MATH 8B
Mathematics, Grade 8, Second Semester
#8127 (v.2.1)
To the Student:
After your registration is complete and your proctor has been approved, you may take the
Credit by Examination for Mathematics, Grade 8, second semester.
WHAT TO BRING
• several sharpened No.2 pencils
• lined notebook paper
• graph paper
• straight edge
ABOUT THE EXAM
The examination for the second semester of Grade 8 mathematics consists of 40 questions
and is based on the Texas Essential Knowledge and Skills (TEKS) for this subject. The
full list of TEKS is included at the end of this document (it is also available online at the
Texas Education Agency website, http://www.tea.state.tx.us/). The TEKS outline specific
topics covered in the exam, as well as more general areas of knowledge and levels of
critical thinking. Use the TEKS to focus your study in preparation for the exam.
For the exam, you must be able to do the following:
• generate a different representation of data given another representation of data
(such as a table, graph, equation, or verbal description);
• predict, find, and justify solutions to application problems using appropriate tables,
graphs, and algebraic equations;
• find and evaluate an algebraic expression to determine any term in an arithmetic
sequence;
• draw three-dimensional figures from different perspectives;
• use geometric concepts and properties to solve problems;
• find lateral and total surface area of prisms, pyramids, and cylinders using concrete
models and nets;
• connect models of prisms, cylinders, pyramids, spheres, and cones to formulas;
• estimate measurements and use formulas to solve application problems involving
lateral and total surface area and volume;
4/12
www.ttusid.ttu.edu
• describe the resulting effect on volume when dimensions of a solid are changed
proportionally;
• find the probabilities of dependent and independent events;
• use theoretical probabilities and experimental results to make predictions;
• select and use different models to simulate an event;
• select appropriate measure of central tendency or range to describe a set of data and
justify the choice;
• draw conclusions and make predictions by analyzing trends in scatterplots;
• select and use an appropriate representation for presenting and displaying
relationships among collected data;
• evaluate methods of sampling to determine validity of an inference made from a set
of data;
• recognize misuses of graphical or numerical information and evaluate predictions
and conclusions based on data analysis;
• solve problems connected to everyday experiences, communicate through informal
mathematical language and models, and use reasoning to make conjectures and
verify conclusions.
Since questions are not taken from any one source, you can prepare by reviewing any of
the state-adopted textbooks that are used at your school. The textbook used with our
MATH 8B course is:
Randall I. Charles, et al. (2008). Texas Mathematics: Course 3. Boston,
MA.: Pearson Prentice Hall. ISBN 0-13-134010-7
If you choose to purchase this textbook, you should study the following:
• Chapter 6 (sections 6-1 to 6-3)
• Chapter 11 (section 11-1)
• Chapter 7 (sections 7-1, 7-2, 7-4, 7-5, 7-6, and 7-7)
• Chapter 8 (sections 8-1 to 8-8)
• Chapter 9 (sections 9-1 to 9-9)
• Chapter 5 (section 5-8)
• Chapter 10 (section 10-1 to 10-4)
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You will have three hours to complete the CBE. A formula chart will be provided for you.
You will NOT be allowed to use a calculator. You may not use any notes or books. A
percentage score from the examination will be reported to the official at your school.
A sample exam and an answer key are included in this document to let you practice the
way you will work the problems on the actual CBE. Work the sample problems according
to the directions given, then check your answers with the key that follows. This may
indicate some areas where you need more study. Remember, the sample exam is intended
only to illustrate the format of the actual exam, not to serve as a comprehensive review
sheet. If you study only the problems on the sample exam, you will not be adequately
prepared for the CBE.
For more information about CBE policies, visit http://www.uc.ttu.edu/takeacbe/.
Good luck on your examination!
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Texas Essential Knowledge and Skills
MATH 8 – Mathematics, Grade 8
§111.24. Mathematics, Grade 8.
(a) Introduction.
(1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 8 are using basic principles of algebra to analyze and
represent both proportional and non-proportional linear relationships and using probability to describe data and make predictions.
(2) Throughout mathematics in Grades 6-8, students build a foundation of basic understandings in number, operation, and quantitative reasoning;
patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use
concepts, algorithms, and properties of rational numbers to explore mathematical relationships and to describe increasingly complex situations.
Students use algebraic thinking to describe how a change in one quantity in a relationship results in a change in the other; and they connect
verbal, numeric, graphic, and symbolic representations of relationships. Students use geometric properties and relationships, as well as spatial
reasoning, to model and analyze situations and solve problems. Students communicate information about geometric figures or situations by
quantifying attributes, generalize procedures from measurement experiences, and use the procedures to solve problems. Students use appropriate
statistics, representations of data, reasoning, and concepts of probability to draw conclusions, evaluate arguments, and make recommendations.
