SAT Math Practice Test Two
SAT数学模拟试
题
快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题
二
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9. 10. 11.
12. 13. 14. 15.
16. 17. 18.
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A EDCB
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Test IIA
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Test IIC
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Test IIB
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235
Practice Test II
Practice TPractice Test Iest I IA: 25 Minutes, 1IA: 25 Minutes, 18 Questions (8 Multiple-8 Questions (8 Multiple-Choice andChoice and
1100 Grid-in)Grid-in)
Practice TPractice Test Iest I II B: 25 Minutes, 20 Multiple-B: 25 Minutes, 20 Multiple-Choice QuestionsChoice Questions
Practice TPractice Test Iest I IIC: 20 Minutes, 1C: 20 Minutes, 16 Multiple-6 Multiple-Choice QuestionsChoice Questions
Practice Test IIA
Time: 25 minutes
18 questions (8 multiple-choice and 10 grid-in)
Directions: This section is composed of two types of questions. Use the 25 minutes allotted to answer both question
types. For Questions 1–8, select the one correct answer of the five choices given and mark the corresponding circle on
your answer sheet. Your scratch work should be done on any available space in the section.
Notes
1. All numbers used are real numbers.
2. Calculators may be used.
3. Some problems may be accompanied by figures or diagrams. These figures are drawn as accurately as possible
EXCEPT when it is stated in a specific problem that a figure is not drawn to scale. The figures and diagrams are
meant to provide information useful in solving the problem or problems. Unless otherwise stated, all figures and
diagrams lie in a plane.
Data That Can Be Used for Reference
rectangle
A = lw
Area
triangle
A = 1⁄2 bh
circle
A = πr 2
C = 2πr
rectangular solid
V = lwh
Volume
right circular cylinder
V= πr 2h
Pythagorean Relationship
30° − 60° − 90°
Special Triangles
45° − 45° − 90°
A circle is composed of 360°
A straight angle measures 180°
The sum of the angles of a triangle is 180°
w
l
h
b
r
M
r
h
l
h
w
a2 + b 2 = c 2
C B
A
c
a
b
30°
60°
2x
x
x√3
45°
45°
x
x x√2
236
Part III: Math Practice Tests
1. If 7x – 5 = 4x – 17, what is the value of x?
A. –6
B. –4
C. 1
D. 4
E. 5
Note: Figure not drawn to scale.
2. In the figure above, if x = 50, what is the value of
m + n?
A. 50
B. 65
C. 75
D. 110
E. 130
3. In the xy-plane, the line with equation y = 3x – 12
crosses the x-axis at one point. What is the
x-coordinate of this point?
A. –12
B. –4
C. 0
D. 3
E. 4
4. The average (arithmetic mean) of 5x and 3y is
equal to 4 less than the product of x and y. Which
of the following equations states the relationship
given in the previous sentence?
A. x y xy2
5 3 4+ = -
B. x y xy2
5 3
4
+
=
C. x y xy2
5 3 4- = -
D. x y xy2
5 3 4+ = -
E. x y xy2
5 3 4- = -
5. The number that results from 3n, where n is a
positive integer, CANNOT end in which of the
following digits?
A. 1
B. 3
C. 5
D. 7
E. 9
6. A discount of 20%, followed by another discount
of 25%, is equivalent to a single discount of what
percent?
A. 33%
B. 40%
C. 45%
D. 55%
E. 60%
7. The equation x2 3 7- = is true for which value(s)
of x?
A. 2 only
B. 5 only
C. 2 and 5
D. –2 and 5
E. 2 and –5
Note: Figure not drawn to scale.
8. The figure above shows the graph of y = k – x2,
where k is some positive constant. If V is the
midpoint of side BC of rectangle ABCD, and if the
area of ABCD is 16, what is the value of k?
A. 2
B. 2 2
C. 4
D. 4 2
E. 8
x
y
OA D
V
B C
y = k − x 2
m°
x°
n°
237
Practice Test II
P
ractice Test II
GO ON TO THE NEXT PAGE
Directions for Student-Produced Response Questions (Grid-ins): Questions 9–18 require you to solve the problem
and enter your answer by carefully marking the circles on the special grid. Examples of the appropriate way to mark the
grid follow.
Answer 3.7 Answer 1/2
Answer 2 1/2
Do not grid-in mixed numbers in the form of mixed numbers. Always change mixed numbers to improper fractions or
decimals.
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Decimal point
238
Part III: Math Practice Tests
Answer 123
Space permitting, answers may start in any column. Each grid-in answer below is correct.
