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GWD MATH错题集

GWD MA TH错题集

The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A.56

B.64

C.68

D.81

E.100

Answer: B

2A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?

A. 5

B. 6

C.9

D.24

E.36

Answer: A

3 If w and c are integers, is w > 0?

(1) w + c > 50

(2) c > 48

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E

4 If n = 811– 8, what is the units digit of n?

A. 0

B. 1

C. 4

D. 6

E. 8

Answer: C

5 Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

AnswerA

6 A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?

A. 0

B. 1/9

C. 2/9

D. 1/3

E. 1

Answer:C 3X2X1/3X3X3

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ? foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5? ft

B. 7? ft

C. 8 ? ft

D. 9? ft

E. 10 ft

Answer: B

8 The operation ? is defined for all nonzero numbers a and b by a ? b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?

I. x ? xy = x(1 ? y)

II. x ? y = -(y ? x)

III. 1/x ? 1/y = y ? x

A. I only

B. II only

C. III only

D. I and II

E. II and III

Answer: E

9 Is the sum of the integers x and y a prime number?

(1) x is an even prime number.

(2) y is a prime number between 10 and 20.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E

10 AMOUNT OF BACTERIA PRESENT

Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?

A. 12.0

B. 12.1

C. 12.2

D. 12.3

E. 12.4

Answer:A

11 What is the remainder when the two digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5.

(2) The remainder when x is divided by 9 is 5.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D

12In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?

A. 16%

B. 25%

C. 32%

D. 40%

E. 52%

Answer:B 0.64是E, 0.48是男&E,0.16是女&E,0.16/0.64是女&E在所有E的比例

13How many seconds will it take for a car that is traveling at a constant rate of 45 miles per hour to travel a distance of 22 yards? (1 mile = 1,160 yards)

A. 8

B. 9

C. 10

D. 11

E. 12

Answer: C

14Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

A. k/m %

B. (k-m) %

C. [100(k-m)]/(100+k) %

D. [100(k-m)]/(100+m) %

E. [100(k-m)]/(100+k+m) %

Answer: D假设前年Price per share =x, 前年earning per share =y 那么去年的price per share 为（1＋k％）x，去年的earning per share 为（1＋m％）y 求去年的price per share 与earning

per share的比率比前年的比率增加了多少。

[（1＋k％）x]/[（1＋m％）y ]/(x/y) -1

＝（1＋k％）/(1＋m％）-1

＝（k%－m%)/(100-m%)

= [100(k-m)]/(100+m) %

那个k％的百分号要化来化去的，细心一点就ok。

15If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?

A. 600

B. 700

C. 900

D. 2,100

E. 4,900

Answer: A

16In the sequence of nonzero numbers t1, t2, t3, …, t n, …, t n+1 = t n / 2 for all positive integers n. What is the value of t5?

(1) t3 = 1/4

(2) t1 - t5 = 15/16

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D

17Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper B, which of the following expresses r in terms of p?

A. 100p / (125 –p)

B. 150p / (250 –p)

C. 300p / (375 –p)

D. 400p / (500 –p)

E. 500p / (625 –p)

Answer D (1X+1.25Y)×r%=1X 设卖出的总数是T,X=T*P%,Y=T*(1-P%)，把这两个代入1 18 If the symbol ▼ represents either addition, subtraction, multiplication, or division, what is the value of 6 ▼ 2?

(1) 10 ▼ 5 = 2

(2) 4 ▼ 2 = 2

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: A

19 If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?

A. 20

B. 40

C. 50

D. 80

E. 120

Answer: D

20If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30?

(1) None of the four numbers is greater than 60.

(2) Two of the four numbers are 9 and 10, respectively.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C

21 A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese?

[Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]

A. 1/4

B. 7/12

C. 2/3

D. 7/8

E. 8/7

Answer: B 设migrated geese为X，male=0.2X/30, and female=0.8X/70 ration=7/12 总g x male: 30% x female: 70%x 总migrant y mm : 20% y mf : 80% y

22At a certain company, 25 percent of the employees are male and 50 percent of the

employees are sales staff. What is the number of employees at this company? (1) Exactly 7 of the employees at the company are males who are sales staff. (2) There are 16 more female employees than male employees at the company.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: B

23 The selling price of an article is equal to the cost of the article plus the markup. The markup on a certain television set is what percent of the selling price? (1) The markup on the television set is 25 percent of the cost. (2) The selling price of the television set is $250.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: a

24 Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 18910

B. 19615

C. 22516

14425 E.

12839

Answer: e 约去公因子后，分母必须是2、5、10的幂数，肯定就是'terminating decimal' 。所以答案选E

25 If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

A. 5 to 4

B. 3 to 2

C. 2 to 1

D. 5 to 1

E. 6 to 1

Answer: e

26 Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x > y? (1) y > 4

(2) The cost of the 10 kilograms of material K is less than $40.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: b 1、x+y=10 y>4并不能保证x>y

2、3x+5y<40 带入x+y=10 得到y<5 则必然有x>5 x>y 选B

27 If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women,

is p > 21?