(3) Problem solving in meaningful contexts, language and communication, connections within and outside mathematics, and formal and informal
reasoning underlie all content areas in mathematics. Throughout mathematics in Grades 6-8, students use these processes together with graphing
technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve problems as they do
mathematics.
(b) Knowledge and skills.
(1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different
situations. The student is expected to:
(A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals;
(B) select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships;
(C) approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as p, Ö2);
(D) express numbers in scientific notation, including negative exponents, in appropriate problem situations; and
(E) compare and order real numbers with a calculator.
(2) Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify
solutions. The student is expected to:
(A) select appropriate operations to solve problems involving rational numbers and justify the selections;
(B) use appropriate operations to solve problems involving rational numbers in problem situations;
(C) evaluate a solution for reasonableness; and
(D) use multiplication by a given constant factor (including unit rate) to represent and solve problems involving proportional relationships
including conversions between measurement systems.
(3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem
situations and solves problems. The student is expected to:
(A) compare and contrast proportional and non-proportional linear relationships; and
(B) estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
(4) Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship.
The student is expected to generate a different representation of data given another representation of data (such as a table, graph, equation, or
verbal description).
(5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and
solve problems. The student is expected to:
(A) predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and
(B) find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change).
(6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to:
4
(A) generate similar figures using dilations including enlargements and reductions; and
(B) graph dilations, reflections, and translations on a coordinate plane.
(7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:
(A) draw three-dimensional figures from different perspectives;
(B) use geometric concepts and properties to solve problems in fields such as art and architecture;
(C) use pictures or models to demonstrate the Pythagorean Theorem; and
(D) locate and name points on a coordinate plane using ordered pairs of rational numbers.
(8) Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to:
(A) find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models);
(B) connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects; and
(C) estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.
(9) Measurement. The student uses indirect measurement to solve problems. The student is expected to:
(A) use the Pythagorean Theorem to solve real-life problems; and
(B) use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.
(10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to:
(A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and
(B) describe the resulting effect on volume when dimensions of a solid are changed proportionally.
(11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is
expected to:
(A) find the probabilities of dependent and independent events;
(B) use theoretical probabilities and experimental results to make predictions and decisions; and
(C) select and use different models to simulate an event.
(12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:
(A) use variability (range, including interquartile range (IQR)) and select the appropriate measure of central tendency to describe a set of data
and justify the choice for a particular situation;
(B) draw conclusions and make predictions by analyzing trends in scatterplots; and
(C) select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line
graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of
technology.
(13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to:
(A) evaluate methods of sampling to determine validity of an inference made from a set of data; and
(B) recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.
(14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday
experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other
mathematical topics;
(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution
for reasonableness;
(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern,
systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and
(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number
sense to solve problems.
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(15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical
language, representations, and models. The student is expected to:
(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic
mathematical models; and
(B) evaluate the effectiveness of different representations to communicate ideas.
(16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student
is expected to:
(A) make conjectures from patterns or sets of examples and nonexamples; and
(B) validate his/her conclusions using mathematical properties and relationships.
Source: The provisions of this §111.24 adopted to be effective September 1, 1998, 22 TexReg 7623; amended to be effective August 1, 2006, 30
TexReg 1930; amended to be effective February 22, 2009, 34 TexReg 1056.
6
MATH 8B Sample Questions
Use your own paper to work the following problems.
Multiple Choice. Identify the choice that best completes the statement or answers the question.
1. Name the solid that has one base that is a rectangle and four lateral surfaces that are
triangles.
A.
B.
C.
D.
square pyramid
cone
rectangular prism
rectangular pyramid
2. Identify the solid that this net forms.
A.
B.
C.
D.
hexagonal prism
hexagonal pyramid
rectangular pyramid
rectangular prism
3. The graphs below show the number of honor-roll students in each grade at Ferndale
Middle School. Which of the following statement is true?
A.
B.
C.
D.
The two graphs are exactly the same.
The two graphs use completely different data.
The scale on the second graph does not distort the lengths of the bars.
The scale on the first graph gives the most accurate picture of the relative number of
honor-roll students for each class.
7
Determine whether or not the following question is biased. Explain.
4. Do you prefer bringing a healthy lunch to school or eating cafeteria food?
A.
B.
C.
D.
Biased; it suggests that cafeteria food is not healthy.
Biased; it assumes that you eat lunch.
Biased; it assumes you bring only healthy lunches to school.
All of the above.
