Liberal Arts Mathematics
Reporting Category
Standard
Benchmark Number
Benchmark
Also Assesses or Assessed
by
Item Types
Benchmark Clarification
Content Limits
Algebra
Real and Complex Number Systems
MA.912.A.1.3:
Simplify real number expressions using the laws of exponents.
Blank
Stimulus Attributes
Blank
Response Attributes
Blank
Sample Item
Blank
Blank
Blank
Blank
1
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Algebra
Real and Complex Number Systems
MA.912.A.1.4:
Perform operations on real numbers (including integer exponents, radicals, percents,
scientific notation, absolute value, rational numbers, irrational numbers) using multi-step
and real-world problems.
Blank
Also
Assesses or
Assessed by
Blank
Item Types
Benchmark Blank
Clarification
Blank
Content
Limits
Blank
Stimulus
Attributes
Blank
Response
Attributes
Sample Item Blank
2
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses or
Assessed by
Item Types
Benchmark
Clarification
Content Limits
Stimulus
Attributes
Response
Attributes
Sample Item
Algebra
Real and Complex Number Systems
MA.912.A.1.8:
Use the zero product property of real numbers in a variety of contexts to identify
solutions to equations.
Blank
Blank
Blank
Blank
Blank
Blank
Blank
3
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also
Assesses or
Assessed by
Item Types
Benchmark
Clarification
Content
Limits
4
Algebra
Relations and Functions
MA.912.A.2.3
Describe the concept of a function, use function notation, determine whether a given
relation is a function, and link equations to functions.
N/A
This benchmark will be assessed using MC and FR items.
Students will identify and/or analyze relations and functions given in various forms,
including graphs, tables, sets of ordered pairs, and equations.
Items may ask students to write given functions as equations. In items that require
students to determine the equation of a function, only continuous linear and/or quadratic
functions should be used. Items presenting a relation as a set of ordered paris may not
exceed 6 ordered pairs in the set. In items presenting relations as graphs for the purpose
of determining if the relations is a function, the graph need not be continuous. Items
should utilize function notation as appropriate.
Items may be set in either real-world or mathematical contexts.
Stimulus
Attributes
Fill-in response items may require that students provide a slope or the x-coordinate (or yResponse
coordinate) of a point of interest. Fill in response items may have a negative answer.
Attributes
Sample Item Sample Item 1 FR
For one child, a childcare facility charges $300 per month for preschool and $3.50 per
hour of childcare after preschool. The function below can be used to determine f (h), the
monthly fee for childcare and preschool, where h represents the number of hours spent in
childcare after preschool. f(h) = 300 + 3.5h If the one-month charges for one child
totaled $637.75, what was the total number of hours the child spent in childcare after
preschool?
9
6
.
5
Sample Response: 96.5
Item Context: Real World, Mathematics
Liberal Arts Mathematics
5
Reporting Category
Standard
Benchmark Number
Benchmark
Item Types
Benchmark
Clarification
Algebra
Linear equations and inequalities
MA.912.A.3.3
Solve literal equations for a specified variable.
This benchmark will be assessed using Multiple Choice items.
Students will manipulate an equation in order to isolate or solve for a
specified variable.
Content Limits
Items must contain more than two variables and require two or more
procedural steps to complete.
Items may be set in either real-world or mathematical contexts.
Formulas could often be used.
Multiple choice responses would have the equation solved for a
variable in several different ways, only one being correct. Fill-in
response or gridded response would not effectively assess this
benchmark.
Sample Item 1 MC
Stimulus Attribute
Response Attributes
Sample Item
Solve the formula P  2l  2w for w.
A. w  P  2l  2
w
B.
P  2l
2
C. w  P  2l
w
D.
P  2l
2
Answer B
Item Context Mathematics
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses or
Assessed by
Item Types
Benchmark
Clarification
Content Limits
Stimulus
Attributes
Response
Attributes
Algebra
Linear equations and inequalities
MA.912.A.3.4
Solve and graph simple and compound inequalities in one variable and be
able to justify each step in a solution.
N/A
This benchmark will be assessed using MC items.
Students will solve simple and compound inequalities and graph solutions
on a number line.
Items will not include inequalities without a solution.
