奔跑吧数学(完整版)sat数学考试试题

2020年11月18日发(作者：卫宗武)
SAT数学真题精选
1. If 2 x + 3 = 9, what is the value of 4 x – 3 ?
(A) 5 (B) 9 (C) 15 (D) 18 (E) 21
2. If 4(t + u) + 3 = 19, then t + u = ?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
3. In the xy-coordinate (坐标) plane above, the line contains the points (0,0) and (1,2).
If line M (not shown) contains the point (0,0) and is perpendicular （垂直） to L, what
is an equation of M?
(A) y = -12 x
(B) y = -12 x + 1
(C) y = - x
(D) y = - x + 2
(E) y = -2x
4. If K is divisible by 2,3, and 15, which of the following is also divisible by these
numbers?
(A) K + 5 (B) K + 15 (C) K + 20 (D) K + 30 (E) K + 45
5. There are 8 sections of seats in an auditorium. Each section contains at least 150
seats but not more than 200 seats. Which of the following could be the number of
seats in this auditorium?
(A) 800 (B) 1,000 (C) 1,100 (D) 1,300 (E) 1,700
6. If rsuv = 1 and rsum = 0, which of the following must be true?
(A) r < 1 (B) s < 1 (C) u= 2 (D) r = 0 (E) m = 0
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7. The least integer of a set of consecutive integers (连续整数) is –126. if the sum of
these integers is 127, how many integers are in this set?
(A) 126 (B) 127 (C) 252 (D) 253 (E) 254
8. A special lottery is to be held to select the student who will live in the only deluxe
room in a dormitory. There are 200 seniors, 300 juniors, and 400 sophomores who
applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2
time; and each sophomore’s name, 1 times. If a student’s name is chosen at random
from the names in the lottery, what is the probability that a senior’s name will be
chosen?
（A）18 (B) 29 (C) 27 (D) 38 (E) 12

Question #1: 50% of US college students live on campus. Out of all students living on
campus, 40% are graduate students. What percentage of US students are graduate
students living on campus?
(A) 90% (B) 5% (C) 40% (D) 20% (E) 25%
Question #2: In the figure below, MN is parallel with BC and AMAB = 23. What is the
ratio between the area of triangle AMN and the area of triangle ABC?

(A) 59 (B) 23 (C) 49 (D) 12 (E) 29
Question #3: If a
2
+ 3 is divisible by 7, which of the following values can be a?
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(A)7 (B)8 (C)9 (D)11 (E)4
Question #4: What is the value of b, if x = 2 is a solution of equation x
2
- b · x + 1 = 0?
(A)12 (B)-12 (C)52 (D)-52 (E)2
Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ?
(A)-12 (B)12 (C)1 (D)-1 (E)2
Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality
m
n
< 100?
(A)2 (B)3 (C)4 (D)5 (E)7
Question #7: The US deer population increase is 50% every 20 years. How may times
larger will the deer population be in 60 years ?
(A)2.275 (B)3.250 (C)2.250 (D)3.375 (E)2.500
Question #8: Find the value of x if x + y = 13 and x - y = 5.
(A)2 (B)3 (C)6 (D)9 (E)4
Question #9:
US
3
1
4
UK
2
4
1
Medals
gold
silver
bronze
The number of medals won at a track and field championship is shown in the table
above. What is the percentage of bronze medals won by UK out of all medals won by
the 2 teams?
(A)20% (B)6.66% (C)26.6% (D)33.3% (E)10%
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Question #10: The edges of a cube are each 4 inches long. What is the surface area, in
square inches, of this cube?
(A)66 (B)60 (C)76 (D)96 (E)65



Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equal
to 1 and the product of the solutions is equal to -20. What are the solutions of the
equation f(x) = 16 - x ?
(a) x1 = 3 and x2 = -3 (b) x1 = 6 and x2 = -6
(c) x1 = 5 and x2 = -4 (d) x1 = -5 and x2 = 4
(e) x1 = 6 and x2 = 0
Question #2: In the (x, y) coordinate plane, three lines have the equations:
l
1
: y = ax + 1
l
2
: y = bx + 2
l
3
: y = cx + 3
Which of the following may be values of a, b and c, if line l
3
is perpendicular to both
lines l
1
and l
2
?
(a) a = -2, b = -2, c = .5 (b) a = -2, b = -2, c = 2
(c) a = -2, b = -2, c = -2 (d) a = -2, b = 2, c = .5
(e) a = 2, b = -2, c = 2
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Question #3: The management team of a company has 250 men and 125 women. If
200 of the managers have a master degree, and 100 of the managers with the master
degree are women, how many of the managers are men without a master degree?
(a) 125 (b) 150 (c) 175 (d) 200 (e) 225
Question #4: In the figure below, the area of square ABCD is equal to the sum of the
areas of triangles ABE and DCE. If AB = 6, then CE =

