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Texas End of Course Exams Are You Ready? presented by Sheila Hoza Cunningham, EdD Adjunct Professor UT Arlington for Sam Houston State University February 19, 2011 drsgh@att.net. Why Are We Here?. Awareness of EOC TAKS vs EOC Impact on teaching and assessment. EOC Requirements.

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slide1

Texas End of Course ExamsAre You Ready?presented bySheila Hoza Cunningham, EdDAdjunct Professor UT ArlingtonforSam Houston State UniversityFebruary 19, 2011drsgh@att.net

why are we here
Why Are We Here?
  • Awareness of EOC
  • TAKS vs EOC
  • Impact on teaching and assessment
eoc requirements
EOC Requirements
  • The purpose is to measure students’ academic performance in core high school courses and to become part of the graduation requirements beginning with the freshman class of 2011–2012
slide5

The EOC assessments for lower-level courses (Algebra I and Geometry) must include questions to determine readiness for advanced coursework. The assessments for higher-level courses (Algebra 2) must include a series of special purpose questions to measure college readiness and the need for developmental coursework in higher education.

readines standards
Readines Standards

Readiness Standards Meet One or More of the Following

  • Are essential for success in the current grade or course
  • Are important for preparedness for the next grade or course
  • Support college and career readiness
  • Necessitate in-depth instruction
  • Address broad and deep ideas

TEA Student Assessment Update

staar
STAAR

Readiness and Supporting Standards

  • Readiness and Supporting Standards are identified in the assessed curriculum documents.
  • These documents are posted on the TEA student assessment website at http://www.tea.state.tx.us/student.assessment/staar/.

Texas Education Agency

Student Assessment Division

staar8
STAAR

Readiness Standards

  • Encompass 30–40% of the eligible TEKS
  • Will make up 60–65% of the assessment

Supporting Standards

  • Encompass 60–70% of the eligible TEKS
  • Will make up 35–40% of the assessment

TEA Student Assessment Update

staar9
STAAR

Algebra II Assessment—Eligible TEKS for Assessment

(2A.11) Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to

(A) develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses; Readiness Standard (60-65%)

(B) use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior; Supporting Standard (35-40%)

(C) determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities; Supporting Standard (35-40%)

(D) determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods; Supporting Standard (35-40%)

(E) determine solutions of exponential and logarithmic inequalities using graphs and tables; and Supporting Standard (35-40%)

(F) analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem. Readiness Standard (60-65%)

Texas Education Agency Student Assessment Division

staar10
STAAR

Prototype Blueprint

TEA Student Assessment Update

staar11
STAAR

GeometryBlueprint

Texas Education Agency

Student Assessment Division

staar12
STAAR

Release of Test Questions

  • Primary forms of STAAR will be released every three years as required
  • TEA may defer releasing assessments to the extent necessary to develop additional assessments
  • Prior to 2012, TEA plans to release a small set of assessment items

TEA Student Assessment Update

staar13
STAAR

Griddable Questions

  • A type of open-ended question used for science and mathematics assessments
  • Purpose is to provide students opportunities to derive answers independently without being influenced by answer choices provided with the questions

Texas Education Agency

Student Assessment Division

staar14
STAAR
  • Algebra I, Geometry, and Algebra II
    • Will have 5 griddable questions
    • Will use new grid

Texas Education Agency

Student Assessment Division

staar15
STAAR

Griddable Questions for High School

  • Correct answer can be positive or negative number.
  • If answer is negative number, students must enter a negative sign; otherwise answer will default to positive.
  • Answer grid includes a floating decimal point.
  • If answer is a decimal number, students must enter a decimal point.

Texas Education Agency

Student Assessment Division

staar16
STAAR

Griddable Questions for High School

  • Students must enter their answer in the boxes (paper and online) and then fill in the corresponding bubbles (paper only).
  • Students do not have to use all the boxes.
  • Students can place their answer in any set of consecutive boxes.
  • Extra zeros may be filled in (either before or after the answer) as long as their placement does not affect the value of the answer.

