Math Test—No Calculator
20 Questions
Turn to Section 3 of your answer sheet to answer the questions
in this section.
Directions
For questions 1 through 15, solve each problem, choose the
best answer from the choices provided, and indicate your answer
choice on your answer sheet. For questions 16 through 20,
solve the problem and indicate your answer, which is to be recorded
in the spaces provided on the answer sheet. Please refer to the
directions before question 16 on how to record your answers in
the spaces provided. You may use scratch paper for scratch
work.
Notes
1. The use of a calculator is not permitted.
2. All variables and expressions used represent real
numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless
otherwise indicated.
4. All figures lie in a plane unless otherwise
indicated.
5. Unless otherwise indicated, the domain of a given
function f is the set of all real numbers x for which f
of x is a real number
Reference
Begin skippable figure descriptions.
The figure presents information for your reference in solving
some of the problems.
Reference figure 1 is a circle with radius r. Two equations
are presented below reference figure 1.
A equals pi times the square of r.
C equals 2 pi r.
Reference figure 2 is a rectangle with length ℓ and
width w. An equation is presented below reference
figure 2.
A equals ℓ w.
Reference figure 3 is a triangle with base b and
height h. An equation is presented below reference
figure 3.
A equals one half b h.
Reference figure 4 is a right triangle. The two sides that form
the right angle are labeled a and b, and the side
opposite the right angle is labeled c. An equation is
presented below reference figure 4.
c squared equals a squared plus b squared.
Special Right Triangles
Reference figure 5 is a right triangle with a 30 degree
angle and a 60 degree angle. The side opposite the
30 degree angle is labeled x. The side opposite the
60 degree angle is labeled x times the
square root of 3. The side opposite the right angle is
labeled 2 x.
Reference figure 6 is a right triangle with two 45 degree
angles. Two sides are each labeled s. The side opposite the
right angle is labeled s times the square root
of 2.
Reference figure 7 is a rectangular solid whose base has
length ℓ and width w and whose height is h. An
equation is presented below reference figure 7.
V equals ℓ w h.
Reference figure 8 is a right circular cylinder whose
base has radius r and whose height is h. An equation is
presented below reference figure 8.
V equals pi times the square of
r times h.
Reference figure 9 is a sphere with radius r. An equation
is presented below reference figure 9.
V equals four thirds pi times the cube of r.
Reference figure 10 is a cone whose base has radius r and
whose height is h. An equation is presented below
reference figure 10.
V equals one third times pi times the square of
r times h.
Reference figure 11 is an asymmetrical pyramid whose base has
length ℓ and width w and whose height is h. An
equation is presented below reference figure 11.
V equals one third ℓ w h.
End skippable figure descriptions.
Additional Reference Information
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2 pi.
The sum of the measures in degrees of the angles of a triangle
is 180.
Question 1 is based on the following equation.
2 z plus 1, equals z
Question 1.
What value of z satisfies the preceding equation?
A. negative 2
B. negative 1
C. one half
D. 1
Question 2.
A television with a price of $300 is to be purchased with an
initial payment of $60 and weekly payments of $30. Which of the
following equations can be used to find the number of weekly
payments, w, required to complete the purchase, assuming there are
no taxes or fees?
A. 300 equals, 30 w minus 60
B. 300 equals, 30 w
C. 300 equals, 30 w plus 60
D. 300 equals, 60 w minus 30
Question 3 is based on the following table.
Shipping Charges
Merchandise weight (pounds)
Shipping charge
5
$16.94
10
$21.89
20
$31.79
40
$51.59
Question 3.
The preceding table shows shipping charges for an online
retailer that sells sporting goods. There is a linear relationship
between the shipping charge and the weight of the merchandise.
Which function can be used to determine the total shipping charge
f of x, in dollars, for an order with a merchandise
weight of x pounds?
A. f of x equals, 0.99 x
B. f of x equals, 0.99 x, plus 11.99
C. f of x equals, 3.39 x
D. f of x equals, 3.39 x, plus 16.94
Question 4 is based on the following figure.
Begin skippable figure description.
The figure presents the graph of a line in the x yplane,
with the origin labeled O. The numbers 1 through 6, in increments
of 1, are indicated on the xaxis. The numbers 7 through 42, in
increments of 7, are indicated on the yaxis. The line is labeled
“y, equals h of x,” and begins at the origin. The line slants
upward and to the right, and passes through the point with
coordinates 2 comma 14, and the point with coordinates
5 comma 35.
End skippable figure description.
Question 4.
