(2021年整理)SAT数学真题精选

SAT数学真题精选

SAT数学真题精选

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SAT数学真题精选

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 = —1/2 x (B） y = —1/2 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?

SAT数学真题精选

(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

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）1/8 （B) 2/9 (C） 2/7 （D） 3/8 (E） 1/2

SAT考试数学练习题(一）

SAT数学真题精选

1。 If f(x） = x² – 3, where x is an integer， which of the following could be a value of f（x）？

I 6

II 0

III —6

A. I only

B. I and II only

C. II and III only

D. I and III only

E. I， II and III

Correct Answer： A

解析:

Choice I is correct because f（x) = 6 when x=3。 Choice II is incorrect because to make f（x) = 0， x² would have to be 3. But 3 is not the square of an integer. Choice III is incorrect

because to make f（x） = 0, x² would have to be –3 but squares cannot be negative. （The minimum

value for x2 is zero； hence， the minimum value for f（x) = -3）

2。 For how many integer values of n will the value of the expression 4n + 7 be an integer

greater than 1 and less than 200？

A. 48

B。 49

C。 50

D。 51

E。 52

Correct Answer: C

解析：

1 〈 4n + 7 < 200. n can be 0， or —1. n cannot be -2 or any other negative integer or the

expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4.

193/4 = 48.25， hence 48。 The number of integers between -1 and 48 inclusive is 50

3. In the following correctly worked addition sum, A,B,C and D represent different digits,

and all the digits in the sum are different。 What is the sum of A，B，C and D?

A. 23

B。 22

C。 18

D。 16

E。 14

Correct Answer： B

解析:

First you must realize that the sum of two 2-digit numbers cannot be more that 198 （99 +

99）。 Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum

5A + BC = 143。 A + C must give 3 in the units place, but neither can be 1 since all the digits

have to be different. Therefore A + C = 13. With one to carry over into the tens column， 1 +

5 + B = 14， and B = 8. A + C + B + D = 13 + 8 + 1 = 22

SAT数学真题精选

4. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth,

and 40 cm height. How high （in cm) will the water rise?

(1 litre = 1000cm³)

A. 6

B。 8

C。 10

D。 20

E. 40

Correct Answer： B

解析:

Total volume of water = 12 liters = 12 x 1000 cm3。 The base of the aquarium is 50 x 30 =

1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000

/ 1500 = 8

5. Six years ago Anita was P times as old as Ben was。 If Anita is now 17 years old, how old

is Ben now in terms of P ?

A。 11/P + 6

B. P/11 +6

C。 17 - P/6

D。 17/P

E。 11.5P

Correct Answer: A

解析:

Let Ben’s age now be B。 Anita’s age now is A. (A — 6) = P（B — 6)

But A is 17 and therefore 11 = P（B — 6)。 11/P = B-6

（11/P) + 6 = B

SAT考试数学练习题（二)

1. The distance from town A to town B is five miles。 C is six miles from B。 Which of the following

could be the distance from A to C？

I 11

II 1

III 7

A。 I only

B. II only

C。 I and II only

D。 II and III only

E. I, II， or III。

Correct Answer: E

解析：

Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles

apart. Draw a circle centered on B, with radius 6。 C could be anywhere on this circle。 The minimum

distance will be 1， and maximum 11， but anywhere in between is possible.

2. √5 percent of 5√5 =

SAT数学真题精选

A。 0.05

B. 0.25

C。 0。5

D. 2.5

E。 25

Correct Answer: B

解析:

We can write the statement mathematically， using x to mean ‘of’ and /100 for ‘per cent’.

So （ √5/100) x 5√5 = 5 x 5 /100 = 0。25

3。 If pqr = 1 ， rst = 0 ， and spr = 0, which of the following must be zero?

A。 P

B。 Q

C. R

D. S

E. T

Correct Answer: D

解析：

If pqr = 1， none of these variable can be zero. Since spr = 0 ， and since p and r are not

zero, s must be zero。 (Note that although rst = 0， and so either s or t must be zero, this is

not sufficient to state which must be zero)

4。

A. 1/5

B。 6/5

C. 6³

D。 64 / 5

E. 64

Correct Answer： E

解析：

65 = 64x 6

(64 x 6) — 64 = 64（6 - 1） = 64 x 5 Now， dividing by 5 will give us 64

5. -20 , -16 ， —12 , —8 .。。。

In the sequence above, each term after the first is 4 greater than the preceding term。 Which

of the following could not be a term in the sequence？

A。 0

B。 200

C. 440

D. 668

E。 762

Correct Answer: E

解析:

All terms in the sequence will be multiples of 4. 762 is not a multiple of 4

SAT考试数学练习题㈢

SAT数学真题精选

1. Which of the following could be a value of x， in the diagram above？

A。 10

B. 20

C。 40

D。 50

E. any of the above

2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or

35 small cakes per hour。 The kitchen is available for 3 hours and 20 large cakes and 700 small

cakes are needed. How many helpers are required？

A. 10

B。 15

C。 20

D. 25

E。 30

3。 Jo’s collection contains US, Indian and British stamps。 If the ratio of US to Indian

stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US

to British stamps?

