Download The S A T ® Practice Test #6 - collegereadiness

The SAT®
Practice Test #6
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.
©2016 The College Board.
Page 1
Reference
Begin skippable figure descriptions.
The figure presents information for your reference in solving some of
the problems.
©2016 The College Board.
Page 2
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 bh.
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.
©2016 The College Board.
Page 3
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.
©2016 The College Board.
Page 4
Question 1.
Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor
charges a one-time service fee for processing the purchase of the tickets. The
equation
T equals 15n plus 12 represents the total amount T, in
dollars, Salim will pay for n tickets. What does 12 represent in the equation?
A.
B.
C.
D.
The price of one ticket, in dollars
The amount of the service fee, in dollars
The total amount, in dollars, Salim will pay for one ticket
The total amount, in dollars, Salim will pay for any number of tickets
Question 2.
A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials
by weight and Fertilizer B contains 40% filler materials by weight. Together, the
fertilizers bought by the gardener contain a total of 240 pounds of filler materials.
Which equation models this relationship, where x is the number of pounds of
Fertilizer A and y is the number of pounds of Fertilizer B?
A.
0.4x, plus, 0.6y, equals 240
B.
0.6x, plus, 0.4y, equals 240
C.
D.
40x, plus, 60y, equals 240
60x, plus, 40y, equals 240
©2016 The College Board.
Page 5
Question 3.
What is the sum of the complex numbers
where
A. 17
B. 17i
C.
D.
2 plus 3i and
4 plus 8i,
i equals the square root of negative 1?
6 plus 11i
8 plus 24i
Question 4 refers to the following equation.
4x squared minus 9, equals, open parenthesis, px
plus t, close parenthesis, times, open parenthesis, px minus t, close parenthesis
Question 4.
In the preceding equation, p and t are constants. Which of the following could be
the value of p ?
A.
B.
C.
D.
2
3
4
9
©2016 The College Board.
Page 6
Question 5.
Which of the following is the graph of the equation
minus 5 in the xy-plane?
y equals 2x
Each option presents the graph of a line in the xy-plane with the origin labeled O.
The numbers negative 5 and 5 are indicated on each axis.
A.
Begin skippable figure description.
The line begins in quadrant 3 and moves upward and to the right. It crosses the
x-axis at negative 5 and the y-axis at 2.5, ending in quadrant 1.
End skippable figure description.
©2016 The College Board.
Page 7
B.
Begin skippable figure description.
The line begins in quadrant 2 and moves downward and to the right. It crosses the
x-axis at negative 2.5 and the y-axis at negative 5, ending in quadrant 4.
End skippable figure description.
C.
Begin skippable figure description.
The line begins in quadrant 3 and moves upward and to the right. It crosses the
x-axis at negative 2.5 and the y-axis at 5, ending in quadrant 1.
End skippable figure description.
©2016 The College Board.
Page 8
D.
Begin skippable figure description.
The line begins in quadrant 3 and moves upward and to the right. It crosses the
y-axis at negative 5 and the x-axis at 2.5, ending in quadrant 1.
End skippable figure description.
Question 6.
If
x equals two-thirds y and
y equals 18, what is the value of
2x minus 3?
A.
B.
C.
D.
21
15
12
10
©2016 The College Board.
Page 9
Question 7.
A bricklayer uses the formula
n equals 7 l h to estimate the number of
bricks, n, needed to build a wall that is l feet long and h feet high. Which of the
following correctly expresses l in terms of n and h ?
A.
l equals the fraction whose numerator is 7 and whose denominator is
nh, end fraction
B.
l equals the fraction whose numerator is h and whose denominator is
7n, end fraction
C.
l equals the fraction whose numerator is n and whose denominator is
7h, end fraction
D.
l equals the fraction whose numerator is n and whose denominator
is 7 plus h, end fraction
©2016 The College Board.
Page 10
Question 8 refers to the following figure.
Begin skippable figure description.
The figure presents a 3-column table with 5 rows of data. The heading for
column 1 is “x,” the heading for column 2 is “w of x,” and the heading for
column 3 is “t of x.” The five rows of data are as follows.
Row 1: x, 1; w of x, negative 1; t of x, negative 3.
Row 2: x, 2; w of x, 3; t of x, negative 1.
Row 3: x, 3; w of x, 4; t of x, 1.
Row 4: x, 4; w of x, 3; t of x, 3.
Row 5: x, 5; w of x, negative 1; t of x, 5.
End skippable figure description.
Question 8.
The preceding table shows some values of the functions w and t. For which value
of x is
w of x plus t of x equal to x?
A.
B.
C.
D.
1
2
3
4
©2016 The College Board.
Page 11
Question 9.
If
the square root of x, end root, plus the square root of 9, end
root, equals the square root of 64, what is the value of x ?
A.
the square root of 5
B. 5
C. 25
D. 55
Question 10.
Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least
280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles
the second week, and 320 miles the third week. Which inequality can be used to
represent the number of miles, x, Jaime could bicycle on the 4th week to meet
his goal?
