Download Semester_Review 2017

Name:
Class:
Date:
Semester Review
1. For the diagram, assume line AB || line CD. Prove or give a counter example for each of the following.
a. If
, then quadrilateral ABCD is a parallelogram.
b. If
, then quadrilateral ABCD is a parallelogram.
c. If
, then quadrilateral ABCD is a parallelogram.
2. In the diagram at the right,
a. Prove that
b. Using the fact that
Powered by Cognero
and
.
, explain why you can conclude that C is the midpoint of
.
Page 1
Name:
Class:
Date:
Semester Review
3. Consider the diagram below.
a. If
, which lines must be parallel? Explain your reasoning.
b. If
and line IH is parallel to line LG, find the measures of each angle.
i.
ii.
iii.
4. In the diagram below,
Powered by Cognero
and line a is parallel to line b. Prove that
.
Page 2
Name:
Class:
Date:
Semester Review
5. Corn is an important part of many animals’ diets. A group of researchers believe that a new type of corn will help
their animals grow faster. They design an experiment where they randomly assign 7 one-day-old chicks to get the
new corn and 7 one-day-old chicks to get the old type of corn. After 21 days, they record the weight gain of all of
the chicks and compare the two groups.
a. What are the treatments for this experiment?
b. Is this experiment subject blind? Explain your reasoning.
c. Explain how this experiment could be performed so that it is evaluator blind.
6. The weight gain (in kg) of each of the chicks in the experiment described in Task 10 is given in the table below.
a. Find the value of mean weight gain new corn
gain old corn.
mean weight
b. Describe how to use a randomization test to determine if the
new corn helps chickens to gain weight faster than the old
corn.
c. Victoria performed 200 runs and created the
randomization distribution below. Use the
histogram to estimate the probability of getting a
difference as extreme as that from the actual
experiment if the type of corn makes no
difference.
p-value:
d. Is the difference in weight gains statistically
significant? Explain your reasoning.
Powered by Cognero
Page 3
Name:
Class:
Date:
Semester Review
7. Solve the inequality
. Indicate your solution on a number line graph.
8. Find all solutions to
. Display the solutions using symbols.
9. The height in feet h(t) of a basketball t seconds after being shot from mid-court is shown on the graph below.
a. Estimate solutions to
.
b. Estimate solutions to
.
c. Estimate solutions to
.
d. Write an inequality whose solution will indicate when the ball was less than 8 feet above the floor.
10. Draw a graph that indicates the solution to
Powered by Cognero
.
Page 4
Name:
Class:
Date:
Semester Review
11. In a linear programming situation, the feasible region is defined by the following inequalities:
a. Sketch a graph of the feasible region. Be sure to clearly identify which region is the feasible region.
b. Using the profit function
region.
Powered by Cognero
, find (x, y) combinations that yield maximum profit within the feasible
Page 5
Name:
Class:
Date:
Semester Review
12. In the diagram below,
line ℓ.
is a size transformation of
and
is a reflection image of
across
a. On the grid, locate
the center of the size
transformation that
maps
to
.
b. What is the
magnitude of the
size transformation
from
to
?
c. Draw line ℓ, the line
of reflection.
d. Explain why
.
13. Determine if each pair of triangles below are congruent, similar but not congruent, or neither. If they are
congruent or similar, write a congruence or similarity relation showing the correspondence between vertices and
cite an appropriate congruence or similarity theorem to support your conclusion.
a.
b.
Powered by Cognero
Page 6
Name:
Class:
Date:
Semester Review
c.
d.
14. Weights of chicken eggs are normally distributed with a mean of 59 grams and a standard deviation of 2.5 grams.
a. Sketch a graph of the distribution of the scores. Be sure to include a scale on the axis.
b. Approximately what percentage of chicken eggs will weigh between 56.5 g and 61.5 g?
c. Approximately what percentage of the eggs will weigh less than 64 g?
d. Approximately what percentage of the eggs will weigh more than 60 g?
15. Scores on the SAT Subject Tests are approximately normal. The scores on the Spanish Reading Tests have a
mean of 632 and a standard deviation of 124. The scores on the German Reading Test have a mean of 604 and a
standard deviation of 127. Janelle got a 690 on the Spanish Reading Tests and a 670 on the German Reading
Test. On which test was her percentile ranking higher? Explain your reasoning.
Powered by Cognero
Page 7
Name:
Class:
Date:
Semester Review
16. The weights of 19-day-old pigs are approximately normally distributed with a mean weight of 11.9 pounds and
standard deviation of 2.7 pounds.
a. Find the standardized value for a 19-day-old pig that weighs 15 pounds. Write a sentence explaining what the
standardized value means.
b. Mason has a 19-day-old pig that weighs only 7.85 pounds. What is the pig’s percentile for weight? Write a
sentence explaining what the percentile means.
c. Graciela has a big 19-day-old pig. When she looks at a chart, she realizes that only 10% of 19-day-old pigs are
bigger than her pig. Approximately how much does Graciela’s pig weigh?
