Middle Level Mathematics (Grades 5–8)
Subtest 2 Sample Items
Recommendation for individuals using a screenreader: please set your punctuation settings to "most."
Expand All  Collapse All
Question 1
1. A vertical pole that is 10 ft. high starts leaning to one side. If the top of the leaning pole is
1 ft. lower than its height when it was vertical, approximately how many degrees from the vertical position
is the pole leaning?
 3°
 8°
 26°
 37°
Answer to question 1
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0008) The angle x,
formed by the leaning pole and a 9foot line drawn straight down from the pole to the ground, has the
same measurement as the angle the pole traveled to its leaning position. The cosine of the angle between
the leaning pole and the straight line can be determined by the ratio of the lengths,
Correct Response: C. (Objective 0008) The angle x, formed by the leaning
pole and a 9foot line drawn straight down from the pole to the ground, has the same measurement as
the angle the pole traveled to its leaning position. The cosine of the angle between the leaning pole
and the straight line can be determined by the ratio of the lengths, cosine x equals nine over ten leads
to x equals inverse cosine of nine over ten leads to x equals twenty six degrees.
Question 2
2. If the radius of a cylinder is tripled while the height remains constant, the volume of the cylinder
is increased by a factor of:
 3.
 6.
 9.
 27.
Answer to question 2
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0008) The volume of a cylinder
with radius r and height h is equal to πr^{2}h. The volume
of a cylinder with radius 3r and height h is equal to π(3r)^{2}h
= 9πr^{2}h. Thus, the volume of the second cylinder increases by a factor
of 9.
Correct Response: C. (Objective 0008) The volume of a cylinder with radius
r and height h is equal to pi r squared h. The volume of a cylinder
with radius 3 r and height h is equal to pi open parenthesis 3 r close parenthesis
squared h equals 9 pi r squared h. Thus, the volume of the second cylinder
increases by a factor of 9.
Question 3
3. Shipping boxes come in four different sizes and costs. The table below shows the capacity of the
different sizes of boxes. What is the cost for the smallest number of boxes that could be used to replace
the capacity of 52 small boxes?
Box Size

