Math topic中文

Inequality symbols

use of the symbols <<, >>, ⩽\leqslant, ⩾\geqslant

Practice questions

  1. 1Mrs Ang runs a small tuition centre for secondary school students. The tables provide information on the cost of running…
  2. 2The equation of a curve is y=x2e2xy = x^2 e^{2x}. Obtain an expression for dydx\dfrac{dy}{dx}. Find the range of values of xx…
  3. 3直角坐标系中，点P(x,y)P(x,y)，xy<0xy < 0，x<yx < y，且PP到xx轴、yy轴的距离分别为33，77，则PP点的坐标为 ___ ．
  4. 4A piece of wood which was 50 cm long, was in the shape of a uniform cylinder. A prism is cut out from the wood such that…
  5. 5如果三角形的两条边分别为4和6，那么连结该三角形三边中点所得的周长可能是下列数据中的【 】 A. 6 B. 8 C. 10 D. 12
  6. 6Solve the inequality 4x+3−2≤5\dfrac{4x+3}{-2} \le 5.
  7. 7The solution of the inequality −1<1−x2≤k+1-1 < \frac{1 - x}{2} \le k + 1, where k is a constant, is represented on the number lin…
  8. 8Solve the inequality x−5<2x5≤x2+15\displaystyle x - 5 < \frac{2x}{5} \le \frac{x}{2} + \frac{1}{5}. Answer ...
  9. 9The 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…
  10. 10The 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…
  11. 11若a−4\sqrt[] { a-4 }有意义，则aa的值可以是（ ） A. −1-1 B. 00 C. 22 D. 66
  12. 12The first four terms in a sequence of numbers are 3+k, 1+k, −1+k, −3+k, …3 + k,\ 1 + k,\ -1 + k,\ -3 + k,\ \dots where kk is a constant. Fin…
  13. 13The following stem-and-leaf diagram shows the marks obtained by 20 pupils in a class test that has a total mark of 50. S…
  14. 14Solve 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…
  15. 15Write 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…
  16. 16Solve 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}…
  17. 17Solve x/5+(2x−3)/4=−6x/5 + (2x-3)/4 = -6. Answer x = ... Simplify 2(p−3q)/(10r)+(3q−p)2/r2(p-3q)/(10r) + (3q-p)^2/r. Answer ... Solve the inequality x+1≤7x−24<5x+195x+1 \le \dfrac{7x-2}{4} < \dfrac{5x+19}{5}…
  18. 18The diagram shows a parallelogram ABCD on horizontal ground where AC is a path. AB = 15 m and BC = 8 m. The bearing of B…
  19. 19A factory prints posters for corporate events. The prices of printing posters of different sizes are listed below. The f…
  20. 2042×()>20042×(\quad)>200中，括号内最小能填()(\quad) A. 33 B. 44 C. 55
  21. 21一袋水果糖，总数不到40块，平均分给7个小朋友，还余3块，这袋糖最多有 块。
  22. 22The table shows some values for y=310x3−x+1y = \frac{3}{10}x^3 - x + 1 for −3≤x≤3-3 \le x \le 3. | x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |…
  23. 23Complete the table of values for y=2x+20x−15y = 2x + \dfrac{20}{x} - 15. | x | 1 | 2.5 | 5 | 10 | 12.5 | 15 | 20 | |---|---|---|-…
  24. 24若|a|=1，|b|=2，且a＞b，则代数式a-b的值是___．
  25. 25Gillian wants to make cylindrical soy wax candles as farewell gifts for 50 classmates and friends in school. The diagram…
  26. 26Mr Lee and his wife are going for a family trip to Thailand. The table shows the travel insurance premiums payable for i…
  27. 27若长度分别为aa，33，55的三条线段能组成一个三角形，则aa的值可以是 ()(\quad) A. 11 B. 22 C. 33 D. 88
  28. 28The exchange rate between pounds (£) and Singapore dollars ($) is £1 = $1.86. The exchange rate between Singapore doll…