Note: Circles must be filled in correctly to receive credit. Mark only one circle in each column. No credit will be given
if more than one circle in a column is marked. Example:
Answer 258 (no credit)
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239
Practice Test II
P
ractice Test II
GO ON TO THE NEXT PAGE
Answer 8/9
Accuracy of decimals: Always enter the most accurate decimal value that the grid will accommodate. For example: An
answer such as .8888 . . . can be gridded as .888 or .889. Gridding this value as .8, .88, or .89 is considered inaccurate
and therefore not acceptable. The acceptable grid-ins of 8/9 are:
Be sure to write your answers in the boxes at the top of the circles before doing your gridding. Although writing out the
answers above the columns is not required, it is very important to ensure accuracy. Even though some problems may
have more than one correct answer, grid only one answer. Grid-in questions contain no negative answers.
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240
Part III: Math Practice Tests
9. Dividing a number by 5
2
and then multiplying the
result by 3
4 gives the same result as just dividing
the original number by what fraction?
10. If
x y2
5
3
2
= , what is the value of y
x ?
11. If m2 + n2 = 29 and if mn = 7, then the value of
(m + n)2 =
12. If x 23
1
=
-
and if y 22
1
= , what is the value of xy?
13. What is the largest of 5 consecutive even integers
whose sum is 170?
14. In the figure above, the circle with center C and
radius 5 is tangent to both the x and y axes. AB is
tangent to the circle at point B. What is the slope
of AB?
15. �ABC in the xy-plane has vertices at A (5, 2),
B (11, 2), and C (11, 6). What is the area of
�ABC?
16. If m2 + 2mn = 3n – 4w, what is the value of n when
m = 3 and w = –5?
17. The figure above consists of three circles having
the same center. Their radii are 2, 3, and 4. The
shaded area is what fraction of the area of the
largest circle?
18. If 720 = ambncr, where a, b, and c are different
positive prime integers, what is the value of
m + n + r?
x
y
(9,−8)
A
C
B
241
Practice Test II
P
ractice Test II
IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS
SECTION ONLY. DO NOT WORK ON ANY OTHER SECTION IN THE TEST. STOP
Practice Test IIB
Time: 25 minutes
20 multiple-choice questions
Directions: Select the one correct answer of the five choices given and mark the corresponding circle on your answer
sheet. Your scratch work should be done on any available space in the section.
Notes
1. All numbers used are real numbers.
2. Calculators may be used.
3. Some problems may be accompanied by figures or diagrams. These figures are drawn as accurately as possible
EXCEPT when it is stated in a specific problem that a figure is not drawn to scale. The figures and diagrams are
meant to provide information useful in solving the problem or problems. Unless otherwise stated, all figures and
diagrams lie in a plane.
Data That Can Be Used for Reference
rectangle
A = lw
Area
triangle
A = 1⁄2 bh
circle
A = πr 2
C = 2πr
rectangular solid
V = lwh
Volume
right circular cylinder
V= πr 2h
Pythagorean Relationship
30° − 60° − 90°
Special Triangles
45° − 45° − 90°
A circle is composed of 360°
A straight angle measures 180°
The sum of the angles of a triangle is 180°
w
l
h
b
r
M
r
h
l
h
w
a2 + b 2 = c 2
C B
A
c
a
b
30°
60°
2x
x
x√3
45°
45°
x
x x√2
242
Part III: Math Practice Tests
2, 3, 5, 8, 13, . . .
1. The first term in the sequence above is 2 and the
second term is 3. For each term after the second
term, its value represents the sum of the two terms
preceding it. What is the tenth term of this
sequence?
A. 34
B. 55
C. 89
D. 144
E. 233
2. In the xy-plane, the line l is perpendicular to the
graph of the equation 3x + 4y = 12. Which of the
following is the slope of line l?
A. –4
B. –3
C. 4
3-
D. 3
4
E. 12
3. If 5(x + 3) = 17, what is the value of x?
A. 5
2
B. 2
5
C. 5
14
D. 5
22
E. 9
4. If 3(2x + 4)(5 – x) = 0, what are all the possible
values of x?
A. 0 only
B. –2 and 5 only
C. 2 and –5 only
D. 0, –2, and 5
E. 0, 2, and –5
5. For which of the following functions does
f f5 5!-^ ^h h?
A. f x x=^ h
B. f x 7=^ h
C. f x x 53= +^ h
D. f x x 32= -^ h
E. f x x6 4= +^ h
6. When x = 2, what is the value of
x x x1
1 1
1
1
+
+ +
-
?