Texas Education Agency

Student Assessment Division

staar17
STAAR

Calculator Requirements

  • Each student must have a graphing calculator to use throughout the test (both paper and online)
    • Algebra I
    • Geometry
    • Algebra II

Texas Education Agency

Student Assessment Division

staar18
STAAR
  • Resources available
    • Description of the new assessment model
    • Comparison of TAKS and STAAR
    • Assessed curriculum
    • Assessment blueprints
    • Reference materials
    • Griddable item format
    • Assessing process skills
  • Resources still to come—sample items
  • Posted on the TEA student assessment website at http://www.tea.state.tx.us/student.assessment/staar/

Texas Education Agency

Student Assessment Division

staar19
STAAR
  • Testing policies still being discussed
    • Accommodations
    • Time limits
    • One day administrations versus testing windows
    • Substitute assessments
    • Test release plan

Texas Education Agency

Student Assessment Division

staar20
STAAR

Performance Standards for EOC Assessments

  • Standards will be set in February 2012 prior to first high stakes administration in spring 2012.
  • First reports with performance standards applied will be available in late spring 2012.
  • First retests will be offered in summer 2012.

Texas Education Agency

Student Assessment Division

staar21
STAAR

EOC Assessments

  • Algebra II and English III assessments will include a performance standard that indicates college readiness.
  • Research will be conducted to investigate a college-readiness component for science and social studies EOC assessments.

Texas Education Agency

Student Assessment Division

staar22
STAAR

Graduation Requirements

  • In order to graduate, a student must achieve a cumulative score that is at least equal to the product of the number of EOC assessments taken in that content area and a scale score that indicates satisfactory performance.
  • For each of the four core content areas, the cumulative score ≥ n x passing scale score, where n = number of assessments taken.

Texas Education Agency

Student Assessment Division

staar23
STAAR

Graduation Requirements

  • A student must achieve a minimum score, as determined by the commissioner, for the score to count towards the student’s cumulative score.
  • A student’s cumulative score is determined using the student‘s highest score on each EOC assessment.

Texas Education Agency

Student Assessment Division

staar24
STAAR

Graduation Requirements

  • For students on the minimum high school program, the cumulative score is based on the number of courses taken for which an EOC assessment exists.
  • For students on the minimum high school program, the cumulative score requirement may vary by subject area.

Texas Education Agency

Student Assessment Division

staar25
STAAR

Graduation Requirements

  • In addition to meeting the cumulative score requirement in each of the four core content areas, students on the recommended high school program have to pass EOC assessments for
    • Algebra II
    • English III

Texas Education Agency

Student Assessment Division

staar26
STAAR

Graduation Requirements

  • A student’s score on an EOC assessment will be worth 15% of the student’s final grade for that course.
  • A school district is not required to use the student’s score on subsequent administrations to determine the student’s final grade for that course

Texas Education Agency

Student Assessment Division

staar27
STAAR

Graduation Requirements

  • In the future, TEA is planning three administrations of EOC assessments each year for
    • Students who complete the course at different times of the year
    • Retest opportunities
  • TEA is planning EOC administrations at the end of
    • Spring
    • Summer
    • Fall

Texas Education Agency

Student Assessment Division

eoc expectations
EOC Expectations

Graduation Requirements

  • If a student does not achieve the minimum score on an EOC assessment, the student shall retake the assessment
  • If a student does not perform satisfactorily on the college-readiness component of the EOC assessments for Algebra II or English III, the student may retake the assessment

TEA Student Assessment Update

staar29
STAAR

Graduation Requirements

  • For middle school students who take a high school course (e.g., Algebra I) prior to spring 2012, TEA is considering several options.
    • Students would not be required to take that particular EOC assessment. Their cumulative score for that content area would decrease.
    • Students could choose to take that particular EOC assessment in spring 2012 or beyond. If they take the assessment, the score they receive would only be used in their cumulative score if it benefitted the students.

Texas Education Agency

Student Assessment Division

staar30
STAAR

Graduation Requirements

  • For freshman who complete a high school course in fall 2011 (e.g., students on an accelerated block schedule), TEA is considering several options.
    • Students would not be required to take that particular EOC assessment. Their cumulative score for that content area would decrease.
    • Students could choose to take that particular EOC assessment in spring 2012 or beyond. If they take the assessment, the score they receive would only be used in their cumulative score if it benefitted the students.