Items may be set in either real-world or mathematical contexts.
Responses could include the inequality and the correct number line graph.
6
Liberal Arts Mathematics
Sample Item
7
Sample Item 1 MC
Taylor has a total of $25 to spend on dinner, which includes a 6.5% sales tax
and a 20% tip. Taylor used the inequality shown below to calculate the amount
in dollars, a, she can spend before tax and tip.
1.2(a + 0.065a) ≤ 25
Which of the following shows the solution to this inequality?
A. a ≤ 22.74
B. a ≤ 22.34
C. a ≤ 19.76
D. a ≤ 19.56
Answer: D
Item Context Social Studies/Consumerism
Sample Item 2 MC
Which graph shows the solution to the inequality shown below?
15 ≤ 7n - 2(n - 10) < 35
Answer: D
Item Context: Mathematics
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses
or Assessed by
Item Types
Benchmark
Clarification
Content Limits
Stimulus
Attributes
Response
Attributes
Algebra
Linear equations and inequalities
MA.912.A.3.5
Symbolically represent and solve multi-step and real-world applications that
involve linear equations and inequalities.
This benchmark will be assessed using MC and FR items.
Students will interpret and/or solve real-world problems involving linear equations
or linear inequalities
Items may require students to express inequalities on a number line, or to use an inequality
for a response. Items may include compound inequalities presented in written format,
graphically, and/or algebraically. Items will not include the use of interval notation, e.g.
(3,∞), or set notation, e.g. { x I x > 3}.
Items must be set in real-world contexts. Items should use methods that are
graphical and/or algebraic. Graphics should be used in some of these items, as
appropriate.
Multiple choice responses would be the best way to assess this benchmark for the
inequalities. Linear equations also could be assessed in FR format.
8
Liberal Arts Mathematics
Sample Item 1 MC
You are selling tickets for a play that cost $3 each. You want to sell at least $50 worth.
Write and solve an inequality for the minimum number of tickets you must sell.
A. 3x  50 , 17 tickets
B. 3x  50 . 16 tickets
C. 3x  50 , 17 tickets
D. 3x  50 , 16 tickets
Answer: A
Item Context: Consumerism
Sample Item 2 FR
The Science Club hopes to collect at least 250 aluminum cans for recycling during
a 9-week period. The graph shows the first week’s results. Let x represent the
minimum average number of cans required per week for the remainder of the 9
week period. What is x?
Aluminum Cans Collected in Week
1
5
Number of cans
Sample Item
9
4
3
2
1
0
Mon.
Wed.
Day
Answer: 31
Item Context: Science/Mathematics, Real World
Fri.
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also
Assesses
Item Types
Benchmark
Clarification
Content
Limits
Algebra
Linear equations and inequalities
MA.912.A.3.7
Rewrite equations of a line into slope-intercept form and standard form.
MA.912.A.3.9 and MA.912.A.3.10
This benchmark will be assessed using MC and FR items.
Students will rewrite equations from standard form or point-slope form to
slope-intercept form as well as from slope-intercept or point-slope form to
standard form.
Item will require the student to write the equation of a line in standard form
given two points on the graph of the line. Item may also require the student to
write the equation in slope-intercept form given two points on the graph.
Student may be required to shade in the correct section of the graph for the
inequality.
Items may be in real world or mathematical context. Graphics may be used
where appropriate. Equations should not be in function notation.
All responses will be in equation form.
Stimulus
Attributes
Response
Attributes
Sample Item What are the coordinates of the y-intercept for the given equation below?
y - 2 = ½(x - 4) ; y – 2 = 1/2x – 2 ; y = 1/2x + 0
Y intercept is 0 with the coordinates being (1/2x,0)
10
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Algebra
Linear equations and inequalities
MA.912.A.3.8
Graph a line given any of the following information: a table of values, the x- and yintercepts, two points, the slope and a point, the equation of the line in slope-intercept
form, standard form, or point-slope form .
MA.912.A.3.5
Also
Assesses or
Assessed by
This benchmark will be assessed using MC and FR items.
Item Types
Benchmark Students will identify graphs given: a table of values, the x and y intercepts, two points, the
Clarification slope and a point, or the equation of the line in slope-intercept form, standard form, or
point-slope form.
