国外英语考试《SAT Level 1》预测试题卷一
一、选择题
-
1.
Directions:Select the BEST answer for each of the 50 multiple-choice questions.If the exact solution is not one of the five choices, select the answer that is the best approximation.Then fill in the appropriate oval on the answer sheet.
NOTES:
(1) A calculator will be needed to answer some of the questions on the test.Scientific, programmable, and graphing calculators are permitted.It is up to you to determine when and when not to use your calculator.
(2) All angles on the Level 1 test are measured in degrees, not radians.Make sure your calculator is set to degree mode.
(3) Figures are drawn as accurately as possible and are intended to help solve some of the test problems.If a figure is not drawn to scale, this will be stated in the problem.All figures lie in a plane unless the problem indicates otherwise.
(4) Unless otherwise stated, the domain of a function f is assumed to be the set of real numbers x for which the value of the function, f(x), is a real number.
(5) Reference information that may be useful in answering some of the test questions can be found below.
In △JKL above, what is the value of x?
NOTES:
(1) A calculator will be needed to answer some of the questions on the test.Scientific, programmable, and graphing calculators are permitted.It is up to you to determine when and when not to use your calculator.
(2) All angles on the Level 1 test are measured in degrees, not radians.Make sure your calculator is set to degree mode.
(3) Figures are drawn as accurately as possible and are intended to help solve some of the test problems.If a figure is not drawn to scale, this will be stated in the problem.All figures lie in a plane unless the problem indicates otherwise.
(4) Unless otherwise stated, the domain of a function f is assumed to be the set of real numbers x for which the value of the function, f(x), is a real number.
(5) Reference information that may be useful in answering some of the test questions can be found below.
In △JKL above, what is the value of x?参考答案D
解析In △JKL:∠L = 180- 50- 65 = 65 Since ∠K = 65 and ∠L = 65, then ∠K = ∠L, so the sides opposites these angles, JK and JL, must be equal in length.Hence: JK = JL, 3x-2 =x + 10, 2x = 12, x=-12/2 =6.
2.
If 
, then 
______.
, then ______.参考答案B
解析
3.
If a = b3 and b = 4k, then what is the value of a when k = -1/2?
参考答案B
解析When k = -1/2, b=4(-1/2)=-2, a=(-2)3=-8
4.
(22 × 23)4 = ______.
参考答案C
解析
5.
Each of the following sets of points could be the intersection of two planes EXCEPT: ______.
参考答案B
解析The intersection of two planes is the set of points that they share.If two planes do not intersect, then their intersection is the empty set.If two planes are in fact the same plane, then their intersection is a plane.If two (distinct) planes intersect, then they intersect in a line.It is not possible for two planes to intersect in a point, so the correct answer is B.
6.
If the x-coordinate of two points are the same, then they lie ______.
参考答案D
解析Points with the same x-coordinate lie on a vertical line.
7.
If point A has coordinates(2, 6), point B has coordinates(2, 2), and ABCD is a square, which of the following could be the coordinates of point C?
参考答案C
解析The vertices of a square must always be listed in consecutive order.Therefore, C can be at(-2, 2)or(6, 2).
8.
A cube and a rectangular prism have the same surface area.If the dimensions of the rectangular prism are h=2ft, w=3ft, and l=6ft, how long is each side of the cube?
- A.
ft - B.
ft - C.
ft - D.4 ft
- E.
ft
参考答案B
解析SA of rectangular prism=2(2×3+2×6+3×6)=72.Let s represent the side of the cube, then SA of cube=6s2=72, so
.
.
9.
If 
and 
, then 
______.
and , then ______.参考答案C
解析Multiply the second equation by 2 to get a coefficient of 2 for the x term: 2x + 2y = 32.Then, solve the system using the linear combination method.-2x+y=-7, 3y=15, y=5.If y=5, x+5=16=11.x-y=11-5=6
10.
In the following figure, ∠CAB = 60° and
.What is the length of 
?
.What is the length of ?- A.2
- B.8
- C.24
- D.12
- E.8
参考答案D
解析
ABC is a 30°-60°-90° right triangle.Since the side opposite the 30° angle measures
(the side opposite the 60°) must measure
.
ABC is a 30°-60°-90° right triangle.Since the side opposite the 30° angle measures(the side opposite the 60°) must measure.
11.
If x2=16, y2=25, and(x-4)(y+5)≠O, then x3+y3=?
参考答案B
解析If x2=16, then x=4 or -4, and if y2=25, then y=5 or -5.But if (x-4)(y+5)≠0, then x≠4 and y≠-5.Therefore, x3 +y3 =(-4) 3 +53 =61.
12.