Cost per
Box

Capacity
per Box

extra large

$3.36

2 large

large

$2.92

3 medium

medium

$2.37

4 small

small

$1.29


 $6.72
 $7.75
 $8.76
 $9.09
Answer to question 3
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0008) Using the capacities
given in the table,
. So, 48 of the 52 small boxes can be replaced
by 2 extra large boxes, leaving 4 small boxes that can be replaced by 1 medium box. The cost of the
boxes is given by 2 × $3.36 + 1 × $2.37 = $9.09.
Correct Response: D. (Objective 0008) Using the capacities given in the table,
one extra large box over two large boxes times one large box over three medium boxes times one medium
box over four small boxes equals one extra large box over twenty four small boxes. So, 48 of the 52
small boxes can be replaced by 2 extra large boxes, leaving 4 small boxes that can be replaced by 1
medium box. The cost of the boxes is given by 2 multiplied by $3.36 plus 1 times $2.37 equals $9.09.
Question 4
4. A homeowner is building a concrete patio and starts with a rectangle measuring 8 ft. by 11 ft. The
homeowner decides to add half a circle to each end of the rectangle as shown in the diagram below. If
the concrete will be 6 in. deep, which of the following expressions can be used to calculate the number
of cubic feet of cement needed for the patio?
 4π + 444 pie plus 44
 8π + 448 pie plus 44
 16π + 8816 pie plus 88
 96π + 52896 pie plus 528
Answer to question 4
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0008) The shape of the patio
is modeled by a cylinder with radius 4 ft. and height 0.5 ft. and a rectangular box with dimensions
8 ft. by 11 ft. by 0.5 ft. The number of cubic feet of cement required can be determined by 2(0.5)(π
× 4^{2} × 0.5) + (8 × 11 × 0.5) = 8π + 44.
Correct Response: B. (Objective 0008) The shape of the patio is modeled by a cylinder
with radius 4 feet and height 0.5 foot and a rectangular box with dimensions 8 feet by 11 feet by 0.5
foot. The number of cubic feet of cement required can be determined by 2 open parenthesis 0.5 close
parenthesis open parenthesis pi times 4 squared times 0.5 close parenthesis plus open parenthesis 8
times 11 times 0.5 close parenthesis equals 8 pi plus 44.
Question 5
5. A rectangle has length 12 cm and width 4 cm. Which of the following measurements is closest to the
measure of one of the angles created by the intersection of the rectangle's diagonals?
 37°
 72°
 108°
 112°
Answer to question 5
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0008) Drawing
perpendicular to
makes M the midpoint of
, KM half of BC,
and MB half of AB, so KM = 2 and MB = 6. Using the tangent ratio, tanx =
= 3, so x = tan^{–1} 3 ≈ 71.6°. Thus 2x ≈ 143.2° and m∠BKC=180°
− 143.2;° = 36.8° ≈ 37°.
Correct Response: A. (Objective 0008) Drawing segment K M perpendicular to segment
A B makes M the midpoint of segment A B, K M half of B C, and M B half of A B, so K M equals two and
M B equals six. Using the tangent ratio, tangent x equals six halves which equals three, so x equals
inverse tangent three which approximately equals seventy one point six degrees. Thus two x approximately
equals one hundred forty three point two degrees and the measure of angle B K C equals one hundred eighty
degrees minus one hundred forty three point two degrees which equals thirty six point eight degrees
which approximately equals thirty seven degrees.
Question 6
6. A wheel makes 6 complete rotations every minute. How many degrees does the wheel rotate in 3 sec.seconds?
 18°
 108°
 120°
 1080°
Answer to question 6
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0009) Using the information
in the problem,
which simplifies to
.
The wheel rotates 36° every second, so in 3 seconds it rotates 3 • 36 = 108°.
Correct Response: B. (Objective 0009) Using the information in the problem, six
rotations over one minute times one minute over sixty seconds times three hundred sixty degrees over
one rotation equals two thousand one hundred sixty degrees over sixty seconds which simplifies to thirty
six degrees over one second. The wheel rotates thirty six degrees every second so in three seconds it
rotates three times thirty six which equals one hundred eight degrees.
Question 7
7. Lines m, n, and p are parallel and are intersected by segments 1 and 2,
thus forming angles a, b, c, d, and x.
Starting from the top line m, line n and line p. there is a line segment one that is drawn from a point
on n in an increasing fashion to a point to the right on line m. there is an angle labeled x that is
created with n and the top part of segment one. angle x is a large obtuse angle. angle b is the angle
created by line m and segment one and is a small acute angle. angle a is the angle from the bottom of
segment one to line m. angle x and angle a are alternating angles. there is a line segment two that
is drawn from the same point on line n to a point on line p in a decreasing fashion to the right. line
segment two is much shorter then segment one. angle c is the angle created by the top of segment two
and line n and is an acute angle. angle d is created by the top of segment two and line p. angle d is
an obtuse angle.
Which of the following expressions could be used to describe mx?
 180 − ma
 180 − mb
 180 − mc
 180 − md
Answer to question 7
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0009) The angle that sweeps
from line n to segment 1 is an alternate interior angle with, and so is congruent to,
b and is supplementary
to
x. Thus, mx = 180 −m
b.
Correct Response: B. (Objective 0009) The angle that sweeps from line n
to segment 1 is an alternate interior angle with, and so is congruent to angle b and is supplementary
to angle x. Thus, m angle x equals 180 minus m angle b.
Question 8
8. What is the measure of angle θ in the regular pentagon below?
from the vertex to the right of the top point, there is a line drawn to the bottom left hand vertex.
Theta is labeled as the angle between the vertex and the line drawn. the line creates a triangle with
two sides of the pentagon.
 24°
 27°
 36°
 54°
Answer to question 8
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0009) The interior angles
of a regular pentagon measure 108°. The diagonal adjacent to θ forms an isosceles triangle
with two sides of the regular pentagon. Thus,
.
Correct Response: C. (Objective 0009) The interior angles of a regular pentagon
measure 108 degrees. The diagonal adjacent to theta forms an isosceles triangle with two sides of the
regular pentagon. Thus, one hundred and eight plus two theta equals one hundred and eighty leads to
two theta equals seventy two leads to theta equals thirty six degrees.
Question 9
9. A garden expert recommends wrapping the trunks of new fruit trees with tree wrap to protect them
during the winter. Which of the following dimensions could be used as a model to determine the amount
of tree wrap that is needed?
 the volume of a rectangular box
 the perimeter of a triangle
 the vertical height of a cone
 the surface area of a cylinder
Answer to question 9
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0009) Since the quantity
wanted is the amount of tree wrap that will cover the surface of a tree trunk, and a tree trunk resembles
a cylinder, the dimension that most closely models the situation is the surface area of a cylinder.
Correct Response: D. (Objective 0009) Since the quantity wanted is the amount of
tree wrap that will cover the surface of a tree trunk, and a tree trunk resembles a cylinder, the dimension
that most closely models the situation is the surface area of a cylinder.
Question 10
10. Which of the following geometry postulates supports the statement that the location of two posts
can be used to determine the precise location of a fence?
 Through any two points there is exactly one line
 If some point B is between two points A and C, then AB + BC
= AC.
 If two planes intersect, then their intersection is a line.
 If two points are in a plane, then the line that contains the points is in that plane.
Answer to question 10
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0009) The application of
a geometry postulate to a realworld situation brings an informal proof to real life. If a line is precisely
determined by just two points on a coordinate plane, then certainly the location of a fence (line segment)
can be determined by two fence posts (points).
Correct Response: A. (Objective 0009) The application of a geometry postulate to
a realworld situation brings an informal proof to real life. If a line is precisely determined by just
two points on a coordinate plane, then certainly the location of a fence (line segment) can be determined
by two fence posts (points).
Question 11
11. Use the diagram below to answer the question that follows.
The net of a right square pyramid creates the octagon shown. If the perimeter of the octagon is 80 cm,
which of the following measurements is closest to the volume of the pyramid?
 136 cm^{3}136 centimeters cubed
 254 cm^{3}254 centimeters cubed
 384 cm^{3}384 centimeters cubed
 480 cm^{3}480 centimeters cubed
Answer to question 11
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0009) The volume of a pyramid
can be found using the formula V =
Bh, where B represents the area of the base and h represents the height of
the pyramid. The area of the base of this pyramid is 12 × 12 = 144. To find the height of the
pyramid, first find the altitude of the triangle that forms one of the faces of the pyramid.
. Using the Pythagorean Theorem,
10^{2} = 6^{2} + k^{2}, so k =
= 8. Next find the height of the pyramid, which is also a leg of a right triangle.
. Again using the Pythagorean
Theorem, 8^{2} = 6^{2} + h^{2}, so h =
=
.
The volume of the pyramid is V =
• 144 •
≈ 253.99 cm^{3}.
Correct Response: B. (Objective 0009) The volume of a pyramid can be found using
the formula V equals one third B h, where B represents the area of the base and h represents the height
of the pyramid. The area of the base of this pyramid is twelve times twelve which equals one hundred
forty four. To find the height of the pyramid, first find the altitude of the triangle that forms one
of the faces of the pyramid.
The net of a right square pyramid is shown in which a square has adjacent triangles on each side to
create a concave octagon. The altitude of the top triangle intersects the side of the square to form
a right triangle. In the right triangle, the altitude is labeled k, the other leg is labeled six centimeters,
and the hypotenuse is labeled ten centimeters.
Using the Pythagorean Theorem, ten squared equals six squared plus k squared, so k equals the square
root of the quantity one hundred minus thirty six which equals eight. Next find the height of the pyramid,
which is also a leg of a right triangle.
A right square pyramid is shown with the side length of the base labeled twelve centimeters. A right
triangle is shown within the pyramid using the height of the pyramid as one leg, the altitude of one
face of the pyramid as the hypotenuse, and a segment labeled six centimeters along the base of the pyramid
as the other leg.
Again using the Pythagorean Theorem, eight squared equals six squared plus h squared, so h equals the
square root of the quantity sixty four minus thirty six which equals the square root of twenty eight.
The volume of the pyramid is V equals one third times one hundred forty four times the square root of
twenty eight which approximately equals two hundred fifty three point ninety nine cubic centimeters.
Question 12
12. What is the length of the longest side of the triangle shown below?