(1) More than 21

of the 10 employees are women.

(2) The probability that both representatives selected will be men is less than 101

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer:e

28 If n is an integer and 100 < n <200, what is the value of n ?

(1) 36n

is an odd integer. (2) 45n

is an even integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:B

29 The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?

I. The units digit of x + y is greater than the units digit of either x or y.

II. The tens digit of x + y equals 2.

III. The hundreds digit of y is at least 5.

A. II only

B. III only

C. I and II

D. I and III

E. II and III

Answer:B

30What is the probability that a student randomly selected from a class of 60 students will be

a male who has brown hair?

(1) One-half of the students have brown hair.

(2) One-third of the students are males.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E

31If n and k are positive integers, is n divisible by 6?

(1) n = k(k + 1)(k - 1)

(2) k– 1 is a multiple of 3.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:A

32 If x and y are positive integers and y =

9, what is the value of y?

(1) x < 8

(2) y > 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D Y的值域是1,2，，因为XY都是正整数，

33Q6:

Sue’s monthly earnings consist of a monthly salary and a 4 percent commission on the portion of her monthly sales that is in excess of $2,000. If Sue’s monthly salary was the same in July as in August, how much greater were her sales in July than in August?

(1) Sue’s monthly earnings were $3,620 in July and $3,580 in August.

(2) Sue’s monthly salary was $3,500 in July and in August.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D A

34Q32:

What is the remainder when the positive integer x is divided by 8?

(1) When x is divided by 12, the remainder is 5.

(2) When x is divided by 18, the remainder is 11.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C E

最小公倍数是36，然后求出两个条件给的数，方法如下，

12a+5=18b+11， so a=2 we can get x, x=29+36n(n=integer) 29 divided by 8, remainder is always 5

but if 36n is divided by 8, there are two possible remainders, 4 and https://www.doczj.com/doc/ca1764596.html,bined the above,we know that the ultimate remainder is not fixed, it's can be either 1 or 5.

35Q26:

What is the greatest common factor of the positive integers j and k?

(1) k = j + 1

(2) jk is divisible by 5.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: A 條件一，k=j+1，則最大公因數必為1

條件二， jk is divisible by 5.則最大公因數可為j 或k ，當然也可能是1

36 On Monday a store had a sale on bottles of juice S and juice T . If 21

the total number

of bottles of juice S in stock were sold on Monday, for which juice, S or T , were more of the bottles sold that day?

(1) Two-thirds of the total number of bottles of juice T in stock were sold on Monday. (2) At the beginning of the sale, there was a total of 90 bottles of juice S and 60 bottles of juice T in stock.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: E C

37 A certain quantity is measured on two different scales, the R -scale and the S -scale, that are related linearly. Measurements on the R -scale of 6 and 24 correspond to measurements on the S -scale of 30 and 60, respectively. What measurement on the R -scale corresponds to a measurement of 100 on the S -scale?

A. 20

B. 36

C. 48

D. 60

E. 84

Answer: C 這題我的理解是..有點像地圖的那種比例尺的概念.. 但他不是單純的就像地圖那樣的按照比例算..題目有說他是線性相關的.. 所以就是要寫出一個線性方程 y=ax+b 然後代入.. 另R-scale 為X,S-scale 為y 30=6a+b 60=24a+b a=5/3,,b=20

所以線性方程式 y=5/3X+20..代入 100=5/3X+20-->5/3X=80---->X=48 38 Q31:

In triangle PQR, the measure of angle P is 30° more than twice the measure of angle Q. What is the measure of angle R? (1) PQ = QR

(2) The measure of angle P is 78°.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C D

39One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8? C dollars per kilogram means x+y=1

(1) y > 0.15

(2) C ≥7.30

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C B

40Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?

(1) The price of Tom’s house was $110,000.

(2) The price of Jane’s house was $120,000.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C B

41 2x + y = 12

∣y∣≤12

For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?