Texas Education Agency

Student Assessment Division

eoc expectations31
EOC Expectations

Graduation Requirements

  • A student is not required to retake a course as a condition of retaking an EOC assessment
  • A school district shall provide accelerated instruction to each student who fails to perform satisfactorily on an EOC assessment

TEA Student Assessment Update

current eoc assessments
Current EOC Assessments

Spring 2011 Administrations

  • Most campuses have been assigned mandatory operational testing in
    • Algebra I
    • Geometry
    • Algebra II
  • Includes online and paper modes
  • Testing window is May 9–27
  • Reports will be available to districts

Texas Education Agency

Student Assessment Division

current eoc assessments33
Current EOC Assessments
  • Statewide summary reports for 2008–2010 are available on the TEA student assessment website at http://www.tea.state.tx.us/index3.aspx?id=5155&menu_id=793.
  • Statewide summary reports include “All Students”; this refers only to those students who participated in the EOC assessments.

Texas Education Agency

Student Assessment Division

current eoc assessments34
Current EOC assessments

Algebra I EOC Assessment Performance

TEA Student Assessment Update

current eoc assessments35
Current EOC assessments

Geometry EOC Assessment Performance

TEA Student Assessment Update

curriculum expectations
Curriculum Expectations
  • TEKS Revision – Implemented 2006
  • Textbook Implementation 2007-2008
  • TEKS Revision - 2009 (CRS)
slide38
Term“zeros” of linear functions
  • NEW! Connect “y=” to “f(x)=” moved to Alg. I from Alg. II
  • Added determine domain and range values; Specified:
      • Continuous data
      • Discrete data
slide39
Specified scatterplot data:
    • Positive correlation
    • Negative correlation
    • No correlation

for linear situations

slide40
Connect terminology for solutions:

Solutions

Roots

Zeros

x-intercepts

Horizontal Intercept

properties and attributes of functions
Properties and Attributesof Functions
  • A.4(C) connect the function notation of y = x + 1 and f(x) = x + 1.

This is a new Student Expectation

a sample of a 4 c
A Sample of A.4(C)

A f(m) = 1.90 + 1.60

B f(m) = 1.90m + 1.60

C f(m) = 1.60m + 1.90

D f(m) = 1.90m + 1.60m

(Massachusetts Grade 10 2005)

geometric relationships and spatial reasoning
Geometric Relationships and Spatial Reasoning
  • G.5(A) use numeric and geometric patterns to develop algebraic expressions representing geometric properties.

This is a completely revised

Student Expectation

a sample of g 5 a
A Sample of G.5(A)

(Massachusetts Grade 10 November 2005)

2 and 3 dimensional geometric relationships and shapes
2- and 3-Dimensional Geometric Relationships and Shapes
  • G.7(A) use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures.

Additional geometric figure included

a sample of g 7 a
A Sample of G.7(A)

(North Carolina Geometry EOC – Goal 2)

2 and 3 dimensional geometric relationships and shapes48
2- and 3-Dimensional Geometric Relationships and Shapes
  • G.7(C) derive and use formulas involving length, slope, and midpoint.

Additional characteristic and formula

related to lines included

a sample of g 7 c
A Sample of G.7(C)

(Massachusetts Grade 10 November 2004)

another sample of g 7 c
Another Sample of G.7(C)

(Virginia Geometry EOC Spring 2003)

measurement and similarity
Measurement and Similarity
  • G.8(A) find areas of regular polygons, circles, and composite figures;

Additional geometric figure included

a sample of g 8 a
A Sample of G.8(A)

(Massachusetts Grade 10 March 2005)

some of the changes
Some of the Changes
  • Moved to Algebra I - Ab2(C) The student connects the function notation of “y = “ and “f(x) =“
  • Linear is one of 7 specific parent functions;
  • Knowledge of linear parameter changes assumed
  • Parameter changes applied to other functions such as hyperbolic
taks vs eoc
TAKS vs EOC
  • TAKS – 10 objectives including content from grade 8
  • Algebra I EOC – 5 Objectives focusing on the assessment of Algebra I content
  • Geometry EOC – 5 Objectives focusing on the assessment of Geometry content
  • Algebra II EOC - ?????? – More to Come
algebra eoc objectives
Algebra EOC Objectives
  • Objective 1 Functional Relationships
  • Objective 2 Properties and Attributes of Functions
  • Objective 3 Linear Functions
  • Objective 4 Linear Equations and Inequalities
  • Objective 5 Quadratic and Other Nonlinear Functions
geometry eoc objectives
Geometry EOC Objectives
  • Objective 1 Geometric Structure
  • Objective 2 Geometric Patterns
  • Objective 3 Dimensionality and the Geometry of Location
  • Objective 4 Congruence and the Geometry of Size
  • Objective 5 Similarity and the Geometry of Shape
how can we be prepared
How Can We Be Prepared
  • Strategic Planning for Student Success
  • Understanding the Strengths and Weaknesses of Our Students
  • Thorough Knowledge of Student Expectations Tested
  • Understanding of What Test Items Might Look Like
foundational belief
Foundational Belief