In items presenting relations as graphs for the purpose of determining if the relation is a
Content
function continuous.
Limits
Stimulus
Attributes
Items may be set in either real-world or mathematical contexts. Items may include linear
equations in various forms, including standard, slope-intercept, and point-slope forms.
Graphics should be used in all items. Equations should not be presented in function
notation.
All responses will be in the form of graphs.
Response
Attributes
Sample Item What is the graph of the equation; 4x - 3y = -24? (Answers will all be graphs of lines)
-3y = -4x-24; y = 4/3x+8
.
Have student place a dot on the Y
intercept,8, and then go down 4 and left 3 or up 4 and right three. Explain why you can go
down and left. The graph is the solution, so it should show this line - HPW
11
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also
Assesses or
Assessed by
Item Types
Benchmark
Clarification
Content
Limits
Algebra
Linear equations and inequalities
MA.912.A.3.9
Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or
two points on the line.
MA.912.A.3.10
This benchmark will be assessed using MC and FR items.
Students will determine the slope, x-intercept, and/or y-intercept of a line given its graph,
its equation, or two points on the line.
Missing Content Limits!
Items may be set in either real-world or mathematical contexts. Items may include linear
equations in various forms, including standard, slope-intercept, and point-slope forms.
Graphics should be used in most of these items, as appropriate.
Fill-in response items may require that students provide a slope or the x-coordinate (or yResponse
coordinate) of a point of interest. Fill in response items may have a negative answer.
Attributes
Sample Item Using the graph, which equation defines the given line?
Stimulus
Attributes
NO SAMPLE ITEM‼! There are no equations here.
12
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses
or Assessed by
Item Types
Benchmark
Clarification
Content Limits
Stimulus
Attributes
Response
Attributes
Sample Item
Geometry
Points, Lines, Angles, and Planes
MA.912.G.1.1
Find the lengths and midpoints of line segments in two-dimensional coordinate
systems.
N/A
MC, FR
Students will find the length or midpoint or one of the end points of a segment.
Students will justify lengths of segments.
Items may require multiple steps. Items may include both distance and midpoint.
Items may be set in either real-world or mathematical contexts. Graphics should be
used for most of these items, as appropriate.
Fill-in response items may require that students provide the length of a segment or the
x-coordinate (or y-coordinate) of a point of interest. Fill-in response items may have a
negative answer.
Sample Item 1: MC
The circle shown below is centered at the origin and contains the point (-4, -2).
Which of the following is closest to the length of the diameter of the circle?
A. 13.41
B. 11.66
C. 8.94
D. 4.47
Answer Key: C
Sample Item 2: FR
Answer Key: -22
13
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses or
Assessed by
Item Types
Benchmark
Clarification
Content Limits
Stimulus
Attributes
Response
Attributes
Sample Item
Geometry
Points, Lines, Angles, and Planes
MA.912.G.1.4:
Use coordinate geometry to find slopes, parallel lines, perpendicular
lines, and equations of lines.
N/A
Blank
Blank
Blank
Blank
Blank
Blank
14
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Geometry
Congruent and Similar Polygons
MA.912.G.2.3
Use properties of congruent and similar polygons to solve mathematical or real-world
problems.
MA.912.G.4.4
Also Assesses
or Assessed by
This benchmark will be assessed using MC and FR items.
Item Types
Students will use properties of congruent and/or similar polygons to solve problems.
Benchmark
Clarification
Content Limits All angle measures will be in degrees. Items may require statements and/or
justifications to complete formal and informal proofs.
Stimulus
Attributes
Response
Attributes
Graphics should be used in these items, as appropriate.
MC responses should be used to assess proofs as part of this benchmark. Items
assessing aspects of this benchmark other than proofs can be in MC or FR format.
15
Liberal Arts Mathematics
Sample Item
Sample Item 1: FR
How far are the bumper cars from the ferris wheel, on the illustration below?
Answer Key: 70 yards
Item Context: Consumerism
Sample Item 2: MC
The owners of a water park want to build a scaled-down version of a popular tubular
water slide for the children’s section of the park. The side view of the water slide,
labeled ABC, is shown below.