(a) 5 (b) 6 (c) 2 (d) 3 (e) 4
Question #5:

If α and β are the angles of the right triangle shown in the figure above, then sin
2
α +
sin
2
β is equal to:
(a) cos(β) (b) sin(β) (c) 1 (d) cos
2
(β) (e) -1
Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b are
integers. The product of the same two integers is equal to (b - 1)
2
. What is the value of
a?
(a) a = 9 (b) a = 1 (c) a = 0 (d) a = 5 (e) a = 11

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Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)?
(A) x = 1 (B)x
1
= 1, x
2
= -1
(C)x
1
= 1, x
2
= 0 (D)x = 0
(E)x = -1
Question #2: What is the length of the arc AB in the figure below, if O is the center of
the circle and triangle OAB is equilateral? The radius of the circle is 9

(a) π (b) 2 ·π (c) 3 ·π (d) 4 ·π (e) π2
Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6?
Each dice has sides numbered from 1 to 6.
(a)12 (b)16 (c)112 (d)118 (e)136
Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He
bikes from A to B at a speed of 15 mileshour while his return speed is 10 mileshour.
What is the distance between the 2 towns?
(a)11 miles (b)18 miles (c)15 miles (d)12 miles (e)10 miles
Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the
volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1.
What is the height of C2?
(a)2·a π (b)a π (c)a (2·π) (d)a π (e)a + π
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Question #6: How many integers x are there such that 2
x
< 100, and at the same time
the number 2
x
+ 2 is an integer divisible by both 3 and 2?
(a)1 (b)2 (c) 3 (d) 4 (e)5
Question #7: sin(x)cos(x)(1 + tan
2
(x)) =
(a)tan(x) + 1 (b)cos(x)
(c)sin(x) (d)tan(x)
(e)sin(x) + cos(x)
Question #8: If 5xy = 210, and x and y are positive integers, each of the following
could be the value of x + y except:
(a)13 (b) 17 (c) 23 (d)15 (e)43
Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of
the sum x + y?
(a)11 (b)17 (c)13 (d)15 (e) 9
Question #10: The inequality |2x - 1| > 5 must be true in which one of the following
cases?
I. x < -5 II. x > 7 III. x > 0

1. Three unit circles are arranged so that each touches the other two. Find the radii of
the two circles which touch all three.



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2. Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.






3. (1) Given x = (1 + 1n)
n
, y = (1 + 1n)
n+1
, show that x
y
= y
x
.
(2) Show that 1
2
- 2
2
+ 3
2
- 4
2
+ ... + (-1)
n+1
n
2
= (-1)
n+1
(1 + 2 + ... + n).





4. All coefficients of the polynomial p(x) are non-negative and none exceed p(0). If
p(x) has degree n, show that the coefficient of x
n+1
in p(x)
2
is at most p(1)
2
2.






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5. What is the maximum possible value for the sum of the absolute values of the
differences between each pair of n non- negative real numbers which do not
exceed 1?





6. AB is a diameter of a circle. X is a point on the circle other than the midpoint of the
arc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show
that the line PQ, the tangent at X and the line AB are concurrent.




7. Four points on a circle divide it into four arcs. The four midpoints form a
quadrilateral. Show that its diagonals are perpendicular.





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8. Find the smallest positive integer b for which 7 + 7b + 7b
2
is a fourth power.





9. Show that there are no positive integers m, n such that 4m(m+1) = n(n+1).





10. ABCD is a convex quadrilateral with area 1. The lines AD, BC meet at X. The
midpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle
XYZ.







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11. A square has tens digit 7. What is the units digit?






12. Find all ordered triples (x, y, z) of real numbers which satisfy the following system
of equations:
xy = z - x - y
xz = y - x - z
yz = x - y - z



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