Download Test 2A (Sec. 2-1, 2-2, 2-5, 2-6) Multiple Choice Identify the choice

Test 2A (Sec. 2-1, 2-2, 2-5, 2-6)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Find the next item in the pattern 1, 2, 4, 8, 16, ...
2. Based on the pattern, what is the next figure in the sequence?
3. Complete the conjecture.
The sum of two odd numbers is _____.
4. The table shows the population 65 years and over by age and sex according to the US Census Bureau, Census 2000
Summary file. Make a conjecture based on the data.
Population 65 Years and Over by Age and Sex: 2000
(numbers in thousands)
65 to 74 years
75 to 84 years
85 years and over
10,088
7,482
3,013
8,303
4,879
1,227
Women
Men
5. Show that the conjecture is false by finding a counterexample.
If
, then
.
6. Laisha’s Internet Services designs web sites and recently began a weekly advertising campaign. Laisha noticed an
increase in her customers over a period of five consecutive weeks. Based on the pattern shown in the graph, make a
conjecture about the number of customers Laisha will have in the seventh week.
10
y
Number of Customers
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
x
Week
7. Identify the hypothesis and conclusion of the conditional statement.
If it is raining then it is cloudy.
8. Which choice shows a true conditional, with the hypothesis and conclusion identified correctly?
A Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Monday.
B If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is not Thursday.
C If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is Thursday.
D Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Tuesday.
9. Write a conditional statement from the statement.
A horse has 4 legs.
10. Write the conditional statement that the Venn diagram illustrates.
Quadrilaterals
Squares
11. Determine if the conditional statement is true. If false, give a counterexample.
If a figure has four sides, then it is a square.
12. Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
A Sara Lucas lives in Springfield.
B Jonah Lincoln lives in Springfield, Illinois.
C Billy Jones lives in Chicago, Illinois.
D Erin Naismith lives in Springfield, Massachusetts.
13. Solve the equation
. Write a justification for each step.
Given equation
[1]
Simplify.
[2]
Simplify.
14. Solve the following equation. Write a justification for each step.
15. A gardener has 26 feet of fencing for a garden. To find the width of the rectangular garden, the gardener uses the
formula
, where P is the perimeter, l is the length, and w is the width of the rectangle. The gardener wants
to fence a garden that is 8 feet long. How wide is the garden? Solve the equation for w, and justify each step.
Given equation
[1]
Simplify.
Subtraction Property of Equality
Simplify.
[2]
Simplify.
Symmetric Property of Equality
Use the given property to complete the statement.
16. Transitive Property of Congruence
If
______.
17. Multiplication Property of Equality
If
, then ______.
18. Write a justification for each step.
J
M
(6x + 8)º
(2 x- 4)º
K
m
=m
L
+m
m
[1]
Substitution Property of Equality
Simplify.
Subtraction Property of Equality
[2]
Symmetric Property of Equality
19. Write a justification for each step, given that
E
F
G
.
H
Given information
[1]
Segment Addition Postulate
[2]
Subtraction Property of Equality
20. Use the given plan to write a two-column proof.
Given: m + m = 90 , m + m = 90 , m
=m
4
3
2
1
Prove: m = m
Plan: Since both pairs of angle measures add to 90 , use substitution to show that the sums of both pairs are equal.
Since m = m , use substitution again to show that sums of the other pairs are equal. Use the Subtraction
Property of Equality to conclude that m = m .
Complete the proof.
Proof:
1. m
2. [1]
3. m
4. m
5. m
6. m
+m
+m
=m
+m
=m
Statements
= 90
=m
+m
=m
+m
Reasons
1. Given
2. Given
3. Substitution Property
4. Given
5. [2]
6. [3]
21. Fill in the blanks to complete the two-column proof.
Given:
and
are supplementary. m = 135
1
Prove: m
2
= 45
Proof:
Statements
1.
and
are supplementary.
2. [1]
3. m + m = 180
4. 135 + m = 180
5. m = 45
Reasons
1. Given
2. Given
3. [2]
4. Substitution Property
5. [3]
Open Ended Questions
1. Write the Converse, Inverse, and Contrapositive for the following conditional statement:
If a number is greater than 5, then it is greater than 3.
Also identify the Truth Value of each of these statements by circling either True or False.
Converse:
True - False
Inverse:
True - False
Contrapositive:
True - False
2. Justify each step that is taken below to find the value of x. Hint: you will not use “Given” as a reason.
2x
6x + 8
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