希望杯英语题

1、If a＜b ＜0, then the following inequality must be hold ( )

(英语小词典：following ：下面的； inequality ：不等式) 111111(A) ＜ (B)＞ (C) ＞a b a -b a a b 1⎫1⎫⎛⎛ (D) b +⎪＜ a +⎪ a ⎭b ⎭⎝⎝22

2、(Figure 1) In the parallelogram ABCD,AD=2AB,a point M is mid- point of segment AD,CE⊥AB,if ∠CEM=40°,then the value of∠DME it( ).

(A)150° (B)140° (C)135° (D)130°

3、

If N is natural number,and N

4、Root of the equationx x x x +++=2 is ． 3153563

(英汉小字典：root 根；equation 方程．)

5、In fig. 1, let ∆ABC be an equilateral triangle, D and E be points on edges AB and AC respectively, F be intersection of segments BE and CD, and ∠BFC =120 , then the magnitude relation between Ad and CE is （ ）

A. AD >CE B. AD

（英汉词典：equilateral 等边的；intersection 交点；magnitude 大小，量；indefinite 不确定的）

6、 If p and q are unequal primes, m and n are unequal positive integers satisfying m 2-pm +q =0 and n 2-pn +q =0, then the value of

p q is ________。（英汉词典：prime 质数）

7、（Figure 4）In the trapezium（梯形）ABCD ，AD ∥BC ，point E is midpoint（中点）of the AD ，point F is midpoint of the BC ，EF ＝(BC －AD ) ，the result of the ∠B ＋∠C is （ ）

（A ）90° （B ）100° （C ）110° （D ）120°

3 of the radius of circle 4128、If the radius(半径) of circle Ⅲ in the figure3(图3) is

Ⅱ,and the radius of circle Ⅱ is 4 of the radius of circle

5

the shaded region iswhat part of the area of circle Ⅰ?( (A)79316; (B);(C);(D) 2520255

9、If a,b and c are sieds(边) of the ΔABC,and a2-bc=a(b-c),then the figure(形状) 图3

of the triangle(三角形) is_________.(用汉语填写)

10、Given in the △ABC,a,b,c are three sides of the triangle, a=3, b=10 and perimeter of the triangle is multiple of 5, then the length of c is 。 （英汉小词典：side ：边；perimeter ：周长；multiple ：倍数）

11、Given m is a real number, and |1-m|=|m|+1，simplify an algebraic expression, then =( )

(A)|m|-1 (B)-|m|+1 (C)m-1 (D)-m+1 (英汉小词典simplify ：化简；algebraic expression：代数式)

12、(Figure 3)In a trapezoid ABCD，AE=DE ，CE⊥AD，CE is a bisector to ∠BCD，then the ratio of the area of a quadrilateral ABCE to that of a triangle CDE is _____.

(英汉小词典trapezoid ：梯形；bisector ：平分线；ratio ：比值；quadrilateral ：四边形)

13、Given in the △ABC ，a ，b ，c are three sides of the triangle，and

then ∠A is

A ．acute angle B ．right angle 321=+，a b c

C ．obtues angle D ．acute angle or obtues angle （英汉词典 acute angle：锐角；obtuse angle：钝角）

14、Given a ，b ，c are positive integers ，and a ，b are prime numbers ，a 3+b c +a =2005，then the value of a +b +c is （ ）

A ．14 B ．13 C ．12 D ． 11

(英汉词典 positive integers：正整数. prime numbers：质数)_

15、Let a be integral part of and b be its decimal part．Let c be the integral part of π and d be the decimal part.．if ad －bc ＝m ，then （ ）

（A ）－2＜m ＜－1 （B ）－1＜m ＜0 （C ）0＜m ＜1 （D ）1＜m ＜2

（英汉词典：integral part 整数部分；decimal part 小数部分）

16、 Let a be the length of a diagonal of a square, b and c be the length of two diagonals of a rhombus respectively. If b:a=a:c,then the ratio of area of the square and rhombus is ( )

（A ）1：1． （B ）2

（C ）1

（D ）1：2．

(英汉词典：length 长度；diagonal 对角线；square 正方形；rhombus 菱形；respectively 分别地；ratio 比；area 面积)

17、Let A = be a four-digit number. If is a square of an integer, then

A= 或 ．

（英汉词典：four-digit number 四位数；square 平方、平方数；integer 整数）

18、In the figure，ABCD is a diamond ，points E and F lie on its sides AB and

AE BF BC respectively ，such that ，and △DEF is a regular =BE CF

triangle ．Then ∠BAD is equal to ( )

A ．40

B ．60 E F C C ．80 D ．100

A 19、If one side of a triangle is 2 tines of another side and it has the largest

A ．1:2:3 B ．1:1:2 D possible area，then the ratio of its three sides is ( ) C

．2 D

．1:2（英汉小词：possible 可能的；area 面积；ratio 比率，比值）

20、If the sum of a 4-digit natural number and 17，the difference between it and

72 are all square numbers，then the 4-digit natural number is ． （英汉小词典：4-digit natural number四位自然数；difference 差；square number

完全平方数）

21、The number of integer solutions for the system of inequalities ⎧x -2a ≥0，about x is just 6，then the range of value for real number a is （⎨3-2x >-1⎩

）

B ．-2.5≤a ≤-2 C ．-5

D ．-5≤a ≤-4

（英汉词典：integer solution 整数解，system of inequalities不等式组，the range

of value取值范围）

22、In the rectangular coordinates，abscissa and ordinate of the intersection point of the lines y =x -k and y =kx +2 are integers for integer k ，then the number of the possible values of k is （

A ．4

） D ．7 B ．5 C ．6

（英汉词典：abscissa 横坐标，ordinate 纵坐标，intersection point交点，integer

整数）

23、Given f (x ) =ax 3+bx 2+cx +d ，if when x takes the value of its inverse number ，the corresponding value of f (x ) is also the inverse number ，and f (2)=0，then c +d =_______________． a +b

（英汉词典：inverse number相反数）

b ，c satisfy c correct in the following inequalities？（

b c A ．> a a ） D ．a -c 0 c b 2a 2

C ．> c c

25、

(英汉词典：Fig ．figure 的缩写，图；quadrilateral 四边形；diagonal 对角线；value 数值；variable 变量；to depend on取决于；position 位置

)

26、

(英汉词典：two-placed number两位数；number 数，个数；to satisfy满足；complete 、

square 完全平方(数) ；total 总的，总数)