A. 5 : 1

B。 10 : 5

C. 15 : 2

D. 20 : 2

E。 25 : 2

4. A 3 by 4 rectangle is inscribed in circle。 What is the circumference of the circle？

A。 2.5π

B。 3π

C. 5π

D. 4π

E. 10π

5。 Two sets of 4 consecutive positive integers have exactly one integer in common. The sum

of the integers in the set with greater numbers is how much greater than the sum of the integers

in the other set？

A. 4

B. 7

C. 8

D。 12

E。 it cannot be determined from the information given。

SAT数学真题精选

SAT考试数学练习题㈣

1. If f（x) = (x + 2) / （x—2） for all integers except x=2, which of the following has the greatest

value？

A. f(-1）

B. f（0）

C. f（1）

D。 f（3）

E。 f(4）

2。 ABCD is a square of side 3， and E and F are the mid points of sides AB and BC respectively.

What is the area of the quadrilateral EBFD ？

A。 2.25

B。 3

C. 4

D. 4。5

E。 6

3。 If n ≠ 0, which of the following must be greater than n？

I 2n

II n²

III 2 - n

A. I only

B。 II only

C. I and II only

D。 II and III only

E. None

4. After being dropped a certain ball always bounces back to 2/5 of the height of its previous

bounce。 After the first bounce it reaches a height of 125 inches。 How high (in inches) will

it reach after its fourth bounce？

A。 20

B. 15

C. 8

D。 5

E. 3。2

5。 n and p are integers greater than 1

5n is the square of a number

SAT数学真题精选

75np is the cube of a number。

The smallest value for n + p is

A. 14

B. 18

C. 20

D。 30

E. 50

SAT考试数学练习题㈤

1。 If a² = 12, then a4 =

A。 144

B。 72

C. 36

D。 24

E. 16

Correct Answer: A

解析：

a4 = a2 x a2 = 12 x 12 = 144

2。 If n is even, which of the following cannot be odd?

I n + 3

II 3n

III n² - 1

A. I only

B。 II only

C. III only

D. I and II only

E. I， II and III

Correct Answer: B

解析：

In case I , even plus odd will give odd。 In case II， odd times even will give even. In case

III even squared is even, and even minus odd is odd. （You can check this by using an easy even

number like 2 in place of n). Only case II cannot be odd。

3。 One side of a triangle has length 8 and a second side has length 5. Which of the following

could be the area of the triangle?

I 24

II 20

III 5

A. I only

B. II only

C。 III only

D. II and III only

E。 I， II and III

Correct Answer: D

解析:

SAT数学真题精选

The maximum area of the triangle will come when the given sides are placed at right angles。

If we take 8 as the base and 5 as the height the area = ½ x 8 x 5 = 20. We can alter the angle

between the sides to make it less or more than 90, but this will only reduce the area. （Draw

it out for yourself)。 Hence the area can be anything less than or equal to 20.

4。 A certain animal in the zoo has consumed 39 pounds of food in six days。 If it continues

to eat at the same rate, in how many more days will its total consumption be 91 pounds？

A。 12

B. 11

C. 10

D。 9

E. 8

Correct Answer： E

解析：

Food consumed per day = 39/6. In the remaining days it will consume 91 - 39 pounds = 52 pounds.

Now divide the food by the daily consumption to find the number of days。 52 / （39/6) = 52 x

（6 / 39） = 8

5. A perfect cube is an integer whose cube root is an integer。 For example， 27, 64 and 125

are perfect cubes。 If p and q are perfect cubes, which of the following will not necessarily

be a perfect cube？

A. 8p

B。 pq

C. pq + 27

D. -p

E。 （p - q)6

Correct Answer： C

解析:

A perfect cube will have prime factors that are in groups of 3； for example 125 has the prime

factors 5 x 5 x 5 ， and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x

5 x 5 x 5. Consider the answer choices in turn。 8 is the cube of 2， and p is a cube， and so

the product will also be a cube. pq will also be a cube as shown above。pq is a cube and so is

27, but their sum need not be a cube。 Consider the case where p =1 and q = 8， the sum of pq

and 27 will be 35 which has factors 5 x 7 and is not a cube。 -p will be a cube。 Since the difference

between p and q is raised to the power of 6, this expression will be a cube （with cube root =

difference squared)。

SAT考试数学练习题㈥

1。 What is the length of the line segment in the x—y plane with end points at （—2，—2) and

(2，3）?