A. 7

B. 10

C. 12

D. 13

E. 14

Answer: D XY都得是整数

42Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?

(1) The range of the seven remainders is 6. 余数的跨度是0~6

(2) The seven numbers selected are consecutive integers.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D B

43 Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January? 既然12月比1月多15%，那么就是以1月为基准的。如果实在觉得痛苦，一个最简单的记忆方式：中文的”比“，比后面的就是基准了

A. 391

B. 400

C. 410

D. 423

E. 445

Answer: A B

44 If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips? 上上上下下只有这一种

A. 3/5

B. 1/2

C. 1/5

D. 1/8

E. 1/32

Answer: A E

45 Is ∣x∣< 1?

(1) ∣x + 1∣ = 2∣x - 1∣

(2) ∣x - 3∣≠0

条件1两边平方得到一个一元二次方程，解此方程得x=1/3或者x=3，再结合条件2，可以知道|x|<1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E C

45Q11:

Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to dona te $500 each to Mary’s campaign. If no one

donated more than once and if there were no other donations, what was the value of n ?

(1) The first n people donated 161

of the total amount donated.

(2) The total amount donated was $120,000.

（1）500n=1/16[n(n+1)500](2)500n(n+1)=120000

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: C D

17Q3:

If x and y are nonzero integers, is 18 a factor of xy 2 ?

(1) x is a multiple of 54. (2) y is a multiple of 6.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: A D

Q5:

Can a certain rectangular sheet of glass be positioned on a rectangular tabletop so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop?

(1) The tabletop is 36 inches wide by 60 inches long.

(2) The area of one side of the sheet of glass is 2,400 square inches.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C E

Q10:

Was the average (arithmetic mean) weight of the package mailed at a certain post office yesterday greater than 600 grams?

(1) The total weight of the packages mailed at the post office yesterday was greater than

14,500 grams.

(2) Fewer than 25 packages were mailed at the post office yesterday. 因为fewer

than 25即是小于25 所以package 最多只能是24个

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E C

Q16:

The three-digit integer kss is the sum of the two-digit integers ks and rs , where k , r , and s are the digits of the integers. Which of the following must be true?

I. k = 2

II. r = 9 III. s = 5

ks+rs=kss 因为Ｋ在百位，Ｓ＋Ｓ＝Ｓ，所以，Ｋ＝１，Ｓ＝０，因此Ｒ＝９

A. I only

B. II only

C. III only

D. I and II

E. II and III

Answer: D B

18Q9: Is x < 0 ?

(1) x 3 < x 2 (2) x 3 < x 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: B C

Q15: If R =

, is R ≤ P ? (1) P > 50 (2) 0 < Q ≤ 20

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C E

Q18:

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m +d ?

一大群人有一种特性，该特性的分布是关于平均数m对称的。如果68％的分布位于平均数的一个标准差内，那么该分布小于m+d的比例为多少？

A. 16%

B. 32%

C. 48%

D. 84%

E. 92%

Answer: 实际上题目中给出P{(X-m)的绝对值

所以P{(X-m)的绝对值>=d}=1-0.68=0.32；

因为是均衡分布，所以

P{(X-m)>=d}＝0.5* P{(X-m)的绝对值>=d} =0.16；

要求的percent of the distribution is less than m +d

即P{X=d}=0.84

Q23:

The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?

0.75*2X>13+0.6X

A.14

B.15

C.16

D.28

E.29

Q30:

From May 1 to May 30 in the same year, the balance in a checking account increased. What was

the balance in the checking account on May 30 ?

(1) If, during this period of time, the increase in the balance in the checking account had

been 12 percent, then the balance in the account on May 30 would have been $504.

(2) During this period of time, the increase in the balance in the checking account was 8

percent.

(1)如果上升12%, 则balance 为504. 设may1 的时候为X, 则有方程X*1.12=504 可得X=504/1.12

(2)实际上升8%, 所以may30的确balance=X*8%=(504/1.12)*1.08

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D C

Q36:

If x and y are integers, is y an even integer?

(1) 2y–x = x2–y2

(2) x is an odd integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: CA

20Q14:

Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5 ?

1-6号6个卡片。随机抽一个然后放回，再抽一张，两张数字和是8，问其中有一张是5的概率。

可能是2+6,6+2,5+3,3+5,4+4这5种可能

因为已知两张和是8，而只有这5种可能，这5种可能的概率相等，里面有2种情况含有5

所以是2/5选D

A. 61

B. 51

C. 31

D. 52

2 Answer: C D

Q21: k , n , 12, 6, 17

What is the value of n in the list above?

