Math topic中文

Number systems

negative numbers, integers, rational numbers, real numbers, and their four operations

Practice questions

  1. 1已知∣a→∣=4\left| \overrightarrow{a}\right|=4 ，∣b→∣=2\left| \overrightarrow{b}\right|= \sqrt{2} ，a→\overrightarrow{a}与b→\overrightarrow{b}…
  2. 2Mrs Ang runs a small tuition centre for secondary school students. The tables provide information on the cost of running…
  3. 3计算： (1)(94)12−(−9.6)0−(278)−23+(32)−2(1)(\dfrac{9}{4})^{\frac{1}{2}}-(-9.6)^{0}-(\dfrac{27}{8})^{-\frac{2}{3}}+(\dfrac{3}{2})^{-2}； (2)lg⁡5+lg⁡2⋅lg⁡5+(lg⁡2)2+eln⁡3(e(2)\lg 5+\lg 2\boldsymbol{⋅}\lg 5+(\lg 2)^{2}+e^{\ln 3}(e…
  4. 4n is a positive integer. Explain whether, for all n, (7n+2)2−(7n−1)2(7n+2)^{2}-(7n-1)^{2} is a multiple of 3. Answer ___
  5. 5下列说法正确的是： （只填序号） ①相反数等于本身的是±1、0； ②0不能做除数； ③绝对值等于本身的数是0； ④倒数等于本身的数是±1、0； ⑤0除以任何数都得0．
  6. 6A bag contains 4 black coins, 7 red coins and 11 white coins. Two coins are drawn from the bag at random, one after anot…
  7. 7The diagram shows the positions of a harbour, H, a lighthouse, L, and two buoys P and Q. HPQ is a straight line. The bea…
  8. 8已知两个数的和为正数，则()(\quad) A. 一个加数为正，另一个加数为零 B. 两个加数都为正数 C. 两个加数一正一负，且正数的绝对值大于负数的绝对值 D. 以上三种都有可能
  9. 9给出下列判断：①单项式−12px2-\dfrac{1}{2}px^{2}的系数为−12-\dfrac{1}{2}；②整式x−2xy+1x-2xy+1是二次三项式；③多项式3x2y3−px5+12y3x^{2}y^{3}-px^{5}+\dfrac{1}{2}y的次数…
  10. 10中国古代数学著作《九章算术》中注有“今两算得失相反，要令正负以名之”，意思是今有两数，若其意义相反，则分别叫做正数与负数．如果“盈利6%”记作“+6%”，那么“-5%”表示___．
  11. 11方程∣xy∣+∣x+y∣=1\left|xy\right|+\left|x+y\right|=1的整数解的组数为()(\quad) A. 22 B. 44 C. 66 D. 88
  12. 12“-7+18-9-15“可以读成（ ） A. -7，18，-9，-15的代数和 B. -7加18减-9减15 C. -7加18加+9加+15 D. -7减18减9减-15
  13. 13下列说法正确的有()(\quad) ①两个有理数的和为负数，则这两个数中至少有一个是负数； ②若a<ba< b，则∣a∣<∣b∣|a|< |b|； ③aa为任何有理数，则−∣a−2∣-|a-2|必为负数； ④若∣a∣+a=0|a|+a=0，则aa…
  14. 14计算 (1)−10−8÷(−2)×(−12)(2)(−2)2+(−2)÷(−23)+∣−116∣×(−24)(1)-10-8\div (-2)\times (-\dfrac{1}{2})(2){{(-2)}^{2}}+(-2)\div (-\dfrac{2}{3})+\left| -\dfrac{1}{16} \right|\times (-{{2}^{4}})…
  15. 15现有有理数将这四个数3、4、-6、10（每个数用且只用一次）进行加、减、乘、除运算，使其结果等于24，请你写出三个符号条件的算式．
  16. 16先化简，再求值：(2x−y)(x−y)−(2x−y)2(2x-y)(x-y)-{{(2x-y)}^{2}}，其中x=−1,y=−2.x=-1,y=-2.
  17. 17Given that xx is an integer where 1≤x≤41 \le x \le 4, find the minimum value of x2+2x\frac{x}{2} + \frac{2}{x}.