Powered by Cognero
Page 8
Name:
Class:
Date:
Semester Review
Answer Key
1. Students may produce different proofs or counterexamples.
a. False. ABCD could be an isosceles trapezoid with line AB || line DC and the base angles congruent.
b. True. Since
, it follows that line AD || line BC (corresponding angles are congruent). It is given that
line AB || line CD, so since both pairs of opposite sides are parallel, ABCD is a parallelogram.
c. True. Since line AB || line CD,
is supplementary to
.
, so
is supplementary to
. This implies that line AD || line BC (interior angles on the same side of the transversal are supplementary). So,
ABCD is a parallelogram.
2. a. Since
, we know that alternate interior angles are congruent. Thus,
information. Also,
because they are vertical angles. Thus,
Theorem.
b. Since
,
midpoint, C is the midpoint of
3. a. Line AJ || line FK because
transversal LG.
.
is given
by the ASA Congruence
because they are corresponding sides of congruent triangles. Then by definition of
.
and
are congruent corresponding angles formed bye lines AJ, FK, and the
b. i.
ii.
iii.
4.
5. a. One treatment is new corn, and the other treatment is old corn.
Powered by Cognero
Page 9
Name:
Class:
Date:
Semester Review
b. The experiment is subject blind because the chicks would not know if they were eating the new corn or the old corn.
c. The experiment would be evaluator blind if the person weighing the chicks did not know which type of corn they had
eaten.
6. a. The mean of the new corn weight gains is 1.11 kg.
The mean of the old corn weight gains is 1.01 kg.
mean weight gain new corn mean weight gain old corn
kg
b. Begin by making the assumption that the type of corn the chicks were fed made no difference. Write the 14 weight
gains on 14 identical slips of paper, mix them thoroughly, and deal out 7 to be “fed” the new corn. The rest of the chicks
will be “fed” the old corn. Because it is assumed that the type of corn makes no difference in the growth, the response for
each chick will be the same as in the actual experiment.
Compute the mean weight gain for each treatment group and subtract mean weight gain new corn
corn. Repeat this many times until you see the shape of the distribution.
mean weight gain old
c. The difference in the actual experiment was 0.10. In the 200 runs, a value as extreme as this occurred
times.
So, the probability of getting a difference as extreme as that from the actual experiment if the type of corn makes no
difference is
.
d. Since the probability is greater than 0.05, the difference in weight gains is not statistically significant. The difference
of 0.10 can reasonably be attributed to chance alone.
7. Solve:
Powered by Cognero
Page 10
Name:
Class:
Date:
Semester Review
Since the graph of
is below the graph of
when
and x > 1, the solution is:
8. Solve:
The graph of
9. a.
is at or above the graph of
when
seconds and
b.
when 0.2 seconds
c.
has no solutions.
when
or
.
seconds.
seconds.
d.
10. The shaded region is the solution to the inequality.
Powered by Cognero
Page 11
Name:
Class:
Date:
Semester Review
11. a. The feasible region is the unshaded region. Vertices are labeled for reference in Part b.
b. The maximum profit will occur at one of the five vertices of the feasible region. The vertices of the feasible region are
. Point D(0,10) will yield a higher value of P than any of the other vertices. At
(0,10),
, the maximum profit.
12. a and c.
Powered by Cognero
Page 12
Name:
Class:
Date:
Semester Review
b. The magnitude of the size transformation is 2.
d. A reflection image is always congruent to the original image. Thus, you know that
and
. Additionally, the angle measures of a size transformation image are equal to the corresponding angle measures of the
original. Thus
and
. Thus, you can conclude that
and
. So, by the AA Similarity
Theorem,
.
13. a.
by the ASA Congruence Theorem.
b. It is not possible to conclude the triangles are similar or congruent.
c.
by the AA Similarity Theorem.
d.
by the SAS Congruence Theorem.
14. a.
Powered by Cognero
Page 13
Name:
Class:
Date:
Semester Review
b. 68%
c. 97.5%
d.
Since the standardized weight for 60 g is
, from the table of standardized values, 65.54% of eggs will weigh less
than 60 g. Thus,
of the eggs will weigh more than 60 g.
15. The standardized score for Janelle’s Spanish Reading Test is
The standardized score for her German Reading Test is
.
.
Since the standardized score for the German Reading Test is greater than the standardized score for the Spanish Reading
Test, her percentile ranking will be higher for the German Reading Test.
16. a.
This means that the pig’s weight is 1.15 standard deviations greater than the mean weight.
b.
The pig’s percentile for weight is 0.0668, or 6.68%. This means that this pig weighs more than only 6.68% of all 19-dayold pigs.
c. Graciela’s pig is bigger than 90% of all 19-day-old pigs, so this pig’s standardized score is approximately 1.3. This
tells us that the pig weighs approximately
pounds.
17. a. Since the mean of 4, 8, 0, 0, and 5 is
Powered by Cognero
, this sample is represented within the third bar of the histogram.
Page 14
Name:
Class:
Date:
Semester Review
b. Since the standard deviation of the data displayed in this histogram is clearly less than that of the data displayed by the
histogram in Part a, the sample size must be larger than 5.
Powered by Cognero
Page 15