(1) k < n

(2) The median of the numbers in the list is 10.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E C

Q36:

If a and b are positive integers such that a – b and b

are both even integers, which of the following must be an odd integer?

A. 2a

B. 2b

C. 2b

a + D. 22

+a E.

+b Answer: E D

22 Q32:

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.

(2) The number of girls in the class is twice the number of students in the class who are not studying biology.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:C B B is sufficient..

Assuming that the number of students in the class who are NOT studying

biology is X, then the number of girl in the class is 2X.

18+2X=26+X ..so X can be solved.

Q29:

In the xy-plane, region R consists of all the points (x, y) such that 2x + 3y≤ 6. Is the point (r, s) in region R ?

(1) 3r + 2s = 6

(2) r≤ 3 and s≤ 2

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: B E

Q26:

Of the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. What percent of the families in City X owned a personal computer in 1998?

A. 50%

B. 52%

C. 56%

D. 70%

E. 74%

Answer: D A设1994年有100人, 有电脑的有40人

则1998年有104人, 有电脑的有40×1.3=52人

52/104=50%

Q24:

In the xy-plane, the line k passes through the origin and through the point (a, b), where ab ≠ 0. Is b positive?

(1) The slope of line k is negative.

(2) a < b

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E C

2014~2020全国卷文化常识真题答案

2016~2020全国卷文化常识真题答案 1 C 本题考查考生理解文言实词中文化意义的能力。C项，殿下，古代对仅次于天子的侯王或皇太子的尊称，不包括“丞相”。 2 B 本题考查考生理解文言实词中文化意义的能力。殿试由皇帝主持。 3 C 本题考查考生理解文言实词中文化意义的能力。C项，禁中，指封建帝王所居的宫苑。另外，由原文“大惧，其子攸日夕侍禁中，泣拜恳祈”也可以推知蔡京的儿子蔡攸只可能是向皇帝恳求宽恕，而不涉及其他皇室宗族。因此，选项扩大了范围，故选C。 4 A 本题考查考生理解文言实词中文化意义的能力。A项，郡一级的军事归“郡尉”或“司马”管辖，对太守有牵制作用；此外，隋初，存州废郡，以州刺史代郡守之任，此后太守不再是正式官名，而科举发源于隋炀帝时期，因此太守不可能管辖科举。 5 A “诸子百家是对先秦时期各学术派别的总称”，“农家”不是影响最深远的，故选A。 6 B 此处“武”指的是周武王。 7 C 三晋指春秋末韩、赵、魏三家分晋。 8 C 践祚，指即位、登基，并没有“用武力打败敌对势力，登上国君宝座”的意思。 9 D “师”单用并不能指代国都。京师，指国都。类似的称呼有：都门、毂下、京都、京城、国都、都城、首都。 10C “如令尹、京兆尹，是知府的简称”错误。“尹”是官的统称，“令尹”在春秋战国时相当于宰相，也泛称县、府等地方行政长官。知府古代是太守，州最高行政长官。东汉叫州牧，隋朝称为刺史或太守。唐宋叫知府。 11B “它与血亲有同有异，只是血亲中的一部分”错。姻亲是以婚姻关系为中介而产生的亲属，血亲是基于血统关系的亲属。二者性质完全不同。 12B “然后再作考察，进行犯罪事实的取证工作”错。“考”通“拷”，“拷问”之意。 13C 近侍：左右侍从的人，多指君主身边侍从的臣子。他们的官职未必就是高的，并且对皇帝的影响也不一定大。 14C “可用“有司”来指称朝廷中的各级官员”错。“有司”应指有具体职务、做具体工作的官吏。 15D “实际是官员受到权臣诋毁，不得不请求退职的委婉说法”错。移疾指上书称病，为居官者要求隐退的委婉语。 16Ａ礼部，中国古代官署。南北朝北周始设。隋唐为六部之一。历代相沿。长官为礼部尚书。考吉、嘉、军、宾、凶五礼之用；管理全国学校事务及科举考试及藩属和外国之往来事。礼部下设四司，明清皆为：仪制清吏司，掌嘉礼、军礼及管理学务、科举考试事；祠祭清吏司，掌吉礼、凶礼事务；主客清吏司，掌宾礼及接待外宾事务；精膳清吏司，掌筵飨廪饩（xì）牲牢事务。户部，中国古代官署名，为掌管户籍财经的机关，六部之一，户部尚书主要掌管国家经济，包括户口、税收、统筹国家经费等等。 17D太子又称皇储、储君或皇太子，是我国封建王朝中皇位的继承人。不能指其他儿子。 18 B“长子”及“最年长的儿子”错。均应为“嫡长子”。19．B “南面”指称帝。