A.
the fraction whose numerator is 240 plus 310 plus
320, and whose denominator is 3, end fraction, plus x, is greater than or equal
to 280
B.
240 plus 310 plus 320, is greater than or equal to x
times 280
C.
the fraction 240 over 4, end fraction, plus the
fraction 310 over 4, end fraction, plus the fraction 320 over 4, end fraction,
plus x, is greater than or equal to 280
D.
240 plus 310 plus 320 plus x, is greater than or
equal to 4 times, 280
©2016 The College Board.
Page 12
Question 11 refers to the following figure.
Begin skippable figure description.
The figure presents a parabola labeled, y equals ax squared plus c, in the xy-plane
with the origin labeled O. The parabola opens upward and its vertex lies on the
y-axis a short distance above the origin.
End skippable figure description.
Question 11.
The vertex of the preceding parabola in the xy-plane is
the point with
coordinates 0 comma c. Which of the following is true about the parabola with the
equation
y equals negative a, times, open parenthesis,
x minus b, close parenthesis, squared, plus c?
A. The vertex is
the point with coordinates b comma c, and the graph opens
upward.
B. The vertex is
the point with coordinates b comma c, and the graph opens
downward.
C. The vertex is
the point with coordinates negative b comma c, and the
graph opens upward.
D. The vertex is
the point with coordinates negative b comma c, and the
graph opens downward.
©2016 The College Board.
Page 13
Question 12.
Which of the following is equivalent to
the fraction whose numerator is
4x squared, plus, 6x, and whose denominator is 4x plus 2, end fraction?
A. x
B.
x plus 4
C.
x minus the fraction whose numerator is 2, and whose denominator
is 4x plus 2, end fraction
D.
x plus 1 minus the fraction whose numerator is 2, and whose
denominator is 4 x plus 2, end fraction
Question 13 refers to the following equation.
2x squared minus 4x equals t
Question 13.
In the preceding equation, t is a constant. If the equation has no real solutions,
which of the following could be the value of t ?
A.
B.
C.
D.
negative 3
negative 1
1
3
©2016 The College Board.
Page 14
Question 14.
A laundry service is buying detergent and fabric softener from its supplier. The
supplier will deliver no more than 300 pounds in a shipment. Each container of
detergent weighs 7.35 pounds, and each container of fabric softener weighs
6.2 pounds. The service wants to buy at least twice as many containers of detergent
as containers of fabric softener. Let d represent the number of containers of
detergent, and let s represent the number of containers of fabric softener, where d
and s are nonnegative integers. Which of the following systems of inequalities best
represents this situation?
A.
7.35 d, plus, 6.2s, is less than or equal to 300, and,
d is greater than or equal to 2s
B.
7.35 d, plus, 6.2s, is less than or equal to 300, and,
2d is greater than or equal to s
C.
14.7 d, plus, 6.2s, is less than or equal to 300, and,
d is greater than or equal to 2s
D.
14.7 d, plus, 6.2s, is less than or equal to 300, and,
2d is greater than or equal to s
©2016 The College Board.
Page 15
Question 15.
Which of the following is equivalent to
open parenthesis, a, plus the
fraction b over 2, close parenthesis, squared?
A.
a, squared, plus the fraction b squared over 2
B.
a, squared, plus the fraction b squared over 4
C.
a, squared, plus the fraction ab over 2, end fraction, plus the
fraction b squared over 2
D.
a, squared, plus ab, plus the fraction b squared over 4
©2016 The College Board.
Page 16
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 circles accurately. You will receive
credit only if the circles are filled in correctly.
2. Mark no more than one circle 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
seven slash two. (If
three and one half must be recorded as 3.5 or
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.
©2016 The College Board.
Page 17
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.
©2016 The College Board.
Page 18
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.
©2016 The College Board.
Page 19
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.
©2016 The College Board.
Page 20
Question 16.
If
a, to the power of the fraction b over 4, end power, equals 16 for
positive integers a and b, what is one possible value of b ?
Question 17 refers to the following equation.
two-thirds t equals five-halves
Question 17.
What value of t is the solution of the preceding equation?
©2016 The College Board.
Page 21
Question 18 refers to the following figure.
Begin skippable figure description.
The figure presents triangle ACE, with horizontal side AC. Side AE is
perpendicular to side AC such that point E is above point A. Point B lies on
horizontal side AC, point D lies on hypotenuse CE, and line segment BD is drawn
such that it is parallel to side AE and forms triangle CDB. Side AE is labeled 18,
side BC is labeled 8, side BD is labeled 6, and a right angle symbol is at point A.
End skippable figure description.
Question 18.
In the preceding figure,
of
side CE ?
side BD is parallel to
side AE. What is the length
Question 19.
How many liters of a 25% saline solution must be added to 3 liters of a 10% saline
solution to obtain a 15% saline solution?
©2016 The College Board.
Page 22
Question 20.
Points A and B lie on a circle with radius 1, and arc
AB has length
pi over 3. What fraction of the circumference of the circle is the length of arc
AB ?
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.
©2016 The College Board.
Page 23