A. 6
1
B. 1 5
2
C. 1 6
5
D. 5
E. 11
7. Mark is taller than Rebecca, and Charles is shorter
than Rebecca but taller than Harriet. If m, r, c, and
h represent the heights of Mark, Rebecca, Charles,
and Harriet respectively, which of the following
correctly represent the order of their heights?
A. c < h < r < m
B. r < c < h < m
C. h < r < c < m
D. c < h < r < m
E. h < c < r < m
8. The radius of one circle is 3
1 the radius of a
second circle. What is the ratio of the area of the
smaller circle to the area of the larger circle?
A. 1:9
B. 1:3
C. 3:1
D. 6:1
E. 9:1
9. If 2 ≤ x ≤ 6 and 6 ≤ xy ≤ 30, which of the following
gives the range of all possible values of y?
A. y3
1
8
1# #
B. y3
1
5
1# #
C. 4 ≤ y ≤ 24
D. 3 < y < 5
E. 3 ≤ y ≤ 5
10. The quantity m varies inversely as the square of
the quantity r. If m = 9 when r = 4, what is the
value of m when r = 6?
A. 4
B. 6
C. 36
D. 64
E. 144
243
Practice Test II
P
ractice Test II
GO ON TO THE NEXT PAGE
11. If x�y y
x
= , with y ≠ 0, and if 4�m = 16�2,
what is the value of m?
A. 2
1
B. 1
C. 2
D. 8
E. 16
12. What is the measure of the largest angle of a
triangle, in which the degree measure of its angles
have a ratio of 5:6:7?
A. 10
B. 35
C. 50
D. 70
E. 75
Note: Figure not drawn to scale.
13. For the parabola above, (5, –3) is its vertex. Which
of the following are the x-coordinates of two
points on the graph of the parabola for which their
y-coordinates are equal?
A. 4 and 7
B. 2 and 9
C. 0 and 8
D. –1 and 11
E. 1 and 10
14. Mr. and Mrs. Franklin took their three children to
a theatre to watch a movie. They select a row on
the side having only five seats. If each of the
parents must sit at either end of the row, in how
many different ways can the Franklin family be
seated in the five seats?
A. 3
B. 6
C. 12
D. 24
E. 120
15. How many inches are there in a distance of Y yards,
F feet, and I inches?
A. 3Y + F + 12I
B. 36Y + F + 12I
C. 3Y + 12F + I
D. 36Y + 12F + I
E. 3Y + 12F + 12I
16. In the figure above, AB BC= and AC CD= . If
the length of AB 2= and the length of BC 2= ,
what is the length of AD?
A. 2 2 (approximately 2.82)
B. 2 3 (approximately 3.46)
C. 4
D. 3 2 (approximately 4.24)
E. 2 5 (approximately 4.47)
17. The perimeter of an equilateral triangle is 18.
What is the area of the triangle?
A. 2
9
B. 2
9 2
C. 9 2
D. 9 3
E. 18
C
Dx°
B
A
x°
x
y
(5, −3)
O
244
Part III: Math Practice Tests
Note: Figure not drawn to scale.
18. In the figure above, BC AD. What is the ratio of
the area of �ABF to the area of �CED?
A. :3 2
B. :2 1
C. 3:2
D. :3 1
E. 2:1
19. If m and r are constants and if (x + m)(x + r) =
x2 + cx + w, where c and w are constants, what
is w
c in terms of m and r?
A. r
m
B. m
m r+
C. mr
m r+
D. m r
mr
+
E. It cannot be determined from the given
information.
20. Let the function f be defined by f(x) = x2 – 2x. For
which values of m will f(2m) = 15?
A. –2 only
B. 2
3-
and 2
5
C. 3 and –5
D. –3 and 5
E. 3 only
FA D
B
E
C
30° 45°
245
Practice Test II
P
ractice Test II
IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS
SECTION ONLY. DO NOT WORK ON ANY OTHER SECTION IN THE TEST. STOP
Practice Test IIC
Time: 20 minutes
16 multiple-choice questions
Directions: Select the one correct answer of the five choices given and mark the corresponding circle on your answer
sheet. Your scratch work should be done on any available space in the section.
Notes
1. All numbers used are real numbers.
2. Calculators may be used.
3. Some problems may be accompanied by figures or diagrams. These figures are drawn as accurately as possible
EXCEPT when it is stated in a specific problem that a figure is not drawn to scale. The figures and diagrams are
meant to provide information useful in solving the problem or problems. Unless otherwise stated, all figures and
diagrams lie in a plane.