2014---2019高考语文文化常识真题及答案

威宁县第八中学2019——2020学年度第一学期高二语文第十六次周测卷命题人：余愿审题人：虎恩雄班级：姓名：（2019年全国卷一）1.下列对文中加点的词语相关内容的解说，不正确的一项是（3分）A．诸子百家是先秦至汉初学术派别的总称，其中又以道、法、农三家影响最深远。 B．诏令作为古代的文体名称，是以皇帝的名义所发布的各种命令、文告的总称。 C．礼乐指礼制和音乐，古代帝王常常用兴礼乐作为手段，以维护社会秩序的稳定。 D．就国，是指受到君主分封并获得领地后，受封者前非领地居住并进行统治管理。（2019年全国卷二）2. 下列对文中加点的词语相关内容的解说，不正确一项是 A. 缪公即秦穆公，春秋时秦国国君，在位期间任用贤臣，使国力趋强，称霸西戎。 B. 汤武即商汤与孙武的并称，他们二人均以善于用人用计，战功赫赫，留名于青史。 C. 变法是指对国家的法令制度作出重大变革，商鞅变法为秦国富强奠定了基础。 D. 黥是古代的一种刑罚，在犯人脸上刺上记号或文字并涂上墨，在刑罚之中较轻。（2019年全国卷三）3、下列对文中加点的词语相关内容的解说，不正确的一项是(3分) A、殷纣为商代末代国君，在位期间统治失控，好酒瀣乐，暴敛酷刑，是有名的暴君。 B、武王是周文王之子，继承其父遗志，联合众多部族与商激战，灭商，建立周王朝。 C、三晋，春秋末韩、赵、燕三家分晋，战国时的韩、赵、燕三国，史上又称“三晋” D、令尹，春秋战国时期楚国设置的最高官位，辅佐楚国国君，执掌全国的军政大权。（2018年全国卷一）4．下列对文中加点词语的相关内容的解说，不正确的一项是A．《三坟》《五典》传为我国古代典籍，后又以“坟籍”“坟典”为古代典籍通称。B．“阙”原指皇宫前面两侧的楼台，又可用作朝廷的代称，赴阙也指入朝觐见皇帝。C．“践阼”原指踏上古代庙堂前台阶，又表示用武力打败敌对势力，登上国君宝座。D．逊位，也称为让位、退位，多指君王放弃职务和地位，这里指鲁芝的谦让行为。（2018年全国卷二）5．下列对文中加点词语的相关内容的解说，不正确的一项是 A．豪右，指旧时的富豪家族、世家大户；汉代以右为尊，所以习惯上称为“豪右”。

英语错题本范本

初中生应该如何正确地做英语错题本 (2012-11-08 15:13:29)转载▼ 标签：乐加乐学而思英语初中教育 2011年4月，我带的第一届学生正在为2个月后的中考做最后的冲刺。那时候的孩子们，实在是让人不忍苛责。他们成绩有高有低，但大都非常焦虑。初中英语那点知识早就已经学完了，连复习都已经进入到第三遍，正可谓“翻开书一目了然，合上书一片茫然”。他们每天都要做很多题，因为他们除了做题没什么别的可以做。每天一套模拟题，分数高一点，就非常开心，仿佛这预示着自己中考的分数也会高一点；分数低一点，那么，是时候再来一套了！我将这种状态称为“模拟题狂热症”，这是在考前冲刺的最后阶段极容易陷入的一