Answer to question 12
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0010) The coordinates of
the vertices of the triangle are (4, 2), (0, 1), and (–2, 3). To find the length of the sides
of the triangle, apply the distance formula,
, where d is the distance
between two points (x_{1}, y_{1}) and (x_{2}, y_{2}).
The distance from (–2, 3) to (4, 2) is
=
.
The distance from (4, 2) to (0, 1) is
=
.
The distance from (–2, 3) to (0, 1) is
=
.
Since
is the greatest value, it is the length of the longest side.
Correct Response: D. (Objective 0010) The coordinates of the vertices of the triangle
are four comma two, zero comma one, and negative two comma three. To find the length of the sides of
the triangle, apply the distance formula, d equals the square root of the quantity open parenthesis
x subscript one minus x subscript two close parenthesis the quantity squared plus open parenthesis y
subscript one minus y subscript two close parenthesis the quantity squared, where d is the distance
between two points x subscript one comma y subscript one and x subscript two comma y subscript two.
The distance from negative two comma three to four comma two is the square root of the quantity open
parenthesis negative two minus four close parenthesis squared plus open parenthesis three minus two
close parenthesis squared which equals the square root thirty seven. The distance from four comma two
to zero comma one is the square root of the quantity open parenthesis four minus zero close parenthesis
squared plus open parenthesis two minus one close parenthesis squared which equals the square root of
seventeen. The distance from negative two comma three to zero comma one is the square root of the quantity
open parenthesis negative two minus zero close parenthesis squared plus open parenthesis three minus
one close parenthesis squared which equals the square root of eight. Since the square root of thirty
seven is the greatest value, it is the length of the longest side.
Question 13
13. What is the approximate area of the triangle formed by the intersections of the lines given by
first line is y equals six, which is a horizontal line drawn at y equals six. second line is y equals
fifteen over four baseline x minus twenty four, this line is a continuous line starting low and close
to the y axis in the fourth fourth quadrant and increases at a steep slope passing the x axis into the
first quadrant and passing the the first line then continuing to increase. the third line is y equals
negative five over four baseline x minus four, it starts high in the second quadrant and decreases past
the first line at y equals six and continues to decrease past the x axis into the third quadrant for
a short time then decreases past the y axis into the fourth quadrant and passes the second line. Each
line intersects each of the other two lines at some point.
 80 square units
 120 square units
 124 square units
 149 square units
Answer to question 13
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0010) The vertices of the
triangle are at the intersections of the lines. Two lines intersect y = 6 to form two of the
vertices of the triangle. By substitution,
. The third vertex is the intersection of
. Thus,
]. The vertical distance between (4, −9)
and (4, 6) is the height of the triangle, 15 units. The horizontal distance between (−8, 6) and
(8, 6) is the base of the triangle, 16 units. Therefore, the area of the triangle is
= 120 square units.
Correct Response: B. (Objective 0010) The vertices of the triangle are at the intersections
of the lines. Two lines intersect y equals 6 to form two of the vertices of the triangle. By
substitution, six equals fifteen over four baseline x minus twenty four leads to x equals eight and
six equals negative five over four baseline minus four leads to x equals negative eight. The third vertex
is the intersection of y equals fifteen over four baseline minus twenty four and y equals negative five
over four baseline x minus four. Thus, fifteen over four baseline minus twenty four equals negative
five over four baseline x minus four leads to x equals four and y equals negative nine. The vertical
distance between open parenthesis 4 comma minus 9 close parenthesis and open parenthesis 4 comma 6 close
parenthesis is the height of the triangle, 15 units. The horizontal distance between open parenthesis
negative 8 comma 6 close parenthesis and open parenthesis 8 comma 6 close parenthesis is the base of
the triangle, 16 units. Therefore, the area of the triangle is one half open parenthesis fifteen close
parenthesis open parenthesis sixteen close parenthesis equals 120 square units.
Question 14
14. Parallelogram JKLM is situated on a coordinate plane such that J(–negative 3, –negative
2), K(0, –negative
6), and L(5, 6) are known and M is unknown.
What is the length of the diagonal between points M and K?




Answer to question 14
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0010) The length of side
JK is the hypotenuse of a right triangle with sides 3 and 4 and is a line segment with a slope
of
; thus it is 5
units long. Since JKLM is given as a parallelogram, side LM must be parallel to segment
JK and be 5 units long. Use the slope
to determine that the possible coordinates of vertex M could be (8, 2) or (2, 10). If point
M is located at (8, 2), segment KM is a side and not a diagonal. Thus, the length
of the diagonal joining points M and K is found by
.
Correct Response: C. (Objective 0010) The length of side J K is the hypotenuse
of a right triangle with sides 3 and 4 and is a line segment with a slope of negative four thirds; thus
it is 5 units long. Since J K L M is given as a parallelogram, side L M must be parallel
to segment J K and be 5 units long. Use the slope negative four thirds equals negative four
over three equals four over negative three to determine that the possible coordinates of vertex M
could be open parenthesis 8 comma 2 close parenthesis or open parenthesis 2 comma 10 close parenthesis.
If point M is located at 8 comma 2 close parenthesis , segment K M is a side and not
a diagonal. Thus, the length of the diagonal joining points M and K is found by start
square root open parenthesis ten minus left bracket negative six right bracket close parenthesis squared
plus open parenthesis two minus zero close parenthesis end root equals square root of two hundred and
sixty equals two times the square root of sixty five.
Question 15
15. Use the information below to answer the question that follows.
Given: ABCD is a rectangle.
The coordinates of point
C are (2a, 2b).
Points J, K, L,
and M are midpoints.
the lines create a rectangle a, b, c, d that is taller on the y axis than wide on the x axis. The origin
is labeled a, travelling right you hit point j then point b. Point j is the midpoint between a and b.
From point b go straight up to point k then point c which is labeled as coordinate point open parenthesis
two a comma two b close parenthesis. Point k is the midpoint between b and c. From point c you head
left to point l then point d. Point l is the midpoint between c and d and has the same x value as point
j. from point d, which is on the y axis, you head straight down to point m then back to point a to complete
the rectangle. Point m is the midpoint between d and a and has the same y value as point k.
If JKLM is a rhombus, which of the following equations must be true?