If l yards of a wire cost m dollars, ______ express the cost of n yards.
- A.
- B.
- C.
- D.
- E.
参考答案B
解析Let x represent the cost of n yards, then you can build up a proportion, comparing yards to dollars.
.Cross multiply: 
.
.Cross multiply: .
13.
In the sequence below, the first 7 is followed by one 10, the second 7 is followed by two 10s, and so on.If the sequence continues in this manner, how many los are there between the 100th and 104th appearances of the number 7?
7, 10, 7, 10, 10, 7, 10, 10, 10, 7, …
7, 10, 7, 10, 10, 7, 10, 10, 10, 7, …
参考答案C
解析There will be100+101+102+103=406, 10s between the 100th and 104th appearances of the number 7.
14.
Each of the following statements is divue EXCEPT: ______.
参考答案D
解析The complement of an acute angle must always measure less than 90°, so A is true.Let’s take an obtuse angle measuring 100°.Its supplement is 80°, which is an acute angle.B is true.Answer C states the opposite of B and is also true.D and E involve right angles.Since 90 + 90 ＝ 180, a right angle and another right angle are in fact supplementary, so answer E must be true.That leaves D.A right angle does not have a complement.90+0＝90, and we’ve already determined that an angle cannot measure 0.
15.
If a=3b=2c, then 6a is equal to which of the following expressions?
Ⅰ.12C
Ⅱ.6b+8c
Ⅲ.2b+10c
Ⅰ.12C
Ⅱ.6b+8c
Ⅲ.2b+10c
参考答案A
解析Determine whether each Roman numeral expression is equal to 6a.
Ⅰ.Since 12c=6(2c)=6a, Statement Ⅰ is true.
Ⅱ.Since 6b+8c=2(3b)+4(2c)=2a+4a=6a, Statement Ⅱ is true.
Ⅲ.Since 2b+10c=2b+5(2c)=2b+5(3b)=17b≠6a, Statement Ⅲ is false.
Ⅰ.Since 12c=6(2c)=6a, Statement Ⅰ is true.
Ⅱ.Since 6b+8c=2(3b)+4(2c)=2a+4a=6a, Statement Ⅱ is true.
Ⅲ.Since 2b+10c=2b+5(2c)=2b+5(3b)=17b≠6a, Statement Ⅲ is false.
16.
If 
, x= ______.
, x= ______.参考答案B
解析If, then 2x+3=15 or 2x+3= -15, so x=6 or x= -9.
, then 2x+3=15 or 2x+3= -15, so x=6 or x= -9.
17.
In the following figure, if l1∥l2, then x= ______.
参考答案D
解析Draw an extra line through the vertex of the angle that is parallel to the other two.Notice that this forms two “Z” pairs.Therefore, x=38+42=80.
18.
If 
, then x= ______.
, then x= ______.- A.
- B.
- C.11
- D.
- E.
参考答案D
解析, 3(4x－1)=8, 12x－3=8, 
.
, 3(4x－1)=8, 12x－3=8, .
19.
A line has paramedivic equations x=t-12 and y=4t-1, given t is the parameter.What is the y-intercept of the line?
参考答案C
解析Because x = t - 12, t = x + 12.Substitute this value into the second equation to get: y = 4(x + 12)-1= 4x + 48- 1= 4x + 47.The y-intercept of the resulting line is (0, 47).
20.
A fair six-sided die has faces bearing the numbers 1, 2, 3, 4, 5, and 6.When the die is thrown, the numbers on the five visible faces are added.What is the probability that this sum is greater than 17?
- A.
- B.
- C.
- D.
- E.
参考答案C
解析1+2+3+4+5+6=21, 21-18=3.Only if the “down” face is 1, 2 or 3, the sum can be greater than 17.So the probability
.
.
21.
Which of the following is equivalent to the statement “The distance from 2 to x is greater than the distance from 4 to x”?
Ⅰ.
Ⅱ
or 
Ⅲ.
Ⅰ.
Ⅱ
or Ⅲ.
参考答案C
解析The distance from 2 to x is
and the distance from 4 to x is 
, so Ⅲ is clearly correct.To see why Ⅰ is true, notice that 3 is the only number equidistant from 2 and 4, so all numbers that are farther from 2 than from 4 are greater than 3.
and the distance from 4 to x is , so Ⅲ is clearly correct.To see why Ⅰ is true, notice that 3 is the only number equidistant from 2 and 4, so all numbers that are farther from 2 than from 4 are greater than 3.
22.
If
, then x =
, then x =参考答案B
解析, 
, x = (25)2, x=210 =1,024.
, , x = (25)2, x=210 =1,024.
23.
If the supplement of twice an angle is 124°, then what is the measure of the angle?