个状态。但是，也有少数孩子非常“淡定”，每天忙而不乱，有条不紊地进行着知识的整理和总结，最后取得了很好的效果。为什么他们这么淡定？就是因为他们做了错题本。一个小小的本子能有这么大的作用吗？是的。在冲刺阶段，大家的知识水平都已经差不多，就看谁有方向，谁更淡定，谁能够脚踏实地地学习。而错题本能清楚地展示出孩子的知识漏洞所在，帮助孩子明确最后阶段的复习方向。错题本这件事，早做比晚做强，晚做也比不做强。即便到考前最后10天，踏踏实实地整理一下错题，也比盲目地东看一眼、西碰一下有效得多。而从学习的开始阶段就养成做错题本的习惯，对孩子的发展更是大有裨益。这次我们给孩子们设计这个英语笔记本+错题本（前面一半是笔记本，后面一半是错题本），就是希望帮助孩子们养成这个习惯。那么，错题本应该怎么做呢？不同类型的题目应该怎么处理？在这里，我把英语题目分两个类型来说明。 1.语法题（包括单项选择、句型转换等题型）这类题目往往较短，整理起来较为轻松。比较好的做法是，在一页纸的左侧记录题目（黑笔），右侧记录错误答案和正确答案（红笔）。这样在复习的时候，只要把右侧折过去，即可把左边的题目当新题来做。更重要的是，要把自己能想到的和这道题相关的知识点都整理在右侧。这样，光是做错题本的过程就非常有用啦！ 2.阅读题（包括完形填空、首字母填空、阅读理解、阅读文章回答问题等题型）很多同学或家长都反映阅读题不好整理错题本，的确如此。如果把时间浪费在抄写文章上，还不如做点更有用的事情。我认为孩子们可以把阅读题的订正做在试卷上。建议家长们给孩子买几个“风琴袋”（如下图），同时帮助孩子们养成收集整理卷子的好习惯。风琴袋的好处是里面格子很多，适用于大量文件的储存。孩子们可以把试卷分别放入每个格子里面，做好标签。在复习的时候只需

高中生必读：如何整理错题集

在我看来，“如何整理错题集”这个问题，其实能分为以下几点来回答：为什么要整理错题集？哪些科目最需要整理错题集？如何整理错题集？毫无疑问，在应试教育体系中，要想通过考试得到认可，最重要的途径是对各种题型进行大量训练，从而积累大量的解题经验和技巧。因此，目前多数学校采取的教学模式，其实就是“解题教学”。除了少数天资聪颖者，几乎没人能够不被这种模式裹挟三年、六年甚至更长时间。但是，大量训练不一定意味着成功。看看我们身边，总会发现这样一类同学：他们勤奋刻苦，不仅完成老师布置的作业，也会为自己“开小灶”，但在各种考试中的成绩往往不尽如人意。究其原因，就是因为他们的解题训练并没有获得实质性的成效。换句话说，他们的训练与打发时间无异。那么，数量在解题训练中难道不重要吗？的确重要，但并不是最重要的一环。说到底，解题训练的根本目的，是缩小自身思维能力与出题者的要求之间的差距。所以，力图缩小这种差距的我们，关注的应该是那些错题，以及错题产生的原因。任何一个想要从考试中脱颖而出的人，都应该会使用错题集来总结自己解错或解不出题目的原因，争取做到有则改之，不重蹈覆辙。

明白整理错题集的重要性后，问题就来了：按照提升自身思维能力的标准，到底哪些科目最需要整理错题集呢？毕竟，如果所有科目都整理错题集，那会相当费时费力。语文和英语都是语言类的科目，考查的题型主要有基础知识、阅读理解和表达应用三类。其中，基础知识多练就熟，本身是不具备较大的思维难度的。至于阅读理解和表达应用，它们的随机性和偶然性都很强，就算有解题方法，基本上也是靠平时多加积累才能总结得出来的。因此，这两科我不建议整理错题集。数学和物理可以说是理科思维的集大成者，光记得公式、定理远远不够，因为要想在这两科的题目中找出理论依据，是需要思维方法的。举个关于物理题的例子，受力分析估计大家都能掌握得不错，但要是整体法和隔离法运用不熟练，光想用受力分析解出那些斜面滑块一起动问你受几个力的问题，就要费很大劲儿了。至于数学，那就更不用提了，几乎每道正常一点的高考题都是到处设坑埋雷，处处必须留心。更何况，数学题型千变万化，解题方法及其组合也是千差万别。所以，对数学错题的研究和反思是十分有价值的。综上所述，我的意见是：数学是最需要整理错题集的科目，物理次之。那么，不需要整理错题集的科目又怎么办呢？

高考古代文化常识分类150题(含答案及解析)

