mathe_china_2010_Maerz_1_en[1] 德国亚琛应用技术大学预科入学考试样卷 德国留学材料.pdf

name: date: app-number: please note: the available time for the test is 60 minutes 1) material: pen, pencil, eraser, no calculators, no table of formulas 可使用工具: 钢笔，铅笔，橡皮, 不可使用工具: 计算器，公式 2) leave the pages together and return all pages! give intermediate steps! use backsides for your drafts! 请在交答卷时将所有考题试纸交回。 1. calculate: 100.642+=a 4 1 3 1 2 1 4 1 3 1 2 1 + =b ()3 2 2 5 4 5 .1210 10 2 . 3 = c a = b = c = 2. the graph of 2)(+= b xaxf passes through p (1|1) and q (2|-2). find)(xf. )(xf= 3. solve for x: () 2 10 1000 10 2 x x = x1 = 4. find a and b: 32log 25. 0 =a 50 5100 b (7 . 05log5lg 10 =) a = b 5. solve for x: () 4 2 2 14 16 9 1 4 3 = +xx x1 = r 60 6. a.) solve for x: 11 2 += ba x a ()0; 0+baba x = b.) what other restrictions (条件限制) exist for a and b? 7. throw a dice (骰子) three times and youll get a natural number n: 111 n 666. what is the probability p of getting a number with 3 different digits (数字)? p = 8. an employee (雇员) was promised a yearly rise (提升) of his salary of 4% in 2008 and 2009. but in 2009 this rise was cut by 30%. find the percentage p of the total rise for these two years. p = 9. compare the following data: a -1 0.5 2 3.5 5 b -3 1.5 0.6 0.375 0.27 which one of the following relations is correct? mark (标出) it and find the factor (系数) k in the relevant equation. 1) a b 1 ; 2) 1 +a a b; 3) 12 1 +a b; 4) a a b 1 + ; =k ; b = 10. check whether x=53 (sin 53 = 0.8) solves the following equation (等式): ()()()xxx+=+180sin2 . 090cos180sin2 11. this is the cross section (横切面) of a cone fitted into a hemisphere (半球体). calculate the two volumes v and find a in: hemispherecone vav= a = sab c d a = 4cmb c = 4.5cm d c )32|2(q 1 2 s p 12 12. consider the areas , 1sad aa = sbc aa = 2 , and abcd aa = 3 . a) for 23 9 5 aa =: find b and d. b) for =60: calculate a1, a2, and a3. b = d = a1 = a2 = a3 = 13. curve (曲线) c is of type ( )bxaxf+=. a) find a and b; also find and sketch (草图)( ) 2 22 1 = x fxg. (use the same coordinate system) b) find the equation of the straight line (直线) l with slope (倾斜度) 3 2 =mpassing throu