 the area of
KLM
= the area of
KJM
 the perimeter of ABCD =
the perimeter of JKLM
Answer to question 15
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0010) The determining characteristic
of a rhombus in addition to those of a parallelogram is that the sides of a rhombus are equal. Once
is determined, the remaining sides can be shown to be the same length.
Correct Response: A. (Objective 0010) The determining characteristic of a rhombus
in addition to those of a parallelogram is that the sides of a rhombus are equal. Once two times the
square root of two is determined, the remaining sides can be shown to be the same length.
Question 16
16. Which of the following transformations maps the graph of y = x^{2} + 3
to the image of y as shown in the graph below?
First parabola is labeled y equals x squared baseline plus three. Where its vertex is at open parenthesis
zero comma three close parenthesis, then increases to the left into the second quadrant passing through
open parenthesis negative one comma four close parenthesis then continues to increase. from the vertex
it increases to the right into the first quadrant passing through point open parenthesis one comma four
close parenthesis. The second parabola is labeled as an image of y. Its vertex is at open parenthesis
one comma zero close parenthesis and increases to the left passing through point open parenthesis negative
one comma four close parenthesis where it intersects the first graph. from the vertex it also increases
to the right passing through point open parenthesis three comma four close parenthesis
 (x, y) → (x + 1, y − 3)
 (x, y) → (x − 1, y + 3)
 (x, y) → (x^{2} + 1, y^{2} − 3)
 (x, y) → (x^{2} − 1, y^{2} + 3)
Answer to question 16
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0010) The image of y,
y>′ is a parabola with vertex (1, 0). The equation of such a parabola must be in part
y′ = (x − 1)^{2}. The translation that yields this equation is
x + 1. Thus, the transformation that maps y to the image of y is (x, y)
(x + 1, y − 3).
Correct Response: A. (Objective 0010) The image of y, y greater than prime
is a parabola with vertex open parenthesis 1 comma 0 close parenthesis. The equation of such a parabola
must be in part y prime equals open parenthesis x minus 1 close parenthesis squared.
The translation that yields this equation is x plus 1. Thus, the transformation that maps
y to the image of y is open parenthesis x comma y close parenthesis open parenthesis
x plus 1 comma y minus 3 close parenthesis.
Question 17
17. Use the graph below to answer the question that follows.

and
are undefined



and
Answer to question 17
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0010) To prove a quadrilateral
is a parallelogram, it is sufficient to prove that the diagonals bisect each other, or have the same
midpoint. The midpoint of AC is
and the midpoint of BD is
.
Proving that
and
is sufficient to prove that ABCD is a parallelogram.
Correct Response: D. (Objective 0010) To prove a quadrilateral is a parallelogram,
it is sufficient to prove that the diagonals bisect each other, or have the same midpoint. The midpoint
of A C is one half r comma one half the quantity k plus t and the midpoint of B D is one half m comma
one half p. Proving that one half r equals one half m and one half the quantity k plus t equals one
half p is sufficient to prove that A B C D is a parallelogram.
Question 18
18. The table below shows the weight of each of five different vehicle models produced by an automobile
manufacturer.
Model

Weight (pounds)

sports car

2750

twodoor sedan

3050

fourdoor sedan

3200

sport utility

4535

heavyduty pickup

4535

Which of the following measures of vehicle weight has the lowest value?
 mode
 mean
 median
 range
Answer to question 18
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0011) The mode of the data,
or the value that occurs most often, is 4,535. The mean, or average, is equal to
. The median, or the middle value
when the data is arranged numerically, is 3,200. The range is equal to 4,535 − 2,750 = 1,785.
The measure of vehicle weight with the lowest value is 1,785, the range.
Correct Response: D. (Objective 0011) The mode of the data, or the value that occurs
most often, is four thousand five hundred thirty five. The mean, or average, is equal to the quantity
two thousand seven hundred fifty plus three thousand fifty plus three thousand two hundred plus four
thousand five hundred thirty five plus four thousand five hundred thirty five all over five which equals
eighteen thousand seventy fifths which equals three thousand six hundred fourteen. The median, or the
middle value when the data is arranged numerically, is three thousand two hundred. The range is equal
to four thousand five hundred thirty five minus two thousand seven hundred fifty which equals one thousand
seven hundred eighty five. The measure of vehicle weight with the lowest value is one thousand seven
hundred eighty five, the range.
Question 19
19. A botanist wants to estimate the number of individuals of a certain species of flowering plant growing
in a 10,000 ft.^{2} field. The botanist first divides the field into sections of 100 ft.^{2}
To most efficiently and reliably estimate the number of plants in the field, the botanist should:
 count the number of plants in the section that appears to be most representative of the entire field
and multiply by 100.
 determine the number of plants in 5 sections around the perimeter of the field and 5 sections in the
center of the field, obtain the average for each section, and multiply by 10.
 count the number of plants in the section with the fewest plants and the section with the most plants,
add the results, and multiply by 50.
 determine the number of plants in 10 randomly selected sections, obtain the average for each section,
and multiply by 100.
Answer to question 19
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0011) Randomly selecting
10 sections of the field implies an equitably representative sample of the entire field, and counting
plants in 10 sections of the field is a reasonable task when faced with the challenge of studying 100
sections. Taking the average of the plants adds another layer of equity to the count. Multiplying that
average by 100 yields a sample count of the entire field.
Correct Response: D. (Objective 0011) Randomly selecting 10 sections of the field
implies an equitably representative sample of the entire field, and counting plants in 10 sections of
the field is a reasonable task when faced with the challenge of studying 100 sections. Taking the average
of the plants adds another layer of equity to the count. Multiplying that average by 100 yields a sample
count of the entire field.
Question 20
20. The box plot below is used to represent the heights, in meters, of a sample of maple trees.
Which of the following measurements describes the median height of the trees?
 22 meters
 24 meters
 25 meters
 28 meters
Answer to question 20
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0011) The construction of
a box plot requires that the line inside the box indicate the median. Thus, the median of the set of
data is 25 meters.
Correct Response: C. (Objective 0011) The construction of a box plot requires that
the line inside the box indicate the median. Thus, the median of the set of data is 25 meters.
Question 21
21. Which of the following sets of data is represented by the frequency distribution bar graph below?
there are two items for number ten, two items for number eleven, three items for number twelve, three
items for number thirteen, one item for number fourteen and finally one item for number fifteen
 {2, 3, 1}
 {10, 11, 12, 13, 14, 15}
 {10, 11, 2, 12, 13, 3, 14, 15, 1}
 {10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 15}
Answer to question 21
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0011) The vertical axis of
this frequency distribution bar graph indicates the frequency of occurrence of the data indicated along
the horizontal axis. Thus, the set containing two tens, two elevens, three twelves, three thirteens,
and one each of fourteen and fifteen is represented by the bar graph.
Correct Response: D. (Objective 0011) The vertical axis of this frequency distribution
bar graph indicates the frequency of occurrence of the data indicated along the horizontal axis. Thus,
the set containing two tens, two elevens, three twelves, three thirteens, and one each of fourteen and
fifteen is represented by the bar graph.
Question 22
22. An office furniture store has collected the following annual sales data for each of its four salespeople.
Salesperson