. . . quality student achievement includes and goes beyond

achieving the highest rating awarded by state and national accountability standards.

slide62

Expectation

We will raise the performance

of all students and close the achievement gap.

slide63
“We must study the curriculum from the viewpoint of the assessment…This does not mean that we are teaching the test.”
slide64

Identifying Required Thinking

Processes and Skills

  • Identify the specific higher-level thinking and logical reasoning skills embedded in the state curriculum and tested on the state assessment
  • Verify the relationship between the verbs in the student expectation (SE) and the levels of thinking tested on the 2003, 2004, 2006, 2009 released state tests.
deconstructing an se
Deconstructing an SE
  • A1d The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities
a1d the student is expected to
A1d The student is expected to…
  • represent relationships among quantities using concrete models
  • represent relationships among quantities using tables
  • represent relationships among quantities using graphs
  • represent relationships among quantities using diagrams
a1d the student is expected to67
A1d The student is expected to…
  • represent relationships among quantities using verbal descriptions
  • represent relationships among quantities using equations
  • represent relationships among quantities using inequalities
deconstructing an se68
Deconstructing an SE
  • G5b The student is expected to use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles
g5b the student is expected to
G5B The student is expected to…
  • use numeric patterns to make generalizations about geometric properties, including properties of polygons
  • use numeric patterns to make generalizations about geometric properties, including ratios in similar figures and solids
g5b the student is expected to70
G5b The student is expected to…
  • use numeric patterns to make generalizations about geometric properties, including angle relationships in polygons and circles
  • use geometric patterns to make generalizations about geometric properties, including properties of polygons
g5b the student is expected to71
G5b The student is expected to…
  • use geometric patterns to make generalizations about geometric properties, including ratios in similar figures and solids
  • use geometric patterns to make generalizations about geometric properties, including angle relationships in polygons and circles
deconstructing an se72
Deconstructing an SE
  • 2A4a The student is expected to identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2), exponential (f(x) = ax), and logarithmic (f(x) = logax) functions , absolute value of x (f(x) = |x|), square root of x (f(x) = vx), and reciprocal of x (f(x) = 1/x)
2a 4a the student is expected to
2A.4a The student is expected to
  • identify graphs of parent functions, including linear (f(x) = x)
  • sketch graphs of parent functions, including linear (f(x) = x)
  • identify graphs of parent functions, including quadratic (f(x) = x2)
  • sketch graphs of parent functions, including quadratic (f(x) = x2)
2a 4a the student is expected to74
2A.4a The student is expected to
  • identify graphs of parent functions, including exponential (f(x) = ax)
  • sketch graphs of parent functions, including exponential (f(x) = ax)
  • identify graphs of parent functions, including logarithmic (f(x) = logax) functions
  • sketch graphs of parent functions, including logarithmic (f(x) = logax) functions
2a 4a the student is expected to75
2A.4a The student is expected to
  • identify graphs of parent functions, including absolute value of x (f(x) = |x|)
  • sketch graphs of parent functions, including absolute value of x (f(x) = |x|)
  • identify graphs of parent functions, including square root of x
  • sketch graphs of parent functions, including square root of x
2a 4a the student is expected to76
2A.4a The student is expected to
  • identify graphs of parent functions reciprocal of x (f(x) = 1/x)
  • sketch graphs of parent functions reciprocal of x (f(x) = 1/x)
critical component
Critical Component

Cognitive Alignment

  • Does the verb in the Student Expectation match the steps in thinking required for answering the questions correctly?
  • What is the level of the question?
  • What text evidence ( in the passage) provides the correct answer for the Level 1 & 2 questions in which the answer is stated?
  • What text evidence supports the correct answer for the Level 3 &4 questions in which the answer is not stated?