Short Answer
5. Solve the equation 7x + 47 = 5.
6. Solve the equation 3(y + 4) = 30.
7. Simplify the expression –9 – 4(c – 6).
8. Raymond buys bottles of water at $1.50 each and a large pizza at $15.99. The total cost
was $20.49. How many bottles of water b did he buy? Write and solve an equation.
9. Find the next three terms in the sequence 5, 10, 15, 20, …
10. Find the first four terms of the sequence represented by the expression 5n + 1.
11. Find the measure of ∠s in the diagram below.
s
35°
Not drawn to scale
12. Identify the pair of angles ∠3, ∠7 as corresponding, alternate interior, both, or neither.
1
8
7 2
5
l
4
3 6
m
8
13. Classify the triangle by its sides and angles.
14. Find the sum of the measures of the interior angles of a polygon with eight sides.
15. A trapezoid has an area of 210 cm2. The length of one base is 15 cm and the height is 12
cm. What is the length of the other base?
16. Find the circumference of a circle with the given radius or diameter. Round your answer
to the nearest tenth of a foot.
17. Find the area of the shaded region. Round your answer to the nearest tenth of a meter.
18. A circle has a circumference of 80.74 mm. Find the radius and the diameter. Round your
answer to the nearest hundredth of a millimeter.
continued →
9
19. A landscaper can use a base plan to describe the shape of a set of stairs. Draw a base
plan for the given stairs, where each square is equal to one square foot.
20. Use the net below to find the surface area of the cylinder. (drawings are not to scale)
5m
5m
14 m
14 m
5m
continued →
10
21. Find the volume of the solid to the nearest yard.
6 yd
6 yd
9 yd
22. Find the volume of a sphere with a radius of 3.5 m.
23. A cone has a radius of 3 cm and a volume of 396 cm3. Find the volume of a similar cone
with a radius of 6 cm.
24. The numbers below represent the ages of the first ten people in line at the movie theater.
Make a line plot for the data.
22, 30, 23, 22, 27, 27, 29, 23, 30, 22
25. A teacher asks her class of 22 students, “What is your age?” Their responses are shown
below.
15, 15, 17, 15, 18, 19, 16, 17, 15, 17, 17, 15, 16, 15, 14, 19, 15, 19, 14, 17, 16, 16
Find the mean, median, and mode for the data. If necessary, round to the nearest tenth.
26. Find the mode and the median of the data in the stem-and-leaf plot below.
Key: 6 | 3 means 63
continued →
11
27. Ms. Alison drew a box-and-whisker plot to represent her students’ scores on a mid-term
test.
Josh received 47 on the test. Describe how his score compared to those of his classmates.
28. Which of the scatter plots below shows a positive trend?
29. All 500 students at Robinson Junior High were surveyed to find their favorite sport. How
many more students played football than soccer?
Favorite Sports at Robinson Junior High
Soccer
10%
Basketball
27%
Football
38%
Baseball
25%
30. You buy one ticket for a raffle at a fundraiser. If 530 tickets are sold and one winner is
chosen at random, what is your probability of winning? Express this probability as a
percent. Round to the nearest hundredth of a percent.
31. A coin is tossed. If heads appears, a spinner that can land on numbers from 1 to 7 is
spun. If tails appears, the coin is tossed a second time instead of spinning the spinner.
What are the possible outcomes?
For questions 32-34, write your answer as a fraction in simplest form.
32. Food Express is running a special promotion in which customers can win a free gallon of
milk with their food purchase if there is a star on their receipt. So far, 51 of the first 54
customers have not received a star on their receipts. What is the experimental probability
of winning a free gallon of milk?
12
33. You select 31 marbles from a bag. The results are as follows: 10 blue marbles, 7 green
marbles, 5 red marbles, 6 white marbles, and 3 yellow marbles. Find P(not red).
34. Your sock drawer contains 4 pairs of gray socks, 8 pairs of white socks, 6 pairs of black
socks, and 2 pairs of beige socks. You choose a pair of socks from the drawer at random
and then replace it. Then you choose a second pair of socks. Find P(white, then gray).
35. You survey every tenth teenager leaving a movie theater on Sunday night to find out how
often teenagers in your town go to the movies. Is this is a random sample? Explain your
answer and describe the population of the sample.
36. Katalin earns $7.75 for each hour she works. On Friday, she worked for six hours. She
also worked on Saturday. If she earned a total of $100.75 for the two days of work, how
many hours did she work on Saturday?
37. A square pyramid has a 10-cm base length and height of 15 cm. A cone has a base
diameter of 10 cm and a height of 15 cm. Which has a greater volume? Explain.
38. Ricardo is wrapping a gift to take to a party and needs a box for the gift. The only box he
has measures 4 in. × 5 in. × 7 in. He needs a box with measurements two times as large.