Annual
Sales

A

$992,258

B

$661,503

C

$496,076

D

$330,543

If a circle graph is used to display these sales data, what is the measure, in degrees, of the central
angle of the part of the graph that represents salesperson C?
 20°
 72°
 90°
 113°
Answer to question 22
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0011) Since the total annual
sales are $2,480,380, salesperson C's sales of $496,076 represent
= 0.20 = 20% of the total annual sales. Thus, the central angle of the part of the circle graph that
represents the annual sales of salesperson C is given by 20% × 360° = 72°.
Correct Response: B. (Objective 0011) Since the total annual sales are $2,480,380,
salesperson C's sales of $496,076 represent start fraction numerator four hundred ninety six thousand
and seventy six denominator two million four hundred and eighty thousand three hundred and eighty end
fraction equals 0.20 equals 20 percent of the total annual sales. Thus, the central angle of the part
of the circle graph that represents the annual sales of salesperson C is given by 20 percent times 360
degrees equals 72 degrees.
Question 23
23. Use the graph below to answer the question that follows.
The number line is labeled test scores and has eleven evenly distributed tick marks labeled zero, ten,
twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, one hundred. Three box plots are shown
above the number line.
The top boxplot is labeled class A. Its leftmost whisker starts at ten and extends to the leftmost
vertical line of the box at approximately sixty five. Inside the box is a vertical line at seventy.
The rightmost vertical line is at approximately eighty five, from which extends the rightmost whisker
to approximately ninety five.
The middle boxplot is labeled class B. Its leftmost whisker starts at fifty and extends to the leftmost
vertical line of the box at seventy. Inside the box is a vertical line at approximately seventy eight.
The rightmost vertical line is at approximately eighty two, from which extends the rightmost whisker
to approximately ninety five.
The bottom boxplot is labeled class C. Its leftmost whisker starts at thirty and extends to the leftmost
vertical line of the box at sixty. Inside the box is a vertical line at seventy. The rightmost vertical
line is at approximately seventy five, from which extends the rightmost whisker to ninety.
Three high school science classes took the same test, the scores of which are shown in the boxandwhiskers
plots. Which of the following statements is true regarding the test scores?
 At least half the students in each class scored 70 or above.
 Class B had the fewest number of students taking the test.
 All three classes had the same median score.
 The mean score for Class A was higher than the mean score for Class C.
Answer to question 23
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0011) The median score, indicated
by the vertical line inside the box, for Class A and C was 70, so at least half of those two classes
scored 70 or above. The first quartile score, indicated by the leftmost vertical line of the box, for
Class B was 70 so 75% of that class scored 70 or above. At least half the students in each class scored
70 or above.
Correct Response: A. (Objective 0011) The median score, indicated by the vertical
line inside the box, for Class A and C was seventy, so at least half of those two classes scored seventy
or above. The first quartile score, indicated by the leftmost vertical line of the box, for Class B
was seventy so seventy five percent of that class scored seventy or above. At least half the students
in each class scored seventy or above.
Question 24
24. If a 6sided die is rolled twice, what is the probability that the sum of the two rolls will be
8?




Answer to question 24
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0012) The sample space consisting
of all possible sums that could be obtained when the die is rolled twice is shown in the table. There
are 36 possible sums; 5 of those sums equal 8. The probability that the two rolls sum to 8 is
.


First Roll

Second
Roll


1

2

3

4

5

6

1

2

3

4

5

6

7

2

3

4

5

6

7

8

3

4

5

6

7

8

9

4

5

6

7

8

9

10

5

6

7

8

9

10

11

6

7

8

9

10

11

12

Question 25
25. Five similar hats belonging to five people are placed in a box. Each person draws a hat without
looking. What is the probability that each hat will be chosen by its owner?




Answer to question 25
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0012) Initially there are
five hats in the box and the probability of the first person drawing his or her hat is
. When the second person draws
a hat, there are four in the box and the probability of the second person drawing his or her hat is
, and so on. The probability
of this compound event is the product of the probability of the individual events, or
.
Correct Response: D. (Objective 0012) Initially there are five hats in the box
and the probability of the first person drawing his or her hat is one fifth. When the second person
draws a hat, there are four in the box and the probability of the second person drawing his or her hat
is one fourth, and so on. The probability of this compound event is the product of the probability of
the individual events, or one fifth times one fourth times one third times one half times one over one
equals one over one hundred and twenty.
Question 26
26. A tetrahedral die is shaped like a pyramid with 4 faces that are each an equilateral triangle and
each numbered 1 through 4. When a tetrahedral die is rolled, it is the number on the down face that
counts as the roll. If a 6sided die and a tetrahedral die are rolled, what is the probability that
the sum of the two numbers rolled is 8 or more?




Answer to question 26
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0012) This problem has a
sample space consisting of all the possible sums that could be obtained when the dice are rolled, as
shown in the table below.
Tetrahedral
die