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9．官员遇父母亡故，一般均解除官职，守丧三年，期满后起复，称为丁忧。( ) 10．(2017·全国卷Ⅰ)母忧是指母亲的丧事，古代官员遭逢父母去世时，按照规定需要离职居家守丧。( ) 11．“起复”“夺情”都是指古代官员守丧期满后，被重新起用，回到原职。( ) 12．“终养”又称“归养”，是指因亲人年老或病重而辞官侍奉。( ) 13．古代官吏告老退休称“致仕”，也称“休致”。官员年老有病，由本人提出申请，获准后致仕，国家据其职位，给予一定的赏赐。( ) 14．(2017·全国卷Ⅲ)告老本指古代社会官员因年老辞去职务，有时也是官员因故辞职的一种借口。( ) 15．(2016·全国卷Ⅱ)移疾指官员上书称病，实际是官员受到权臣诋毁，不得不请求退职的委婉说法。( ) 16．(2016·全国卷Ⅲ)致仕本义是将享受的禄位交还给君王，表示官员辞去官职或到规定年龄而离职。( ) (二)皇室官职 17．统治天下的君主、帝王均称为“皇帝”，又称为“天子”。古人认为君主、帝王是上天的儿子，其政权是受天命建立的。( ) 18．自秦代开始，皇帝的正室称皇后，皇帝的母亲称皇太后，皇帝的父亲称太上皇；祖母称太皇太后，历代相沿不变。( ) 19．(2016·全国卷Ⅱ)中宫是皇后所居之宫，后来又可以借指皇后，这与东宫又可借指太子是同样道理。( ) 20．皇帝指定的皇位继承人称为“皇太子”。一般为皇帝的嫡长子，但也有例外，由皇帝选定册立。帝王之女皆称公主，始于战国。汉代以皇帝之女称“公主”，

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2019年高考最新文化常识试题汇编(附答案)

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数学错题本整理方法及要点盘点

研途宝考研 https://www.doczj.com/doc/ca1764596.html,/zykzl 1.如何整理错题？喜欢抄题的抄题，不喜欢抄题的剪书。 2.对错题的思路总结。这里说的思路指的是你在解这道题时的全部思想活动，包括你对题目条件的分析、初步的想法、推导过程等等。尤其是卡了壳、出了错的部分，更要着重详细地记录下来。 3.错题本不能只增不减。如果你能做到天天看自己的错题集，很快就会发现有的东西会很快掌握，这时候就需要把这部分内容移除。错题集里面只留下那些你真心还没完全搞懂、没有完全记住的东西，保证你每一次翻开错题集都能再加深学习。 4.错题本要经常复习。不要等到考试前再复习，平时有空的时候，就要经常复习，把不懂的、没把握的知识变成掌握的最牢固的知识。重要考点盘点： 1.高等数学极限、导数和不定积分这三个部分是考试中考查的重点，其他部分都是在这三个的基础上进行延伸。 2.线性代数是初等变换，含有参数的线性方程式解的讨论，还有就是方程的特征值、特征向量，有了他们，线性代数的复习就会很流畅。 3.概率论与数理统计第一章的概念，其中的条件概念，乘法公式、等三个方面; 第二章是几何分布，这章是该理论的核心，特别是二维联系变量的平均分布密度、条件分布密度，离散型的实际变量的特征和定义; 第三章数据变量的数据特征，主要就是四个概念数学期望、方差、线方差、相关系数。此外，大家在复习的过程中，应重视自己的错题，因为他们在一定程度上反映出你的知识漏

研途宝考研 https://www.doczj.com/doc/ca1764596.html,/zykzl 洞。在数学试卷中，客观题部分主要分填空和选择。其中填空6道题，选择8道题，共56分。占据了数学三分之一多的分数。在历年的考试中，这部分题丢分现象比较严重，很多一部分同学在前面的56分可能才得了20多分，如果基本题丢掉30多分，这个时候总分要上去是一件非常不容易的事情。【填空题】 (1)考查点：填空题比较多的是考查基本运算和基本概念，或者说填空题比较多的是计算。 (2)失分原因：运算的准确率比较差，这种填空题出的计算题题本身不难，方法我们一般同学拿到都知道，但是一算就算错了，结果算错了，填空题只要是答案填错了就只能给0分。 (3)对策：这就要求我们同学平时复习的时候，这种计算题，一些基本的运算题不能光看会，就不去算，很多的同学看会在草稿纸上画两下，没有认真地算。平时没有算过一定量的题，考试的时候就容易错，这就要求我们平时对一些基本的运算题，不是说每道题都认真地做到底，但每一种类型的计算题里面拿出一定量进行练习，这样才能提高你的准确率。【选择题】 (1)考查点：选择题一共有八道题，这个丢分也很严重，这个丢分的原因跟填空题有差异，就是选择题考的重点跟填空题不一样，填空题主要考基本运算概念，而选择题很少考计算题，它主要考察基本的概念和理论，就是容易混淆的概念和理论。 (2)失分原因：首先，有些题目确实具有一定的难度。其次，有些同学在复习过程中将重点放在了计算题上，而忽视了基础知识，导致基础只是不扎实。最后，缺乏一定的方法和技巧。由于对这种方法不了解，用常规的方法做，使简单的题变成了复杂的题。 (3)对策：第一，基本理论和基本概念是我们的薄弱环节，就必须在这下功夫，实际上它的选择题里边要考的东西往往就是我们原来的定义或者性质，或者一个定理这些内容的外延，所以我们复习一个定理一个性质的时候，即要注意它的内涵又要注意相应的外延。比如说原来的条件变一下，这个题还对不对，平时复习的时候就有意识注意这些问题，这样以后考到这些的时候，你已经事先对这个问题做了准备，考试就很容易了，平时在复习的时候要注意基本的概念和理论，本身有些题有难点，但是也不是说选择题有很多有难度的题，一般来说每年的卷子里边八道选择题里面一般有一两道是比较难的，剩下的相对都是比较容易的。第二，客观题有一些方法和技巧，我们通常做客观题用直接法，这是用得比较多的，但是也有一些选择题用排除法更为简单。【计算题】 (1)考查点：计算题在整份试卷中占绝大部分，还有一部分是证明题，计算题就是要解决计算的准确率的问题。

