 77, then b = 5.
A.
b
B.
13b + 12
C.
b=5
D.
13b + 12 = 17
Take the given hypothesis and conclusion and write a true statement in if-then form.
Hypothesis: The pitcher is getting tired.
Conclusion: He cannot throw fastballs anymore.
A.
If the pitcher cannot throw fastballs anymore, then he is getting tired.
B.
If the pitcher is getting tired, then he cannot throw fastballs anymore.
C.
If the pitcher is in the first inning, then he will not be tired.
D.
If the pitcher is not getting tired, then he can throw fastballs.
UNIT 1 Project (28pts)
Demonstrate your knowledge by giving clear, concise solutions to each problem. Be sure to include all
relevant drawings and justify your answers (show all your work). You may show your solution in more
than one way to investigate beyond the requirements of the problem.
1. Some important formulas are given below.
Area of a circle is
where r is the radius of the circle.
a) Write a formula for the area of the figure below. (5pts)
b) Simplify the formula in part a. Justify each step in your simplification by naming the
property used. (5pts)
c) Find the area of the figure when a = 2 (5pts)
In each sentence, circle or highlight key words or phrases that indicate the mathematical operation and
write the corresponding mathematical symbol above each. Then, write an equation for each sentence.
a) Three times a number decreased by five is equal to twenty five. (2pts)
b) The sum of the square of a number and a second number is eighteen. (2pts)
c) A number multiplied by 6 and divided by five gives four more than a number. (2pts)
d) One-half of a number added to itself equals twice the difference of the number and four.
(2pts)
3. Think of a situation that can be modeled by the graph. Then, label the axes of the graph and write
several sentences describing the situation (5pts)

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