Points A', B' and C ', shown above, are the corresponding points of the scaled-down
slide. Which of the following would be closest to the coordinates of a new point C ' that
will make slide A'B'C ' similar to slide ABC ?
A. (90,20)
B. (77,20)
C. (50,20)
D. (47,20)
Answer Key: B
Item Context: Social Studies/Consumerism
16
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses
or Assessed by
Item Types
Benchmark
Clarification
Content Limits
Stimulus
Attributes
Response
Attributes
Geometry
Perimeter and Area of Polygons
MA.912.G.2.5
Explain the derivation and apply formulas for perimeter and area of polygons (triangles,
quadrilaterals, pentagons, etc.).
MA.912.G.2.7
This benchmark will be assessed using MC and FR items.
Students will solve problems by using and/or deriving formulas for perimeter and/or
area of polygons.
Items requiring students to calculate area may require the use of the apothem.
Composite figures may include circles.
Items may be set in either mathematical or real-world contexts. Graphics should be
used in most of these items, as appropriate.
Either multiple choice or fill-in response could be used for this benchmark.
17
Liberal Arts Mathematics
Sample Item
Sample Item 1 MC
Marisol is creating a custom window frame that is in the shape of a regular hexagon. She wants
to find the area of the hexagon to determine the amount of glass needed. She measured diagonal
d and determined it was 40 inches. A diagram of the window frame is shown below.
Which of the following is closest to the area, in square inches, of the hexagon?
A.
B.
C.
D.
600
849
1,039
1,200
Answer: C
Item Context: Social Studies/Consumerism
Sample Item 2 FR
A package shaped like a rectangular prism needs to be mailed. For this package to be mailed at
the standard parcel-post rate, the sum of the length of the longest side and the girth (the
perimeter around its other two dimensions) must be less than or equal to 108 inches (in.). Figure
1 shows how to measure the girth of a package.
What is the sum of the length, in inches, of the longest side and the girth of the package shown
in Figure 2?
Answer: 102
Item Context: Social Studies/Consumerism
18
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Geometry
Quadrilaterals
MA.912.G.3.1
Describe, classify, and compare relationships among quadrilaterals including the square,
rectangle, rhombus, parallelogram, trapezoid, and kite.
N/A
Also
Assesses
This benchmark will be assessed using MC and FR items.
Item Types
Benchmark Classify and understand relationships among quadrilaterals (rectangle, parallelogram, kite,
Clarification etc.). Relate geometry to algebra by using coordinate geometry to determine regularity,
congruence, and similarity. Use properties of congruent and similar quadrilaterals to solve
problems involving lengths and area, and prove theorems involving quadrilaterals. This
bench examines properties of quadrilaterals one at a time.
Students should be able to identify which quadrilateral best fits a set of peroperties.
Content
Students should be able to use the properties to solve problems involving given
Limits
quadrilaterals.
Stimulus
Attributes
Response
Attributes
Items may be set in either mathematical or real-world contexts. Graphics should be used in
most of these items, as appropriate.
Either multiple choice or fill-in response could be used to assess this benchmark.
19
Liberal Arts Mathematics
Sample
Item
20
Sample Item 1 MC
Andy wants to make a flower garden in the shape of a quadrilateral. He wants it to have the
following properties:
1.
2.
3.
4.
Opposite sides are parallel
Opposite angles are congruent
Diagonals are perpendicular
Diagonals bisect each other
Which quadrilateral has all of those properties?
A.
B.
C.
D.
Parallelogram
Rhombus
Rectangle
Trapezoid
Answer B
Item Context Agriculture/Consumerism
Sample Item 2 MC
A car jack is shaped like a rhombus. As two of the opposite vertices get closer together,
the other two opposite vertices get farther apart. The sides of a car jack at 17 cm long.
When the horizontal distance between the vertices is 30 cm, what is the vertical distance
between the other two vertices?
17 cm
17 cm
30 cm
17 cm
A.
B.
C.
D.
???
17 cm
8
16
17
30
Answer B
Item Context Social Studies/Consumerism
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Geometry
Similar and Congruent Triangles
MA.912.G.4.4
Use properties of congruent and similar triangles to solve problems involving lengths and
areas.