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如何整理和运用历史“错题集”

如何整理和运用历史“错题集” 一、整理：．．．．．纠错型，即将所有做错的题目按错误的原因进行分类整理。其整理步骤为： 1.分类整理。将所有的错题分类整理，分清错误的原因：概念模糊类、粗心大意类、顾此失彼类、图型类、技巧类、新概念类、历史思想类、规律类等等，并将各题注明属于某一章某一节，这样分类的优点在于既能按错因查找，又能按各章节易错知识点查找，给今后的复习带来简便，另外也简化了“错题集”，整理时同一类型问题可只记录典型的问题，不一定每个错题都记，但一定要有错误归因。 2.记录方法。老师试卷评讲时，要注意老师对错题的分析讲解，该题的引入语、解题的切入口、思路突破方法、解题的技巧、规范步骤及小结等等。并在该错题的一边注释，写出自己解题时的思维过程，暴露出自己思维障碍产生的原因及根源的分析。这种记述方法开始时可能觉得较困难或写不出，不必强行要求自己，初始阶段可先用自己的语言写出小结即可，总结得多了，自然会有心得体会，渐渐认清思维的种种障碍(即错误原因)。 3.必要的补充。前面的工作仅是一个开始，最重要的工作还在后面，对“错题集”中的错题，不一定说订正得非常完美了，就证明你这一知识的漏洞就已经弥补好了。对于每一个错题，还必须要查找资料或课本，找出与之相同或相关的题型，并作出解答。如果没有困难，说明这一知识点，你可能已经掌握了，如果还是不能解决，则对于这一问题的处理还要再深入一点。因为在下一次测试中，在这一问题上，

你可能还要犯同样的错误。 4、及时总结同类知识。如：11．下列条约中，割地、赔款、开放通商口岸三项都有的是①《南京条约》②《天津条约》③《北京条约》④《瑷珲条约》A．①③B．①④C．②③D．②④（选A）如果此题有不清楚的地方，就在改错本上将不平等条约中分别有割地、赔款、开放通商口岸的内容详细列一遍，以弄清自己到底哪儿还有知识缺漏，以及时改进和提高。二、运用：．．．．．对于相关错误知识点的整理与总结，虽然工作繁杂，但其作用决不仅仅是明白了一道错题是怎样求解这么简单，更重要的是通过整理“错题集”，你将学会如何学历史、如何研究历史，掌握哪些知识点在将来的学习中会犯错误，真正做到“吃一长一智”。一本好的“错题集”就是自己知识漏洞的题典，平时要注意及时整理与总结，在历史复习时“错题集”就是你最重要的复习资料，最初复习时一定要多回头看，以后隔一段时间可以加长一点，就能够起到很好的复习效果。虽然每位同学的“错题集”不尽相同，但其他同学的“错题集”中的优点是可以借鉴的，故同学们平时也要注意相互之间的交流。错题集上，容易混淆的记忆要点也有必要整理归纳，要写清楚自己弄不懂的就行了，另外，最好多准备几种颜色的笔随身带着错题集当然不错，如果做不到，建议有空的时候，下课的时候看看，至少考试前翻一翻，减少同一问题失分，另外，如果没时间，参考书上做个记录翻一翻，也有一点错题集的功效一般要

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如何整理和运用历史“错题集”