(inferred or implied)

level of questions
Level of Questions
  • Level 1: Concept Level
    • Answer requires understanding of the concept at the concept (noun) and skill (thinking-verb) level without the context of a problem situation
  • Level 2: Operations Level
    • Answer requires making an operation decision about which operation to use to solve the problem situation-addition, subtraction, multiplication, or division-and computation to solve the problem.
level of questions79
Level of Questions
  • Level 3: Problem-Solving/Application Level
    • Answer requires applying one or more concepts within one specific TEKS curriculum strand in a complex problem-solving situation.
  • Level 4: Mathematical Processes and Tools
    • Answer requires applying one or more concepts across all TEKS curriculum strands in a complex problem situation.
ongoing assessment
Ongoing Assessment
  • All assessments should be written prior to instruction and reflect the depth and complexity of the TEKS
  • The assessments should use the nouns, verbs, vocabulary and synonyms used in the student expectations
slide81

“Schools that display and teach the nouns, verbs, and vocabulary in the context of the Student Expectation (SE) for the lesson had scores that went through the roof!”

Margaret Kilgo

slide82

“If the SE’s are taught to the depth and complexity to which they are tested, then students will be successful on the assessment regardless of socio-economic status.”

M. Kilgo

preparing for eoc
Preparing for EOC
  • Curriculum alignment with assessment expectations
  • Ongoing…weekly throughout the year
  • Systematic…focus on weakest areas using a standard process for problem solving
  • Final push…EOC Short Course/Review
campus district eoc to taks transition data
Campus/District EOC toTAKS Transition Data
  • As a group, define the following:
    • Strength
    • Marginal Weakness
    • Significant Weakness
transition data definition
Transition DataDefinition
  • Data for student performance on students expectations that were previously tested on TAKS and will now be tested on EOC
algebra i eoc geometry eoc to taks transition data
Algebra I EOC/Geometry EOC toTAKS Transition Data
  • In pairs, look at your Algebra I EOC or Geometry EOC to TAKS Transition Data, discuss the areas that you consider to be a significant weakness in student performance for your campus/district.
  • Based on your experiences in working with students and teachers on your campus, discuss what you believe to be the cause of these weaknesses.
algebra i eoc geometry eoc to taks transition data88
Algebra I EOC/Geometry EOC toTAKS Transition Data
  • List three strategies for improving these areas on your campus.
  • Discuss how you can address the areas of Algebra I/Geometry that have not previously been assessed to ensure that your students are prepared for EOC.
slide90

Algebra I A2d

Five students in Miss Brown’s algebra class reported the number of hours that they studied for a test. The number of hours and their test scores are in the table below.

According to a line of best fit for the data, what is the predicted test score of a student who studied 1 hour for the

test?

A 75 B 78 C 81 D 84

North Carolina EOC Sample Question

slide91

Algebra I A11b

In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board.  If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 6 feet long?

slide92

Algebra I A11c

A city’s population, P (in thousands),can be modeled by the equation P = 130(1.03)x , where x is the number

of years after January 1, 2000.

For what value of x does the model predict that the population of the city will be approximately 170,000?

A 8

B 9

C 10

D 11

North Carolina EOC Sample Question

slide93

Geometry G2a

Which statement is demonstrated by the following construction?

A Through a point not on a given line, exactly one line can be drawn perpendicular to the given line.

B If two lines cut by a transversal form congruent alternate interior angles, then the two lines are parallel.

C If two lines cut by a transversal form congruent corresponding angles, then the two lines are parallel.

D If two lines cut by a transversal form same side interior angles that are supplementary, then the two lines are parallel.

slide94

Geometry G2a

The diagram shows a method for constructing

A a perpendicular from a point to a line

B a perpendicular through a point on a line

C a line parallel to a given line through a given point

D a circle through a given point on a line

slide95

Geometry G3a

Which of the following statements is false but its converse is true?

I If you have a ticket, then you will win the lottery.

II If a number is divisible by 3, then it is divisible by 6.

III If quadrilateral ABCD is a rhombus, then it is a square.

A I only B II only

C III only D I, II and III

slide96

Geometry G3b

Which statement is always true about a parallelogram?

A Diagonals bisect each other.

B Diagonals are perpendicular.

C Adjacent sides are congruent.

D Diagonals bisect the angles.

slide97

Geometry G3c

Two lines, AB and CD , intersect at point E. Which of the following must contain all the same points as the two intersecting lines?