A。 3

B. √31

C。 √41

D. 7

E。 9

SAT数学真题精选

Correct Answer： C

解析：

Sketch a diagram and calculate the distance (hypotenuse of a right triangle） using Pythagoras

theorem.

Vertical height of triangle = 5 ; horizontal side = 4 ； hypotenuse = √（25 + 16) = √41

2。 n is an integer chosen at random from the set

｛5， 7， 9， 11 ｝

p is chosen at random from the set

｛2, 6， 10， 14, 18}

What is the probability that n + p = 23 ？

A. 0.1

B. 0.2

C。 0。25

D. 0。3

E。 0。4

Correct Answer: A

解析：

Each of the integers in the first set could be combined with any from the second set, giving

a total of 4 x 5 = 20 possible pairs. Of these the combinations that could give a sum of 23 are

（5 + 18）， and （9 + 14)。 This means that the probability of getting a sum of 23 is 2/20 =

1/10

3。 A dress on sale in a shop is marked at ＄D。 During the discount sale its price is reduced

by 15%. Staff are allowed a further 10％ reduction on the discounted price。 If a staff member

buys the dress what will she have to pay in terms of D ?

A. 0.75D

B. 0。76D

C。 0。765D

D. 0.775D

E. 0。805D

Correct Answer： C

解析:

If the price is reduced by 15 %, then the new price will be 0。85D。 If this new price is

further reduced by 10％， the discounted price will be 0.9 x 0.85D = 0.765D

SAT数学真题精选

4。 All the dots in the array are 2 units apart vertically and horizontally。 What is the

length of the longest line segment that can be drawn joining any two points in the array without

passing through any other point ?

A。 2

B. 2√2

C。 3

D。 √10

E. √20

Correct Answer： E

解析：

The longest line segment that can be drawn without passing through any dots other than those

at the beginning and end of the segment， such a line could go from the middle dot in the top

row to either the bottom left or right dot. In any case the segment will be the hypotenuse of

a right triangle with sides 2 and 4。 Using Pythagoras theorem the hypotenuse will be √(2 ²

+ 4 ² ) = √20

5。 If the radius of the circle with centre O is 7 and the measure of angle AOB is 100， what

is the best approximation to the length of arc AB ？

A. 9

B. 10

C. 11

D. 12

E. 13

Correct Answer: D

解析:

If the radius is 7， the circumference = 14π. The length of the arc is 100/360 of the

circumference。 Taking π as 22/7 we get. (100 x 14 x 22) / (360 x 7） which reduces to 440/ 36

= 12。22 (i。e. approx. 12）

SAT数学重要公式14个

SAT数学考试并不需要考生记忆数学公式，对于一些常用的简单公式都会列在试卷的前面。但是对于一些可以帮助大家解题的小公式,大家还是了解记忆一些比较有好处.下面为大家搜集了这样的SAT数学公式，共14个，供大家参考。

SAT数学真题精选

1.正整数n有奇数个因子，则n为完全平方数

2。因子个数求解公式:将整数n分解为质因子乘积形式，然后将每个质因子的幂分别加一相乘。n=a*a＊a*b*b*c则因子个数=（3+1)（2+1)（1+1）

eg。 200=2＊2＊2 ＊ 5*5 因子个数=（3+1）（2+1)=12个

3.能被8整除的数后三位的和能被8整除;能被9整除的数各位数的和能被9整除。能被3整除的数,各位的和能被3整除。

4.多边形内角和=(n—2）x180

5。菱形面积=1/2 x 对角线乘积

6.欧拉公式: 边数=面数+顶点数-2

8。三角形余玄定理

C2=A2+B2—2ABCOSβ，β为AB两条线间的夹角

9.正弦定理：A/SinA=B/SinB=C/SinC=2R(A，B，C是各边及所对应的角，R是三角形 外接圆的半径）

10.Y=k1X+B1，Y=k2X+B2，两线垂直的条件为K1K2=—1

11。N的阶乘公式:

N！=1*2＊3＊。.。。（N-2）＊(N—1)＊N 且规定0!=1 1！=1

Eg:8！=1＊2＊3＊4＊5＊6＊7*8

12. 熟悉一下根号2、3、5的值

sqrt（2)=1。414 sqrt（3)=1.732 sqrt(5)=2.236

13. 。。.2/3 as many A as B： A=2/3*B

。。。twice as many。.. A as B: A=2*B

14. 华氏温度与摄氏温度的换算

换算公式:(F—32）＊5/9=C

PS.常用计量单位的换算：(自己查查牛津大字典的附录吧)

以上就是关于SAT数学重要公式的全部内容，包括了很多可以节省大家的解题时间，提高解题效率的小窍门。大家可以在备考自己的SAT数学考试的时候,进行适当的参考和练习，以便更好的应对SAT数学考试。