The line in the preceding x yplane represents the
relationship between the height h of x, in feet, and the
base diameter x, in feet, for cylindrical Doric columns in
ancient Greek architecture. How much greater is the height of a
Doric column that has a base diameter of 5 feet than the
height of a Doric column that has a base diameter of
2 feet?
A. 7 feet
B. 14 feet
C. 21 feet
D. 24 feet
Question 5 is based on the following expression.
the square root of 9 x squared, end root
Question 5.
If x is greater than 0, which of the following is equivalent to
the given expression?
A. 3 x
B. 3 x squared
C. 18 x
D. 18 x to the fourth power
Question 6 is based on the following equation.
the fraction with numerator x squared, minus 1, and
denominator x minus 1, end fraction, equals
negative 2
Question 6.
What are all values of x that satisfy the preceding
equation?
A. negative 3
B. 0
C. 1
D. negative 3 and negative 1
Question 7 is based on the following figure.
Begin skippable figure description.
The figure presents the graph of a curve in the x yplane,
with the origin labeled O. The numbers negative 6 through 6,
in increments of 2, are indicated on the xaxis. The numbers
negative 2 through 4, in increments of 2, are indicated on the
yaxis. The curve is labeled “y, equals f of x.” It goes through the
point with approximate coordinates one half comma 5, curves
downward and to the left, and crosses the yaxis at the point with
coordinates 0 comma 4. It curves further downward and to the left,
and approaches the xaxis closely at x equals negative 5, moves
all the way left closely to, but never touching, the xaxis.
End skippable figure description.
Question 7.
The graph of y equals, f of x is shown in the x yplane.
What is the value of f of 0 ?
A. 0
B. 2
C. 3
D. 4
Question 8 is based on the following figure.
Begin skippable figure description.
The figure presents horizontal line segment A D, with
point D to the right of point A. Point B lies on
line segment A D and point C is vertically above
point B, such that line segment B C is perpendicular
to A D. Two line segments are drawn from point B between
line segments B C and B D, dividing
angle C B D into three angles labeled
x degrees, 2 x degrees, and
2 x degrees.
End skippable figure description.
Question 8.
In the preceding figure, point B lies on line
segment A D. What is the value
of 3 x ?
A. 18
B. 36
C. 54
D. 72
Question 9 is based on the following figure.
Begin skippable figure description.
The figure presents the graph of line l in the
x yplane, with the origin labeled O. The numbers
negative 4 through 4, in increments of 2, are indicated on
each axis. The line slants downward and to the right, crossing the
xaxis at negative 4, and crossing the yaxis at
negative 4.
End skippable figure description.
Question 9.
Which of the following is an equation of line l in the preceding
x yplane?
A. x minus y, equals negative 4
B. x minus y, equals 4
C. x plus y, equals negative 4
D. x plus y, equals 4
Question 10 is based on the following figure.
Begin skippable figure description.
The figure presents the graph of a parabola in the
x yplane, with the origin labeled O. No numbers are indicated
on the xaxis. A number k is indicated on the yaxis above the
origin. The parabola opens upward. It begins to the left of the
yaxis, above the xaxis, and moves downward and to the right. It
crosses the xaxis, turns just below the xaxis, crosses the xaxis
again, and moves upward and to the right. It crosses the yaxis at k
before it ends.
End skippable figure description.
Question 10.
The graph of y equals, 2 x squared, plus 10 x,
plus 12 is shown. If the graph crosses the yaxis at the point with
coordinates 0 comma k, what is the value
of k ?
A. 2
B. 6
C. 10
D. 12
Question 11.
A circle in the x yplane has center with coordinates 5
comma 7 and radius 2. Which of the following is an equation of
the circle?
A. open parenthesis, x minus 5, close parenthesis,
squared, plus, open parenthesis, y minus 7, close parenthesis,
squared, equals 4
B. open parenthesis, x plus 5, close parenthesis, squared,
plus, open parenthesis, y plus 7, close parenthesis, squared,
equals 4
C. open parenthesis, x minus 5, close parenthesis,
squared, plus, open parenthesis, y minus 7, close parenthesis,
squared, equals 2
D. open parenthesis, x plus 5, close parenthesis, squared,
plus, open parenthesis, y plus 7, close parenthesis, squared,
equals 2
Question 12 is based on the following figure.
Begin skippable figure description.
The figure presents triangle A B C and a bigger
triangle D E F. Angle A and angle D are
both marked with the right angle symbol. Side A B is
labeled 12, side A C is labeled 5, and side B C
is labeled 13. The sides of triangle D E F are
not labeled.
End skippable figure description.