参考答案D
解析Let x = the measure of the angle.The supplement of twice the angle is 180－2x.180－2x=124－2x=-56, x=28°.
24.
Which of the following could be the remainders when four consecutive positive integers are each divided by 4?
参考答案C
解析When you divide any positive integer by 4, the remainder must be less than or equal to 3.All the choices except C.include remainders greater than 3, so C.is the only possible correct choice.
25.
Find the ratio of 1 foot 8 inches to 1 yard.
参考答案C
解析1 ft.8 in.=20 in. 1 yd.=36 in.
.
.
26.
Given diviangles ABC and MNP.If ∠A=∠M, ∠B=∠N, and ∠C=∠P, then the diviangles are ______.
参考答案C
解析Two triangles are similar is the corresponding angles are equal.
27.
If 
, what is 
?
, what is ?参考答案E
解析Given：, So that 
.From the information given, we cannot determine whether equals 4 or -4.
, So that .From the information given, we cannot determine whether equals 4 or -4.
28.
If 
and y = 2n, then what is the value of x when n =-4?
and y = 2n, then what is the value of x when n =-4?- A.2
- B.-2
- C.8
- D.-8
- E.
参考答案B
解析When n = -4, y = 2(-4) = -8.
.
.
29.
What amount does the product of 6 and 30 exceed the product of 12 and 5?
参考答案D
解析(6×30)-(12 × 5)=120
30.
A camp employs 7 men, 8 women, 9 girls, and 6 boys.In the middle of the summer, 2 girls are fired and replaced by women.What part of the staff is then made up of women?
- A.
- B.
- C.
- D.
- E.
参考答案C
解析The number of staff members is still 30.Of these, 10 are now women.Therefore
or of the staff are women.
or of the staff are women.
31.
In diviangle MNP, if ∠N is an obtuse angle, then ______.
参考答案A
解析MP is the longest side since in a triangle the longest side is opposite the largest angle, which, in this case, is ∠N.
32.
If point P(3, h)is on the line that contains A(1, 0)and B(-1, -4), what is the value of h?
参考答案B
解析Slope of EA=Slope of AB=(-4-0)/(-1-1)=2.Hence, slope of EA=(h-O)/(3-1)=2.Therefore, h=4.
33.
The following histogram shows students’ scores on a given test:
Each of the following is divue EXCEPT:
Each of the following is divue EXCEPT:参考答案E
解析The most number of students scored in the interval between 80 and 89, since it is the highest bar in the histogram, making answer A correct.There’s not enough information to find the exact median of the data, but you can see that the middle term, the seventh term, falls in the interval between 70 and 79.Answer B is therefore also correct.Nine (3+4+2) students scored higher than 70 and 13 students (1+3+3+4+2) students took the test, so answers C and D are correct.That leaves E.On quickly looking at the graph, you may mistakenly think that the highest score on the test was 100 percent.A his to gram represents intervals of data, however.Two students scored in the highest interval, but you don’t know enough information to conclude that a student received 1 00 percent.
34.
Solve the quadratic equation x2/-5x-14=0.
参考答案D
解析Factor the expression in x2-5x-14=0 to get(x-7)(x+2)=0.So, either(x-7)=0 or(x+2)=0.Therefore, x=7 or x= -2.
35.
If a3b2c<0, which of the following must be less than zero?
参考答案C
解析If a3b2c<0, then either a or c is negative, but both cannot be negative.A negative times a positive is negative.So ac<0.
36.
Given
has an exterior altitude, the diviangle could be which of the following?
has an exterior altitude, the diviangle could be which of the following?参考答案B
解析Exterior altitudes extend from one vertex and are perpendicular to the line containing the opposite side.This only occurs when a triangle has an obtuse angle.
37.
The points (4, -2) and (x, y) are symmedivic to each other with respect to the origin.(x, y) =
参考答案E
解析Reflecting the point (4, -2) about the origin results in the point (-4, 2).In other words, the origin is the midpoint of the segment with endpoints (4, -2) and (-4, 2).
38.
What is the minimum value of the function 
?
?参考答案B
解析The minimum value of the function is the y-coordinate of its vertex.Graph the functionon your graphing calculator to find its vertex (0, 1).The minimum value is 1.
on your graphing calculator to find its vertex (0, 1).The minimum value is 1.
39.
If 
, and if the domain of x consists of all real numbers defined by the inequality -3contains all of the following members except：
, and if the domain of x consists of all real numbers defined by the inequality -3contains all of the following members except：- A.0
- B.5
- C.10
- D.-5
- E.
参考答案C
解析f(-3)=3(-3)-5=-14.f(5)=3(5)-5=10.So -14
40.