6sided die


1

2

3

4

5

6

1

2

3

4

5

6

7

2

3

4

5

6

7

6

3

4

5

6

7

8

9

4

5

6

7

8

9

10

There are 24 possible sums; 6 of those sums equal 8 or more. Therefore, the probability that the sum
of the numbers rolled is 8 or more is
6 over 24
or
1 fourth.
Question 27
27. Which of the following aspects of the survey process is most important for producing a reliable
survey?
 the cost of the study
 generalizable results
 a random sample
 a very large sample size
Answer to question 27
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0012) The reliability of
a survey depends on obtaining a representative sample of the population being studied. Surveying a properly
designed random sample is the best way to ensure that the data collected are representative of the population.
Correct Response: C. (Objective 0012) The reliability of a survey depends on obtaining
a representative sample of the population being studied. Surveying a properly designed random sample
is the best way to ensure that the data collected are representative of the population.
Question 28
28. A person throws a beanbag that hits the rectangular target with three holes shown below.
Board that is four foot tall and three feet wide with three rectangular holes cut out of it one on top
of the other. The top hole is labeled one hundred and is centered horizontally and is six inches wide
and eight inches tall. The middle hole is labeled forty and is sixteen inches wide and eight inches
tall. the bottom and last hole is labeled twenty five and is twenty inches wide and eight inches tall.
If the beanbag is equally likely to go through any hole on the target, what is the approximate probability
that the person will get a score of 40?
 7.4%
 10.7%
 12.8%
 31.8%
Answer to question 28
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0012) Since it is equally
likely for the beanbag to go through any hole on the target, the probability that the person will get
a score of 40 depends on the beanbag going through the hole marked 40. This is calculated by comparing
the area of the hole to the area of the entire target, as follows:
Correct Response: A. (Objective 0012) Since it is equally likely for the beanbag
to go through any hole on the target, the probability that the person will get a score of 40 depends
on the beanbag going through the hole marked 40. This is calculated by comparing the area of the hole
to the area of the entire target, as follows: start fraction numerator sixteen times eight denominator
thirty six times forty eight end fraction equals one hundred and twenty eight over one thousand seven
hundred and twenty eight equals zero point zero seven four equals seven point four percent.
Question 29
29. An experimental study enrolled 240 people to test the effects of a certain herbal formulation on
sleep quality. The participants were divided into three equal groups. One group received a low dosage
of the herbal formulation, one group received a high dosage, and one group received a placebo. At the
beginning of the study, participants filled out a questionnaire that asked about their current quality
of sleep and were given a score based on their answers. After two weeks, participants were given the
same questionnaire and a score based on their answers. The results are shown in the table below.
Score Increase After Two
Weeks

Low
Dosage

High
Dosage

Placebo

Less than 2 points

50

223

56

2 to 4 points

27

41

22

More than 4 points

3

16

2

What is the approximate probability that a participant in the study will have a score increase between
2 and 4 points?
 24%
 38%
 62%
 76%
Answer to question 29
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0012) The total number of
participants in the study is 240. The number of participants who had a score increase of 2 to 4 points
is 27 + 41 + 22, or 90. Therefore, the probability that a study participant had a score increase of
between 2 and 4 points is
,
or approximately 38%.
Correct Response: B. (Objective 0012) The total number of participants in the study
is 240. The number of participants who had a score increase of 2 to 4 points is 27 plus 41 plus 22,
or 90. Therefore, the probability that a study participant had a score increase of between 2 and 4 points
is ninety over two hundred and forty, or approximately 38 percent.
Question 30
30. Use the diagram below to answer the question that follows.
There are 8 sections of equal size on a spinner. If the spinner is spun 3 times, which of the following
percents most closely represents the probability that all 3 spins land on a unique color?
 13%
 38%
 66%
 88%
Answer to question 30
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0012) The first spin has
an
chance of landing on a unique color because every color is unique on the first spin. The second spin
has a
chance of landing on a unique spin because there are 7 remaining unique colors. The third spin has a
chance of landing on a unique color because there are 6 remaining unique colors. The probability of
this compound event is the product of the probabilities of the individual events, or
.
Correct Response: C. (Objective 0012) The first spin has an eight eighths chance
of landing on a unique color because every color is unique on the first spin. The second spin has a
seven eighths chance of landing on a unique spin because there are seven remaining unique colors. The
third spin has a six eighths chance of landing on a unique color because there are six remaining unique
colors. The probability of this compound event is the product of the probabilities of the individual
events, or eight eighths times seven eighths times six eighths which equals three hundred thirty six
five hundred twelfths which approximately equals sixty six percent.
Question 31
31. An entry of "1" in the matrix below indicates that a ship can communicate directly with another
ship and an entry of "0" indicates that a ship cannot communicate directly with another ship.
Start four by four matrix row a column a, zero, row a column b one, row a column c one, row a column
d zero. row b column a one row b column b zero, row b column c one, row b column d one, row c column
a zero, row c column b one, row c column c zero, row c column d zero, row d column a one, row d column
b zero, row d column c zero, row d column d zero end matrix.
Which of the following directed graphs contains the communication data of four ships A–D that
could generate the matrix above?




Answer to question 31
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0013) In the given matrix,
cells AB and BA both contain the numeral 1, indicating twoway communication between the two ships.
This twoway communication is represented in the directed graph by a twoway arrow between A and B.
Cell AC contains the numeral 1, but CA contains a 0, indicating that A can communicate with C but that
C cannot communicate with A. This oneway communication is represented in the directed graph as a oneway
arrow from A to C. Use these guidelines to confirm that the directed graph below reflects the information
in the given matrix.
Correct Response: A. (Objective 0013) In the given matrix, cells A B and B A both
contain the numeral 1, indicating twoway communication between the two ships. This twoway communication
is represented in the directed graph by a twoway arrow between A and B. Cell A C contains the numeral
1, but C A contains a 0, indicating that A can communicate with C but that C cannot communicate with
A. This oneway communication is represented in the directed graph as a oneway arrow from A to C. Use
these guidelines to confirm that the directed graph below reflects the information in the given matrix.
directed graph with arrows point from one letter to another with letters a, b, c and d. letter a points
to b and c, letter b points to a c and d, letter c points to b, and letter d points to a.
Question 32
32. A store lowers the price of a coat at the end of each week that the coat has not sold. The table
below shows the sale price of the coat as a function of the number of weeks it has been in the store.
Number of
Weeks (x)

0

1

2

3

4

5

Sale Price
(in Dollars)
(f(x))