Question 12.
In the preceding figure, triangle A B C is
similar to triangle D E F. What is the value of the
cosine of E ?
A. 12 over 5
B. 12 over 13
C. 5 over 12
D. 5 over 13
Question 13.
In the x yplane, the graph of the function f of x, equals,
x squared, plus 5 x, plus 4 has two xintercepts. What is
the distance between the xintercepts?
A. 1
B. 2
C. 3
D. 4
Question 14 is based on the following equation.
the square root of 4 x, end root, equals,
x minus 3
Question 14.
What are all values of x that satisfy the given equation?
Value 1. 1
Value 2. 9
A. Value 1 only
B. Value 2 only
C. Value 1 and value 2
D. Neither value 1 nor value 2
Question 15 is based on the following two equations.
Equation 1: negative 3 x, plus y, equals 6.
Equation 2: a x, plus 2 y, equals 4.
Question 15.
In the preceding system of equations, a is a constant. For which
of the following values of a does the system have no solution?
A. negative 6
B. negative 3
C. 3
D. 6
Directions
For questions 16 through 20, solve the problem and record your
answer in the spaces provided on the answer sheet, as described in
the following directions and examples.
1. Although not required, it is suggested that your answer
be recorded in the boxes at the top of the columns to help fill in
the bubbles accurately. You will receive credit only if the bubbles
are filled in correctly.
2. Mark no more than one bubble in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In
such cases, indicate only one answer.
5. Mixed numbers such as three and one half must be
recorded as 3.5 or seven slash two. (If
three, one, slash, two, is recorded in the spaces
provided on the answer sheet, it will be interpreted as thirty one
halves, not three and one half.)
6. Decimal answers: If you obtain a decimal answer with
more digits than the spaces on the answer sheet can accommodate, it
may be either rounded or truncated, but it must fill all four
spaces.
The following are four examples of how to record your answer in
the spaces provided. Keep in mind that there are four spaces
provided to record each answer.
Examples 1 and 2
Begin skippable figure description.
Example 1: If your answer is a fraction such as seven twelfths,
it should be recorded as follows. Enter 7 in the first space, the
fraction bar (a slash) in the second space, 1 in the
third space, and 2 in the fourth space. All four spaces would be
used in this example.
Example 2: If your answer is a decimal value such as 2.5, it
could be recorded as follows. Enter 2 in the second space, the
decimal point in the third space, and 5 in the fourth space. Only
three spaces would be used in this example.
End skippable figure description.
Example 3
Begin skippable figure description.
Example 3: Acceptable ways to record two thirds are: 2 slash 3,
.666, and .667.
End skippable figure description.
Example 4
Note: You may start your answers in any column, space
permitting. Columns you don’t need to use should be left blank.
Begin skippable figure description.
Example 4: It is not necessary to begin recording answers in the
first space unless all four spaces are needed. For example, if your
answer is 201, you may record 2 in the second space, 0 in the third
space, and 1 in the fourth space. Alternatively, you may record 2
in the first space, 0 in the second space, and 1 in the third
space. Spaces not needed should be left blank.
End skippable figure description.
Question 16 is based on the following equation.
T equals, 5 c, plus 12 f
Question 16.
A manufacturer shipped units of a certain product to two
locations. The preceding equation shows the total shipping
cost T, in dollars, for shipping c units to the closer
location and shipping f units to the farther location. If the
total shipping cost was $47,000 and 3000 units were shipped to
the farther location, how many units were shipped to the closer
location?
Question 17 is based on the following equation.
the absolute value of, 2 x, plus 1, end absolute value,
equals 5
Question 17.
If a and b are the solutions to the preceding equation, what is
the value of the absolute value of, a, minus b, end absolute
value?
Question 18.
Juan purchased an antique that had a value of $200 at the time
of purchase. Each year, the value of the antique is estimated to
increase 10% over its value the previous year. The estimated value
of the antique, in dollars, 2 years after purchase can be
represented by the expression 200 a, where a is a constant.
What is the value of a ?
Question 19 is based on the following two equations.
Equation 1: 2 x, plus 3 y, equals 1200.
Equation 2: 3 x, plus 2 y, equals 1300.
Question 19.
Based on the preceding system of equations, what is the value of
5 x plus 5 y ?
Question 20.
If u plus t, equals 5 and u minus t, equals 2, what is the value
of open parenthesis, u minus t, close parenthesis, times, open
parenthesis, u squared, minus t squared, close
parenthesis?
Stop.
If you finish before time is called, you may check your work on
this section only. Do not go on to any other section.
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