Data That Can Be Used for Reference
rectangle
A = lw
Area
triangle
A = 1⁄2 bh
circle
A = πr 2
C = 2πr
rectangular solid
V = lwh
Volume
right circular cylinder
V= πr 2h
Pythagorean Relationship
30° − 60° − 90°
Special Triangles
45° − 45° − 90°
A circle is composed of 360°
A straight angle measures 180°
The sum of the angles of a triangle is 180°
w
l
h
b
r
M
r
h
l
h
w
a2 + b 2 = c 2
C B
A
c
a
b
30°
60°
2x
x
x√3
45°
45°
x
x x√2
246
Part III: Math Practice Tests
1. Two positive integers are called “relatively prime”
if their only common factor is 1. Which of the
following pair of numbers is “relatively prime?”
A. 6 and 9
B. 10 and 5
C. 8 and 15
D. 12 and 4
E. 9 and 12
2. If the volume of a cube is 8, what is its total
surface area?
A. 6
B. 8
C. 16
D. 18
E. 24
3. The graph above shows the number of votes
received by each of four candidates in an election.
What fraction of the votes did candidate Y receive?
A. 6
1
B. 4
1
C. 3
1
D. 2
1
E. 5
2
4. If f x
x
x
7
3 2
=
-
-^ h , then the value of f(–2) =
A. 5
12-
B. 3
4-
C. 7
6
D. 3
4
E. 5
12
5. At 5:00pm, what is the degree measure of the
angle between the hour and minute hands on
the traditional clock above?
A. 75°
B. 115°
C. 120°
D. 150°
E. 165°
6. The denominator of a fraction is 3 more than its
numerator. If the fraction is equal to 35
14
, what is
the numerator of the fraction?
A. 2
B. 3
C. 5
D. 6
E. 7
10
11
12
6
1
7 5
9 3
2
8 4
CAND. X
50
40
20
10
CAND. Y CAND. A
CAND. B
247
Practice Test II
P
ractice Test II
GO ON TO THE NEXT PAGE
Note: Figure not drawn to scale.
7. In the figure above, what is the value of m?
A. 15
B. 30
C. 45
D. 60
E. 75
8. If 0 < x < 1, which of the following statements
must be true?
I. >x x
1
II. x2 < x
III. x3 – x2 > 0
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
9. The average of two numbers is x. If one of the
numbers is 3m – 5, then the other number, in terms
of x and m, is
A. x m2
3 5+ -
B. 6m – 10 – x
C. 6m – 5 – x
D. x
m6 10-
E. 6m – 10 + x
10. In the xy-plane, the graphs of y = 2x + 7 and
y = –3x + r intersect at the point (–2, m). What is
the value of r?
A. –3
B. –1
C. 2
D. 3
E. 4
3x°
45°
m°
x°
248
Part III: Math Practice Tests
Note: Figure not drawn to scale.
11. The graph above is that of the equation y = f(x). Which of the following could be the graph of y f x= ^ h ?
x
y
64
(B)
x
y
64
(D)
x
y
64
(C)
x
y
64
(A)
−1 −1−3
−1−3 −1−3
−1−3
−3
x
y
64
(E)
x
y y = f (x)
64−1−3
249
Practice Test II
P
ractice Test II
GO ON TO THE NEXT PAGE
12. The radius of a right circular cylinder is doubled,
and its height is tripled. What is the ratio of the
volume of the original cylinder to the volume of
the new larger cylinder?
A. 12
1
B. 6
1
C. 3
1
D. 2
1
E. 6
13. In the figure above, a circle is inscribed within a
square having a perimeter of 32. What is the area
of the shaded region?
A. 64 – 16π
B. 32 – 8π
C. 16 – 4π
D. 8 – 2π
E. 4 – π
14. In the xy-plane, how many different integer pairs
(x, y) are in the solution set of x y 2#+ ?
A. 4
B. 5
C. 8
D. 12
E. 13
15. The sum of three consecutive even integers is 72.
If x represents the smallest, y the middle, and z
the greatest of these even integers, which of the
following equations could be used to represent the
first sentence of this problem?
I. 3x + 6 = 72
II. 3y = 72
III. 3z – 6 = 72
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
16. If x 2
4+ is an integer, and if y 2
3- is an integer,
then xy must be
A. an even integer
B. a negative integer
C. an odd integer
D. a multiple of 12
E. a positive integer
250
Part III: Math Practice Tests
IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS
SECTION ONLY. DO NOT WORK ON ANY OTHER SECTION IN THE TEST. STOP
Scoring Practice Test II
Answer Key for Practice Test II
Practice Test IIA
251
Practice Test II
P
ractice Test II
1. B
2. E
3. E
4. D
5. C
6. B
7. D
8. C
9. 10
3
10. 14
15
or 1.07
11. 43
12.