  18. 18Adam has some 50-cent and 20-cent coins in his wallet. Given that he has a total of 73 coins adding up to a value of $2…
  19. 19锡澄高速公路养护小组，乘车沿南北向公路巡视维护，如果约定向北为正，向南为负，当天的行驶记录如下((单位：千米))： +17+17，−9-9，+7+7，−15-15，−3-3，+11+11，−6-6，−8-8…
  20. 20下列说法正确的是（ ） A. 0是最小的有理数 B. 任何一个有理数的相反数都不能是负数 C. 一个数不是负数就是正数 D. 数轴上，互为相反数的两个数的和为0
  21. 21某天焦作市交警大队的一辆警车在东西街上巡视，警车从百货大楼AA处出发，规定向东方向为正，当天行驶纪录：((单位：千米)+10)+10，−9-9，+7+7，−15-15，+6+6，−5-5，+4+4，−2(1)-2(1)…
  22. 22The diagrams show the speed-time graph and the corresponding distance-time graph of a car. The car travelled from a poin…
  23. 23The marked price of a mobile phone is $1288. After selling the mobile phone at 15% discount, the shop owner still makes…
  24. 24若“m>am>a”是“函数f(x)= (13)x+m−13f(x)=\:(\dfrac{1}{3})^{x}+m-\dfrac{1}{3}的图象不过第三象限”的必要不充分条件，则实数aa能取的最大整数为___.
  25. 25The diagram below shows a gift souvenir formed by joining the plane face of a solid hemisphere of radius 3 cm and a soli…
  26. 26On the Venn Diagram shown in the answer space, shade the set A∩B′A \cap B'. ε=x:x is an integer and 1≤x≤100ε = {x: x \text{ is an integer and } 1 \le x \le 100}…
  27. 27从−3-3，2 \sqrt {2}，00，π2 \dfrac {π}{2}，14 \dfrac {1}{4}这55个数中任意抽取一个，抽到无理数的概率为(    )(\:\:\:\:) A. 15 \dfrac {1}{5}…
  28. 28Simplify −2(−3x−4)+5-2(-3x-4)+5. Answer ...
  29. 29Sam is a 40-year-old man who earns a gross salary of $8000 a month. He is a Singaporean and an employee of a Singapore…
  30. 30A bag contains 12 balls. 2 of the balls are red, n are green balls and the rest are blue balls. Eunice takes two balls f…
  31. 31Find the 8th term of the sequence 10, 11, 13, 16, 20,..., Answer
  32. 32Mr Johnson has a plot of field that grows dandelion plants. An average of 70 dandelion plants grow on each square metre.…
  33. 33下列说法中正确的是（ ） A. 有最小的正数 B. 有最大的负数 C. 有最小的整数 D. 有最小的正整数
  34. 34A survey was carried out to find out the number of emails received in a week by each of a group of students. The table b…
  35. 35Simplify 3a25b3+(12c25ab)2\frac{3a^2}{5b^3} + \left(\frac{12c}{25ab}\right)^2. nn is a positive integer. Show that, for all nn, (3n+2)2−(3n−2)2(3n+2)^2 - (3n-2)^2…
  36. 36一只蜗牛在数轴上爬行，先从原点出发向右爬行55个单位长度，再向左爬行55个单位长度到达终点，那么这个终点表示的数是___.