A quadrilateral ABCD

B triangles AED and CED

D plane containing points A, B and E

E plane containing points A, C and E

slide98

Geometry G3c

There are 26 boys on the high school football team. Many of them are also involved in other sports: 15 play baseball, 11 do wrestling, and 13 do track-and-field. Of these:

4 play baseball and do track-and-field.

3 play baseball and do wrestling.

2 do wrestling and track-and-field.

3 play baseball, do wrestling and do track-and-field.

How many boys on the football team are not involved in any of the other three sports?

A 1 B 2

C 3 D 4

slide99

Geometry G3d

Marcella looks at the pyramid below and determines that the pattern for the number of blocks is 1, 4, 9, 16…

Based on the pattern, Marcella predicts that the tenth layer will have 100 blocks. What kind of reasoning is Marcella using?

A inductive

B deductive

C guess and check

D process of elimination

slide100

Geometry G3e

Look at the following statements:

Judy Smith is a student at Galena Park High.

All students at Galena Park High are between 13 and 19 years of age.

Judy Smith is between 13 and 19 years of age.

If the statements are turned into a deductive argument, and possibly re-ordered, which statement must be the conclusion?

A Judy Smith is a student at Galena Park High.

B All students at Galena Park high are between 13 and 19 years of age.

C Judy Smith is between 13 and 19 years of age.

D none, since the statements cannot be turned into a deductive argument

slide101

Geometry G6a

The picture shows a knife and a stick of butter.

 Assume the knife is like a plane and the butter is a rectangular solid with AB = BC. The knife will cut through the butter at points D, E and F .

If AD < BE and BE = CF, then the intersection of the knife and butter will

be a _________

A square B rectangle

C rhombus D trapezoid

slide102

In the figure, k, m and n are three parallel line segments. Which of the following statements justifies the conclusion that

A If with transversal t, then alternate interior angles are congruent.

B If with transversal t, then vertical angles are congruent.

C If with transversal t, then alternate exterior angles are congruent.

D If with transversal t, then corresponding angles are congruent.

slide103

Geometry G9c

Shanelle and Leon were asked to use their protractors to measure the pairs of base angles in isosceles trapezoid ABCD (shown in the diagram). They recorded their measurements in the following table.

Using inductive reasoning what might you conclude about pairs of base angles in an isosceles trapezoid?

A base angles are supplementary B base angles are congruent

C base angles are complementary D there is no pattern

slide104

Geometry G9c

Which of the following statements are true about a circle?

I All of its chords are congruent.

II The total number of degrees is 360.

III It has exactly two diameters.

A I only

B II only

C III only

D all of the statements are true

slide105

Geometry G9d

Which three-dimensional figure's base and faces are not the same shape?

A rectangular prism

B cube

C triangular pyramid

D rectangular pyramid

slide106

Geometry G10b

If the triangles can be proved congruent using only the information marked on the diagram, give the congruence statement and the reason that supports this statement?

slide107

Geometry G11c

Use the diagram to find the value of x.

A 6 B 8

C 9 D 10

slide108

2A.1a

At 3.6 calories burned per pound of weight each hour, the calories, c, burned in hours, h , by a 125 pound person walking briskly can be modeled by c = 125(3.6) h. For a walk of up to 5 hours, identify the domain and range.

A D: { 0, 1, 2, 3} R: { 0,1,2,…1056}

B D: { 0, 1, 2, 3, 4, 5 } R: { 0, 1, 2,…2250}

C D: { all real numbers } R: { all real numbers }

D D: { -5, -4, -3…} R: { 0, 1, 2…2700}

slide109

2A.3b

Which graph accurately shows the

solution to the system ?

What is the solution to the system?

slide110

A2.8a

Which situation described below would best be modeled using a quadratic equation?

A The volume of a sphere is a function of the radius of the sphere.

B At Sue’s Ice Cream Parlor, the price of a single scoop of ice cream is a function of the number of toppings put onto the ice cream. (Each topping costs the same amount.)

C A sports banner company, Banners Galore, makes its rectangular-shaped banners with a length to width ratio of 4:1. The area of the banner is a function of the length of the banner.

D In a single-elimination card tournament, the number of teams remaining after each round is a function of the number of rounds that have been played.

slide111

2A.2b

North Carolina Algebra 2 EOC Released Question

slide112

2A.2a

North Carolina Algebra 2 EOC Released Question

slide114

2A.11b

North Carolina Algebra 2 EOC Released Question

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