350

340

320

290

250

200

Which of the following functions models these data?
 f(x) = 350 − 10x
 f(x) = 35 − x
 f(x) = 350 − 5x − 5x^{2}
 f(x) = 70 − x − x^{2}
Answer to question 32
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0013) The table below shows
the first and second finite differences in the f(x) values.
The second finite differences are equal, indicating that the function will be a secondorder quadratic
equation of the form y = ax^{2} + bx + c. For x
= 0, f(0) = 350 = a(0)^{2} + b(0) + c
350 = c. For x = 1, f(1) = 340 = a(1)^{2} + b(1)
+ 350
−10 = a + b
b = −a − 10. For x = 2, f(2) = 320 = a (2)^{2}
+ b (2) + 350
−15 = 2a + b. By substitution, −15 = 2a + (−a
− 10)
−5 = a and b = −(−5) − 10 = −5. Thus, the function that models the data
is f(x) = 350 − 5x − 5x^{2}.
Correct Response: C. (Objective 0013) The table below shows the first and second
finite differences in the f of x values.
Data table. First column has row headers first row number of weeks open parenthesis x close parenthesis,
second row sale price open parenthesis in dollars close parenthesis open parenthesis f of x close parenthesis,
third row first finite difference, fourth row second finite difference.
The sale price in zero week is three hundred and fifty, first week three hundred and forty, second week
three hundred and twenty, third week, two hundred and ninety, fourth week two hundred and fifty and
finally the fifth week two hundred.
The first finite difference in week zero and week one from three hundred and fifty to three hundred
and forty is ten, the difference in week one and week two between three hundred and forty and three
hundred and twenty is tweny, the difference in week two and three from three hundred and twenty to three
hundred and thirty, the difference in week three and week four from two hundred and nintey to two hundred
and fifty is forty, and the difference between week four and week five from two hundred and fifty to
two hundred is fifty. The second finite difference between the first finite difference of week zero
and one is ten, the second difference between the first finite difference of week one and week two is
ten, the second difference between the first finite difference of week two and three is ten, the second
difference between the first finite difference of week three and four is ten, and the second difference
between the first finite difference of week four and five is ten.
The second finite differences are equal, indicating that the function will be a secondorder quadratic
equation of the form y equals a x squared plus b x plus c. For
x equals 0, f open parenthesis zero close parenthesis equals 350 equals a
open parenthesis 0 close parenthesis squared plus b open parenthesis 0 close parenthesis plus
c leads to 350 equals c. For x equals 1, f open parenthesis one close parenthesis
equals 340 equals a open parenthesis one close parenthesis squared plus b open parenthesis
one close parenthesis plus 350 leads to negative 10 equals a plus b leads to b
equals negative a minus 10.
For x equals 2, f open parenthesis two close parenthesis equals 320 equals a open parenthesis
2 close parenthesis squared plus b open parenthesis 2 close parenthesis plus 350 leads to negative 15 equals
2 a plus b. By substitution, negative 15 equals 2 a plus open parenthesis negative
a minus 10 close parenthesis leads to negative 5 equals a and b equals negative open parenthesis
negative 5 close parenthesis minus 10 equals negative 5. Thus, the function that models the data is f of
x equals 350 minus 5 x minus 5 x squared.
Question 33
33. A teacher has a total of 25 math problems on a particular topic and would like to create an assignment
using 5 of the problems. How many different assignments could the teacher create?
 25 •times 24
•times 23 •times
22 •times 21
 25!
 25 •times 25
•times 25 •times
25 •times 25

Answer to question 33
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0013) There are 25 problems
to choose from. Since the same 5 problems in any order is the same assignment, this scenario describes
a combination.
The formula for a combination of n things taken r at a time is
.
Correct Response: D. (Objective 0013) There are 25 problems to choose from. Since
the same 5 problems in any order is the same assignment, this scenario describes a combination. The
formula for a combination of n things taken r at a time is start fraction numerator
twenty five factorial denominator twenty factorial times five factorial end fraction.
Question 34
34. Use the diagram below to answer the question that follows.
The map shows the possible routes a van can travel from locations A, B, C, and D. A van has to stop
at all 4 locations to drop off students, starting at location A on the map and ending at location D.
Which of the following expressions can be used to determine the number of ways the van can get from
location A to B to C to D in order?
 3 • 2 • 3three times two times three
 3! • 2! • 3!three factorial times
two factorial times three factorial
 3 + 2 + 3
 3! + 2! + 3!three factorial plus two factorial
plus three factorial
Answer to question 34
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0013) The number of ways
to get from A to B to C to D can be illustrated by the tree diagram shown. There are 3 ways to get from
A to B, then 2 choices to get from B to C, and then 3 routes from C to D. The total number of ways to
get from A to B to C to D in order is 3 • 2 • 3.
Correct Response: A. (Objective 0013) The number of ways to get from A to B to
C to D can be illustrated by the tree diagram shown. There are three ways to get from A to B, then two
choices to get from B to C, and then three routes from C to D. The total number of ways to get from
A to B to C to D in order is three times two times three.
A tree diagram is shown. From the letter A there are three branches, each extending to a letter B. From
each of the letter B's, there are two branches, each extending to a letter C. From each of the letter
C's, there are three branches, each extending to the letter D.
Question 35
35. Use the table below to answer the question that follows.

Admission
Cost

Number of Students

Class ANumber of Students Class A

Class BNumber of Students Class B

Science Museum

$12

15

7

Aquarium

$15

10

18

Planetarium

$20

9

10

Students from two classes are going on 3 field trips. The number of students going on each trip, as
well as the admission price per student, are shown in the table. Which of the following matrix products
represents the total admission costs for each class?