  37. 37下列说法错误的是（ ） A. 符号不同的两个数互为相反数 B. 任何一个数都有相反数 C. 若a+b=0，则a，b互为相反数 D. 1的倒数等于它本身
  38. 38(1)二进制数学1101101(2)1101101_{(2)}转化为十进制数为___. (2)若实数xx，yy满足约束条件{x⩾0y⩽x2x+y−9⩽0\left\{\begin{array}{l}x\geqslant 0\\ y\leqslant x\\ 2x+y-9\leqslant 0\end{array}\right.…
  39. 39设xx是有理数，那么下列各式中一定表示正数的是()(\quad) A. 2008x2008x B. x+2008x+2008 C. ∣x∣+2008|x|+2008 D. ∣2008x∣|2008x|
  40. 40与数轴上的点一一对应的是 A. 有理数 B. 无理数 C. 实数 D. 正数和负数
  41. 41The equation of a curve is given by y=ln⁡3x32x−1y = \ln \sqrt{\dfrac{3x^3}{2x-1}}, where x>12x > \tfrac{1}{2}. Find the coordinates…
  42. 42The approximate mass of the earth is 5.976×10245.976 \times 10^{24} kg. How many times is the earth heavier than an average male…
  43. 43Written as a product of its prime factors, p=33×5×72p = 3^3 \times 5 \times 7^2. Express 450 as a product of its prime factors.…
  44. 44甲、乙、丙三位同学进行数字游戏．甲说一个数a的相反数就是它本身，乙说一个数b的倒数也等于它本身，丙说一个数c的绝对值等于2．求|a-b+c|．
  45. 4512 The area of a farm is represented on two maps, map A and map B. The area of this farm on Map A is sixteen times that…
  46. 46在6 \sqrt {6}、23 \dfrac {2}{3}、1.81.8、π4 \dfrac {π}{4}这44个数中，有理数有()() A. 11个 B. 22个 C. 33个 D. 44…
  47. 47已知x1,x2\mathbf{x}_{\mathbf{1}}\mathbf{,}\mathbf{x}_{\mathbf{2}}是一元二次方程4kx2−4kx+k+1=0\mathbf{4}\mathbf{k}\mathbf{x}^{\mathbf{2}}\mathbf{-4}\mathbf{kx+k+1=0}…
  48. 48“下雪不冷化学寒”，大雪过后冰雪融化非常寒冷，室内温度为0℃，室外温度为零下3℃，室内与室外的温差为多少摄氏度？
  49. 49在下列命题中：①过一点有且只有一条直线与已知直线平行；②平方根与立方根相等的数有1和0；③在同一平面内，如果a⊥b，b⊥c，则a⊥c；④直线c外一点A与直线c上各点连接而成的所有线段中，最短线段的长是5cm，则点A到直线c的距离是5cm；⑤…
  50. 50The following stem-and-leaf diagram shows the marks obtained by 20 pupils in a class test that has a total mark of 50. S…
  51. 51During a game, Lee rolled two fair six-sided die. To obtain the score, he subtracted the lower number from the higher nu…
  52. 52Solve the equation 2cosec⁡(x−π3)=−42\cosec\left(x-\dfrac{\pi}{3}\right)=-4 for 0≤x≤2π0\le x\le 2\pi. Solve the equation cot⁡(2x+10∘)=tan⁡70∘\cot(2x+10^\circ)=\tan70^\circ…
  53. 53In a class of 36 students, each student is either in a sports team or a performing arts club. Each student is also eithe…
  54. 54Mrs Boey deposited $20 000 in a bank that pays 0.8% per annum compound interest compounded half-yearly. Find the total…
  55. 55Write the following numbers in order of size, starting with the smallest. −9.87-\sqrt{9.87}, −227-\dfrac{22}{7}, -314.2%, −3.143-3.143…
  56. 56The cost of manufacturing a sofa is S$1500. It is sold to a retailer at a profit of 15% of the cost. Calculate the pric…
  57. 57某邮局检修队沿公路检修线路，规定前进为正，后退为负，某天自A点出发到收工时所走路程为（单位：千米）+10，-3，+4，-8，+13，-2，+7，+5，-5，-2． （1）求收工时，检修队距A点多远？ （2）若每千米耗油0.3千克，问从A点出…
  58. 58Solve the equation 3−2x7=13(2x−1).\displaystyle \frac{3-2x}{7} = \frac{1}{3}(2x-1). Answer x = ... Simplify 25a2−9b215a−10ab+6b2−9b\displaystyle \frac{25a^{2}-9b^{2}}{15a-10ab+6b^{2}-9b}…
  59. 59The number 12250×pq12250 \times \frac{p}{q} is a perfect cube. pp and qq are prime numbers. Find pp and qq. Answer p = ...…
  60. 60已知(−6)□(−3)=2(-6)□(-3)=2，则□□中的运算符号可以是()(\quad) A. ++ B. −- C. ×× D. ÷÷