N/A
Also
Assesses
This benchmark will be assessed using MC and FR items.
Item Types
Benchmark Triangles - Identify and describe various kinds of triangles (right, acute, scalene, isosceles,
Clarification etc.). Define and construct altitudes, medians, and bisectors, and triangles congruent to
given triangles. Prove that triangles are congruent or similar and use properties of these
triangles to solve problems involving length and areas. Relate geometry to algebra by
using coordinate geometry to determine regularity, congruence, and similarity.
Understand and apply the inequality theorems of triangles.
Students will use the properties of triangles and congruency/similarity properties to find
Content
measures and areas of triangles.
Limits
Stimulus
Attributes
Response
Attributes
Items may be set in either mathematical or real-world contexts. Graphics should be used
in most of these items, as appropriate.
Either multiple choice or fill-in response could be used for this benchmark.
21
Liberal Arts Mathematics
Sample
Item
22
Sample Item 1 FR
In the figure below, ΔADE ≅ΔACB with AE = 80mm AF=40mm. What is the length of
BE? Round your answer to the nearest whole number.
A
E
D
B
F
C
Answer 139mm
Item Context Mathematics
Sample Item 2 FR
Using the same figure above, if ∠AED=30°, ∠ADE=140°, and ΔACE ≅ΔADB, what is
∠DAC?
Answer 100°
Item Context Mathematics
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also
Assesses
Item Types
Benchmark
Clarification
Content
Limits
Geometry
Stimulus
Attributes
Response
Attributes
Items assessing MA.912.G.5.2 may be set in either mathematical or real-world contexts.
All other items must be set in real-world context.
Any radical expressions in multiple-choice options will be provided in simplified or
rationalized form.
Right Triangles
MA.912.G.5.4
Solve real-world problems involving right triangles.
MA.912 G.5.3
MC
Students will solve real-world problems involving right triangles.
Items may require students to apply the Pythagorean theorem, special right triangle
relationships, and/or characteristics of triangles resulting from the altitude of a right
triangle drawn from the right angle to the hypotenuse.
23
Liberal Arts Mathematics
Sample
Item
Sample Item 1: MC
Answer Key: C
Sample Item 2: FR
Nara created two right triangles. She started with LJKL and drew an altitude from point
K to side JL. The diagram below shows LJKL and some of its measurements, in
centimeters (cm).
Based on the information in the diagram, what is the measure of x to the nearest tenth of
a centimeter?
Sample Answer: 11.6
24
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses
Item Types
Benchmark
Clarification
Content Limits
Stimulus
Attributes
Response
Attributes
Geometry
Polyhedra and Other Solids
MA.912.G.7.5
Explain and use formulas for lateral area, surface area, and volume of solids.
MC, FR
Students will explain and/or apply formulas to determine surface area, lateral area, and
volume of solids
Solids will be limited to right prisms, right-circular cylinders, spheres, right pyramids,
right-circular cones, and/or composites of these solids.
Items may not include oblique figures.
Items may ask students to apply knowledge of congruent and similar solids.
Items may be set in either mathematical or real-world contexts.
Graphics should be used in most of these items, as appropriate.
Responses should be numerical part of answer only. No units are required.
25
Liberal Arts Mathematics
Sample Item
Sample Item 1: MC
Abraham works at the Delicious Cake Factory and packages cakes in cardboard
containers shaped like right circular cylinders with hemispheres on top, as shown in the
diagram below.
Abraham wants to wrap the cake containers completely in colored plastic wrap and
needs to know how much wrap he will need. What is the total exterior surface area of
the container?
Answer Key: B
Sample Item 2: FR
Look at the composite solid below, consisting of a hemisphere and a cone.
What is the volume of this composite solid? Use 3.14 for pi and round to the nearest
tenth.
Sample Answer: 6.3
26
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also
Assesses
Item Types
Benchmark
Clarification
Content
Limits
Geometry
Polyhedra and Other Solids
MA.912.G.7.7
Determine how changes in dimensions affect the surface area and volume of common
geometric solids.
MA.912.G.2.7
MC, FR
Students will determine how changes to one parameter will change other parameters when
the perimeter, area, surface area, and volume is held constant
One or two parameters may be changed, resulting in the change of another parameter. Three
parameters may be changed in one item only if all three are changed by a constant factor.