In the figure above, five non overlapping regions, labeled a through e, are formed by sets A, B, and C.Which region represents the set of elements that belong to sets B and C but not to set A?
参考答案D
解析The region in the diagram that represents the set of elements that belong to sets B and C but not to set A is the region in which circles B and C overlap outside of circle A.This region is labeled d.
41.
Dr.Icahn invested $2 000 in an account paying 5% interest annually.How many more dollars must he invest at 3% so that his total annual income is 4% of his entire investment?
参考答案B
解析Let x represent the amount invested at 3%, then 2 000+x is his total investment.0.05×2000+0.03x=0.04(2000+x), x=2 000
42.
If the equation of a circle is x2+y2 =12, then which of the following is a y-intercept?
- A.12
- B.-12
- C.
- D.0
- E.Cannot be determined
参考答案C
解析This is a circle centered at the origin with a radius ofor units.The y-intercepts are the points 
and 
.
or units.The y-intercepts are the points and .
43.
Each of the following statements is divue EXCEPT: ______.
参考答案D
解析The complement of an acute angle must always measure less than 90°, so A is true.Let’s take an obtuse angle measuring 100°.Its supplement is 80°, which is an acute angle.B is true.Answer C states the opposite of B and is also true.D and E involve right angles.Since 90+90＝180, a right angle and another right angle are in fact supplementary, so answer E must be true.That leaves D.A right angle does not have a complement.90+0＝90, and we’ve already determined that an angle cannot measure 0°.
44.
The midpoint of
is (5, -6) and the coordinates of endpoint A are (-1, 2).What are the coordinates of B?
is (5, -6) and the coordinates of endpoint A are (-1, 2).What are the coordinates of B?参考答案B
解析Let point B have coordinates (x, y).Since you know the coordinates of the midpoint, use the mid- point formula to solve for x and y.(-1+x)/2=5, x=11.(2+y)/2=-6, y=-14.
45.
A jar contains only red, blue, and green marbles.The probability of picking a red marble is 0.25, and the probability of picking a blue marble is 0.40.What is the LEAST number of marbles that could be in the jar?
参考答案D
解析To find the LEAST number of marbles that could be in the jar, multiply each answer choice by 0.25, 0.40, and 0.35 until an integer is obtained for each product.Since 4 times 0.40 is 1.6, rule out choice A., 5 times 0.25 is 1.25, so rule out choice B., 10 times 0.35 is 3.5, so rule out choice C..Since 20 times 0.25 is 5, 20 times 0.40 is 8, and 20 times 0.35 is 7, choice D.is correct.
46.
If 
, what is the value of y?
, what is the value of y?参考答案E
解析Multiply by 6 to clear fractions.y+36=2y, y=36.
47.
If two angles are complementary, and one angle is 65 degrees, then the other is ______.
参考答案C
解析x+65=90, or x=25
48.
An ice cream parlor makes a sundae using one of six different flavors of ice cream, one of three different flavors of syrup, and one of four different toppings.What is the total number of different sundaes that this ice cream parlor can make?
参考答案A
解析The total number of different sundaes that the ice cream parlor can make is the t sundaes that the ice cream parlor can make is the number of different flavors of ice cream times the number of different flavors of syrup times the number of different top－pings: 6×3×4 = 72.
49.
If an arc with a length of 6π is of the circumference of a circle, what is the shortest distance between the endpoints of the arc?
of the circumference of a circle, what is the shortest distance between the endpoints of the arc?- A.4
- B.
- C.
- D.
- E.12
参考答案B
解析Call the endpoints of the arc A and B and the center of the circle O.Major arc AB：
.Therefore, minor arc AB：
.Since AO and BO are both radii of the circle, triangle ABO must be an isosceles right triangle, i.e., a 45-45-90 triangle.If 
, then the radius of the circle, r, is 4.So 
.
.Therefore, minor arc AB：.Since AO and BO are both radii of the circle, triangle ABO must be an isosceles right triangle, i.e., a 45-45-90 triangle.If , then the radius of the circle, r, is 4.So .
50.
A rectangular block with a volume of 128 cubic inches was sliced into 2 cubes of equal volume.How much greater, in square inches, is the combined surface area of the 2 cubes than the original surface area of the rectangular block?
参考答案C
解析When the rectangular solid was cut into 2 identical cubes, 2 new faces were formed：l on each cube along the line of the cut.Since the volume or cube=
or the Volume or the rectangular solid, so 
.So the length of the edge of the cube is 
.The total area of these two faces is 2×4×4=32 square inches.
or the Volume or the rectangular solid, so .So the length of the edge of the cube is .The total area of these two faces is 2×4×4=32 square inches.