What is the volume of the box Ricardo needs? How does the volume needed compare to
that of the box he already has?
39. Mr. Green teaches band, choir, and math. This year, there are 51 students who take at
least one of his classes. He teaches band to 28 students. There are 40 students who take
either band or choir or both. There are seven students who take both math and choir with
Mr. Green.
A. Complete the Venn diagram below.
B. How many students take exactly 2 classes from Mr. Green?
Math
6
13
5
Band
10
Choir
continued →
13
40. A box contains 88 pink rubber bands and 55 brown rubber bands. You select a rubber
band at random from the box. Find each probability. Write the probability as a fraction
in simplest form.
A. Find the theoretical probability of selecting a pink rubber band.
B. Find the theoretical probability of selecting a brown rubber band.
C. You repeatedly choose a rubber band from the box, record the color, and put the
rubber band back in the box. The results are shown in the table below. Find the
experimental probability of each color based on the table.
Outcome Occurrences
pink
35
brown
50
14
Sample Exam Answer Key
Multiple Choice
1. D
2. D
3. D
4. D
5. –6
19.
6. 6
7. 15 – 4c
3
3
3
2
2
3
1
1
3
8. 1.50b + 15.99 = 20.49; three bottles
Right
Short Answer
Front
9. 25, 30, 35
20. about 597 m2
10. 6, 11, 16, 21
21. 108 yd3
11. 55°
22. 180 m2
12. corresponding
23. 3,168 cm3
13. isosceles right
24.
14. 1,080°
15. 20 cm
16. 36.4 ft.
17. 214.2 m
25. 16.2; 16; 15
2
26. 82; 72
18. 12.85 mm; 25.7 mm
continued →
15
27. About 75% scored higher; about 25% scored lower.
28. III
29. 140 students
30. 0.19%
31. (T, H), (T, T), (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (H, 7)
32.
1
18
33.
26
31
34.
2
25
35. Not a random sample; the survey does not include teenagers who do not go to the movies
or those who did not go out to see a movie on Sunday. The population is teenagers in
your town.
36. 7 hours
37. The square pyramid; V = Bh, so the volume of the pyramid is (102)(15) = 1500 cm3. The
volume of the cone is 52π(15) = 1178.1 cm3.
38. 1120 in.3 ; the volume of the box Ricardo needs is 8 times that of the box he has.
39. A.
Math
11
6
13
Band
2
5
10
4
Choir
B. 12 students
40. A. P(pink) =
8
13
B. P(brown) =
C. P(pink) =
5
13
7
10
; P(brown) =
17
17
16
Grade 8
Mathematics Chart
LENGTH
Metric
Customary
1 kilometer = 1000 meters
1 mile = 1760 yards
1 meter = 100 centimeters
1 mile = 5280 feet
1 centimeter = 10 millimeters
1 yard = 3 feet
1 foot = 12 inches
CAPACITY AND VOLUME
Metric
1 liter = 1000 milliliters
Customary
1 gallon = 4 quarts
1 gallon = 128 fluid ounces
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces
MASS AND WEIGHT
Metric
Customary
1 kilogram = 1000 grams
1 ton = 2000 pounds
1 gram = 1000 milligrams
1 pound = 16 ounces
TIME
1 year = 365 days
1 year = 12 months
1 year = 52 weeks
1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Continued on reverse
17
Grade 8 Mathematics Chart
square
rectangle
P = 4s
P = 2l + 2w
Circumference
circle
C = 2πr
Area
square
rectangle
A = s2
A = lw
triangle
A=
1
bh
2
trapezoid
A=
1
( b1 + b2 ) h
2
Perimeter
circle
A = πr
or P = 2(l + w)
or C = πd
or A = bh
or A =
bh
2
or A =
( b1 + b2 ) h
2
2
P represents the Perimeter of the Base of a three-dimensional figure
B represents the Area of the Base of a three-dimensional figure.
Surface Area
Volume
Pi
cube (total)
prism (lateral)
prism (total)
S = 6s 2
S = Ph
S = Ph + 2B
pyramid (lateral)
S=
1
Pl
2
pyramid (total)
S=
1
Pl + B
2
cylinder (lateral)
S = 2πrh
cylinder (total)
S = 2πrh + 2πr 2
prism
cylinder
V = Bh
V = Bh
pyramid
V=
1
Bh
3
cone
V=
1
Bh
3
sphere
V=
4 3
πr
3
π
π ≈ 3.14
or
Pythagoream Theorem
a2 + b2 = c2
Simple Interest Formula
I = prt
18
or S = 2πr(h + r)
π≈
22
7