Solids will be limited to right prisms, right circular cylinders, speres, right pyramids, right
circular cones, and/or composites of these solids. Items may not include oblique figures.
Items may involve, explicitly and/or implicitly, no more than four parameters. Changes in
dimension may or may not result in similar figures.
Items may be set in either mathematical or real-world contexts. Graphics should be used in
most of these items, as appropriate.
Responses should be numerical part of answer only. No units are required.
Stimulus
Attributes
Response
Attributes
Sample Item Sample Item 1: MC
Kendra has a compost box that has the shape of a cube. She wants to increase the size of the
box by extending every edge of the box by half of its original length. After the box is
increased in size, which of the following statements is true?
A. The volume of the new compost box is exactly 112.5% of the volume of the original box.
B. The volume of the new compost box is exactly 150% of the volume of the original box.
C. The volume of the new compost box is exactly 337.5% of the volume of the original box.
D. The volume of the new compost box is exactly 450% of the volume of the original box.
Answer Key: C
Sample Item 2: FR
A city is planning to replace one of its water storage tanks with a larger one. The city’s old
tank is a right circular cylinder with a radius of 12 feet and a volume of 10,000 cubic feet.
The new tank is a right circular cylinder with a radius of 15 feet and the same height as the
old tank. What is the maximum number of cubic feet of water the new storage tank will
hold?
Possible Answer:
15,625
27
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also
Assesses
Item Types
Benchmark
Clarification
Content
Limits
Stimulus
Attributes
Response
Attributes
Sample Item
Statistics
Summarizing Data (Descriptive Statistics)
MA.912.S.3.1:
Read and interpret data presented in various formats. Determine whether data is presented
in appropriate format, and identify possible corrections. Formats to include: Bar graphs,
line graphs, stem & leaf plots, circle graphs, histograms, box & whiskers plots, scatter
plots, cumulative frequency (ogive) graphs
MA.912.A.2.2
Blank
Blank
Blank
Blank
Blank
Blank
28
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Statistics
Summarizing Data (Descriptive Statistics)
MA.912S.3.2
Collect, organize, and analyze data sets, determine the best format for the data and present
visual summaries.
MA.912.S.3.1
Also
Assesses
This benchmark will be assessed using FR or MC items.
Item Types
Benchmark Items for collection and organization of data may be represented in frequency distributions
Clarification with classes, frequencies, class limits, class boundaries, class width, and class midpoint.
Items for visual representations may include histogram, frequency polygon, ogive, relative
frequency graph, bar graph, pareto graph, time-series graph, pie graph, stem and leaf plot,
grouped and ungrouped frequency distributions, or categorical frequency distributions.
Students will collect, organize and analyze data and determine how to represent the
Content
information in the correct visual summary. Students organize data with frequency
Limits
distributions. Students will choose and present the data in the correct visual representation.
Stimulus
Attributes
Response
Attributes
Items must be set in real-world context.
Answers will be either in visual representations for students to identify or they will analyze
data given in a visual representation.
29
Liberal Arts Mathematics
Sample
Item
30
Sample Item 1
MC
In a study of a sample of 200 student completion times for a state test the following times
were recorded (in minutes).
29.5-39.5
5
39.5-49.5
24
49.5-59.5
35
59.5-69.5
72
69.5-79.5
36
79.5-89.5
28
What are the class boundaries?
A.
*B.
C.
D.
29-39, 39-49, 49-59, 59-69, 69-79, 79-89
29.5-39.5, 39.5-49.5, 49.5-59.5, 59.5-69.5, 69.5-79.5
30-40, 40-50, 50-60, 60-70, 70-80, 80-90
34.5, 44.5, 54.5, 64.5, 74.5, 84.5
Sample Response
1B
Item Context:
Mathematics (Statistics)
Sample Item 2
MC
In a study of a sample of 200 student completion times for a state test the following times
were recorded (in minutes).
29.5-39.5
5
39.5-49.5
24
49.5-59.5
35
59.5-69.5
72
69.5-79.5
36
79.5-89.5
28
What are the class limits?
A.
B.
*C.
D.