Answer to question 35
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0013) To find the total admission
costs, multiply the number of students attending the field trips by their respective admission costs.
A matrix has dimensions m x n if it has m rows and n columns. In
order for a product of two matrices to be defined, the number of columns in the first matrix must equal
the number of rows in the second matrix. Using the 2 x 3 matrix
to represent the number of students in each class choosing each field trip and the 3 x 1 matrix
to represent the admission costs will allow for a defined product that represents the total admission
costs of
.
Correct Response: D. (Objective 0013) To find the total admission costs, multiply
the number of students attending the field trips by their respective admission costs. A matrix has dimensions
m by n if it has m rows and n columns. In order for a product of 2 matrices to be defined, the number
of columns in the first matrix must equal the number of rows in the second matrix. Using the 2 by 3
matrix; 15, 10, 9, 7, 18, 10; to represent the number of students in each class choosing each field
trip and the 3 by 1 matrix; 12, 15, 20; to represent the admission costs will allow for a defined product
that represents the total admission costs of the 2 by 3 matrix; 15, 10, 9, 7, 18, 10; times the 3 by
1 matrix; 12, 15, 20.
Question 36
36. A mathematics teacher plans the student activities listed below as part of a new unit of study.
 comparing new terminology with related terminology from previous units
 developing nonverbal representations (e.g., charts, illustrations) of new terminology
 classifying new terminology according to specific criteria
 generating analogies with new terminology
These activities are likely to promote students' reading comprehension related to this unit primarily
in which of the following ways?
 by providing the students with strategies for determining the meaning of unfamiliar vocabulary as they
read
 by broadening the students' understanding of new vocabulary words and their associated concepts
 by teaching the students how to use structural analysis as a strategy for building domainspecific
vocabulary
 by promoting the students' ability to decode and spell new vocabulary words accurately
Answer to question 36
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0014) Vocabulary knowledge
is both a key indicator and predictor of reading comprehension ability. Vocabulary knowledge and concept
development are closely interrelated; disciplinespecific vocabulary development involves concept learning
and concept learning supports academic vocabulary development. Vocabulary development is an incremental
process; more exposures to and opportunities to use new vocabulary in context result in greater depth
of understanding. The instructional activities used by the teacher provide students with multiple opportunities
to use the vocabulary from a new unit of study in context, thus promoting the students' vocabulary development
and strengthening their understanding of related concepts.
Correct Response: B. (Objective 0014) Vocabulary knowledge is both a key indicator
and predictor of reading comprehension ability. Vocabulary knowledge and concept development are closely
interrelated; disciplinespecific vocabulary development involves concept learning and concept learning
supports academic vocabulary development. Vocabulary development is an incremental process; more exposures
to and opportunities to use new vocabulary in context result in greater depth of understanding. The
instructional activities used by the teacher provide students with multiple opportunities to use the
vocabulary from a new unit of study in context, thus promoting the students' vocabulary development
and strengthening their understanding of related concepts.
Question 37
37. Some students in a middlelevel mathematics class are English language learners and/or struggling
readers who lack the basic reading skills necessary to fully comprehend assigned readings. Which of
the following strategies would be most appropriate for the middlelevel mathematics teacher to use to
scaffold the reading comprehension of these students?
 providing the students with oral previews of text content and noting key concepts on the board
 having the students conduct alternative content research using online texts rather than printed ones
 teaching the students the basic reading skills they lack and reviewing key skills before assignments
 substituting lowerlevel mathematics texts for the students' reading assignments
Answer to question 37
 AnswerAnswer. Click to expand or collapse.
 Correct Response: A. (Objective 0014) Teachers need to provide
scaffolding to English language learners and struggling readers who lack the basic reading skills necessary
to comprehend assigned contentarea readings. An oral preview of the content covered in a class reading
assignment provides scaffolding by activating students' prior knowledge related to a text and building
needed vocabulary and background knowledge required to make inferences and repair comprehension during
reading. Noting key concepts on the board during the oral preview both reinforces the new concepts and
vocabulary and helps students become familiar with how these elements will appear in print.
Correct Response: A. (Objective 0014) Teachers need to provide scaffolding to English
language learners and struggling readers who lack the basic reading skills necessary to comprehend assigned
contentarea readings. An oral preview of the content covered in a class reading assignment provides
scaffolding by activating students' prior knowledge related to a text and building needed vocabulary
and background knowledge required to make inferences and repair comprehension during reading. Noting
key concepts on the board during the oral preview both reinforces the new concepts and vocabulary and
helps students become familiar with how these elements will appear in print.
Question 38
38. An informational text uses many signal or transition words and phrases such as in the same way,
likewise, in similar fashion, nonetheless, however, though,
and on the other hand. These transition words suggest that the text is most likely organized
according to which of the following text structures?
 descriptive
 cause/effect
 sequential
 comparison/contrast
Answer to question 38
 AnswerAnswer. Click to expand or collapse.
 Correct Response: D. (Objective 0014) Authors use transition
words and phrases to link key ideas in a text. Transitions help establish cohesion and coherence in
written discourse, which help readers follow the text's argument and/or logic. Learning to recognize
the transition words and phrases that signal a particular text structure is a powerful comprehension
tool for students. The transitions in the same way, likewise, and in similar fashion
all indicate comparison, while nonetheless, however, though, and on the
other hand indicate contrast; thus, a text that includes all these transition words and phrases
would follow a comparison/contrast text structure.
Correct Response: D. (Objective 0014) Authors use transition words and phrases
to link key ideas in a text. Transitions help establish cohesion and coherence in written discourse,
which help readers follow the text's argument and/or logic. Learning to recognize the transition words
and phrases that signal a particular text structure is a powerful comprehension tool for students. The
transitions in the same way, likewise, and in similar fashion all indicate
comparison, while nonetheless, however, though, and on the other hand
indicate contrast; thus, a text that includes all these transition words and phrases would follow a
comparison/contrast text structure.
Question 39
39. Which of the following strategies would be most appropriate for students to use after reading a
mathematics text to promote their comprehension of the text?
 setting a goal or goals for reading the text
 making predictions about the text's content
 summarizing the text's key ideas and details
 looking for clues about the text's structure
Answer to question 39
 AnswerAnswer. Click to expand or collapse.
 Correct Response: C. (Objective 0014) Summarizing requires
students to reflect on the information in a text and restate it concisely in their own words. In order
to distill the information in a text in a concise form that uses synonyms and/or explanations for key
concepts that differ from those used in the text (while still conveying the same ideas), students need
to think about the text at a fairly deep level. Such thinking promotes both understanding and retention
of the information in the text. Unlike other comprehension strategies that can be used before, during,
and/or after reading, summarizing is best completed after reading a text.
Correct Response: C. (Objective 0014) Summarizing requires students to reflect
on the information in a text and restate it concisely in their own words. In order to distill the information
in a text in a concise form that uses synonyms and/or explanations for key concepts that differ from
those used in the text (while still conveying the same ideas), students need to think about the text
at a fairly deep level. Such thinking promotes both understanding and retention of the information in
the text. Unlike other comprehension strategies that can be used before, during, and/or after reading,
summarizing is best completed after reading a text.
Question 40
40. Helping students learn how to reflect on, monitor, and regulate their own thinking processes supports
their contentarea reading primarily by improving their ability to:
 read contentarea texts accurately and at an appropriate rate.
 apply comprehension strategies when reading contentarea texts.
 deconstruct the syntax of complex sentences found in contentarea texts.
 determine the meaning of unfamiliar multisyllabic words in contentarea texts.
Answer to question 40
 AnswerAnswer. Click to expand or collapse.
 Correct Response: B. (Objective 0014) There are a variety
of comprehension strategies that can be used before, during, and/or after reading. For students to be
able to select and adapt the right strategy for a particular text or reading situation, they need to
use metacognitive knowledge and metacognitive control; that is, they need to be aware of how they are
thinking and learning as they read and be able to adapt their learning approaches as necessary.
Correct Response: B. (Objective 0014) There are a variety of comprehension strategies
that can be used before, during, and/or after reading. For students to be able to select and adapt the
right strategy for a particular text or reading situation, they need to use metacognitive knowledge
and metacognitive control; that is, they need to be aware of how they are thinking and learning as they
read and be able to adapt their learning approaches as necessary