29-39, 39-49, 49-59, 59-69, 69-79, 79-89
29.5-39.5, 39.5-49.5, 49.5-59.5, 59.5-69.5, 69.5-79.5
30-40, 40-50, 50-60, 60-70, 70-80, 80-90
34.5, 44.5, 54.5, 64.5, 74.5, 84.5
Sample Response
Item Context:
2C
Mathematics (Statistics)
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Statistics
Summarizing Data (Descriptive Statistics)
MA.912.S.3.3
Calculate and interpret measures of the center of a set of data, including mean, median, and
weighted mean, and use these measures to make comparisons among sets of data.
MA912.P.3.3
Also
Assesses
This benchmark will be assessed using FR or MC items.
Item Types
Benchmark Items may include calculations for mean, median, mode, or weighted mean of a data set.
Clarification Items may include the choice of which measure of center is the best representation of the
data set.
Students will calculate, summarize, and interpret data using measures of center including
Content
mean, median, mode, and weigthed mean. Students will use these measures to make
Limits
comparisons and draw conclusions about data sets.
Stimulus
Attributes
Response
Attributes
Items must be set in mathematical or real-world context.
Answers for the mean will follow the Rounding Rule for the Mean (rounded to one more
decimal place than the raw data).
31
Liberal Arts Mathematics
Sample
Item
Sample Item 1
MC
The average grade point average (GPA) for 25 top-ranked students at a local college is
listed below. (Use the rounding rule for the mean).
3.80 3.77 3.70 3.74 3.70
3.86 3.76 3.68 3.67 3.57
3.83 3.70 3.80 3.73 3.67
3.78 3.75 3.73 3.65 3.66
3.75 3.64 3.78 3.73 3.64
Find the mean of the GPAs.
Sample Response 1
A.
3.7236
B.
3.764
*C.
3.724
D.
3.887
Sample Response
1C
Item Context: Mathematics (Statistics)
Sample Item 2
MC
The average grade point average (GPA) for 25 top-ranked students at a local college is
listed below. (Use the rounding rule for the mean).
3.80 3.77 3.70 3.74 3.70
3.86 3.76 3.68 3.67 3.57
3.83 3.70 3.80 3.73 3.67
3.78 3.75 3.73 3.65 3.66
3.75 3.64 3.78 3.73 3.64
Find the median of the GPAs.
Sample Response 2
A.
3.7
*B.
3.73
C.
3.74
D.
3.75
Sample Response
2B
Item Context: Mathematics (Statistics)
32
Liberal Arts Mathematics
Reporting
Category
Standard
Benchmark
Number
Benchmark
Also Assesses
or Assessed by
Item Types
Benchmark
Clarification
Content
Limits
Stimulus
Attributes
Response
Attributes
Sample Item
Statistics
Summarizing Data (Descriptive Statistics)
MA.912.S.3.5
Calculate and interpret the range and quartiles of a set of data.
N/A
This benchmark will assessed using FR or MC items.
Items may include calculations of range, percentile, quartile and decile, calculation of the
inter-quartile range, and the interpretation of the data according to the data set. Items may
include box-and-whisker plots.
Students will identify the position of a data value in a data set using measures of position
such as range, standard scores, percentiles, quartiles and deciles. Students will be able to
apply the five number summary in a box-and-whisker plot.
Items must be set in mathematical or real-world context.
Answers will use rules of procedures for percentile calculations. Answers in box-andwhisker plots will have visible numbers for the 5 number summary.
Sample Item 1
MC
The average grade point average (GPA) for 25 top-ranked students at a local college
is listed below.
3.80 3.77 3.70 3.74 3.70
3.86 3.76 3.68 3.67 3.57
3.83 3.70 3.80 3.73 3.67
3.78 3.75 3.73 3.65 3.66
3.75 3.64 3.78 3.73 3.64
Find the five-number summary for the GPAs.
Sample Response 1
A.
3.64, 3.675, 3.73, 3.775, 3.86
*B.
3.57, 3.67, 3.73, 3.775, 3.86
C.
3.64, 3.67, 3.73, 3.775, 3.80
D.
3.57, 3.67, 3.73, 3.775, 3.9
Sample Response 1 B
Item Context:
Mathematics (Statistics)
33