  29. 29It is given that f′′(x)=e−12x+5(5x−9)2f''(x) = e^{-\tfrac{1}{2}x} + \dfrac{5}{(5x-9)^2}. Given that the x-axis is a tangent to the curve y=f(x)y = f(x)…
  30. 30In stall A, one Chicken pie costs 1.50,oneMushroompiecosts1.50, one Mushroom pie costs 1.30 and one Tuna pie costs 1.80.InstallB,oneChickenpiecosts1.80. In stall B, one Chicken pie costs …
  31. 31关于xx的一元二次方程x2−6x+m=0x^{2}-6x+m=0有两个不相等的实数根，则mm的值可能是()(\quad) A. 88 B. 99 C. 1010 D. 1111
  32. 32两个数相加，如果和小于每一个加数，则这两个数（ ） A. 同为正数 B. 同为负数 C. 一正一负 D. 无法确定
  33. 33Write the following numbers in order of size, starting with the smallest. (310)2\left(\dfrac{3}{10}\right)^2, −2190-\dfrac{21}{90}…
  34. 34Rebecca always travels by taxi to work. To get a taxi, she has two options. She can either flag down a taxi at the roads…
  35. 35一零件的长度在图纸上标为10±0.05(10±0.05(单位：毫米))，表示这种零件的长度为1010毫米，则加工时要求最大不超过多少？最小不少于多少？实际生产时，测得一零件的长为9.99.9毫米，问此零件合格吗？
  36. 36在不等边三角形中，最小的角可以是（ ） A. 80° B. 65° C. 60° D. 59°
  37. 37The diagram below shows an indoor adventure park in the shape of a trapezoidal prism with a square base ABCD. The indoor…
  38. 38Solve 3−4x=21.3 - 4x = 21. 2x<3x+1≤132x < 3x + 1 \le 13
  39. 39Sketch the graph of y=2ln⁡xy = 2\ln x. In order to solve the equation xe2x=13xx e^{2x} = \dfrac{1}{3x}, a suitable straight line ha…
  40. 40Solve the inequalities 2x+13<4(x+2)≤x+412x + 13 < 4(x + 2) \le x + 41. Answer ___ Hence list all the prime integer values of x which sa…
  41. 41Using a separate diagram for each part, represent on the number line the solution set of 3(5−x)>x+133(5 - x) > x + 13 x2−12x<14(3−2x)x^{2} - \frac{1}{2}x < \frac{1}{4}(3 - 2x)…
  42. 42贵阳市今年5月份的最高气温为27℃，最低气温为18℃，已知某一天的气温为t℃，则下面表示气温之间的不等关系正确的是（ ） A. 18＜t＜27 B. 18≤t＜27 C. 18＜t≤27 D. 18≤t≤27
  43. 43A supermarket sold all of its toilet rolls at a price of $xx per pack in January. The revenue made from selling the packs of toilet rolls in January was $5940. Write down an expression in x, for the number of packets of toilet rolls sold in January. Answer ... In February, the supermarket ordered an additional 600 packs to the number sold in January and sold them at 50 cents more per pack. Write down an expression in x, for the total amount of money received in dollars, if all the packs of toilet rolls were sold in February. Answer $ ... The supermarket received $3870 more from the sales of toilet rolls in February as compared to January. Write down an equation in x to represent this information, and show that it reduces to $$…
  44. 44已知一次函数y=x+b的图象经过第一、二、三象限，则b的值可以是（ ） A. －1 B. 0 C. 2 D. 任意实数
  45. 45Emily is considering signing up for a new credit card and has shortlisted three options: Card A, Card B and Card C. Each…
  46. 46关于xx的一元二次方程kx2−x−2=0kx ^{2} -x-2=0有实数根，则实数kk的取值范围是(    )(\:\:\:\:) A. k=−18k=- \dfrac {1}{8} B. k⩾−18k\geqslant - \dfrac {1}{8}…
  47. 47Kyle runs a tennis club. 54 of the members are adults and 31 are children. His aim is that at least 60% the members shou…
  48. 48Express x2+5x+7x^2+5x+7 in the form (x+a)2+b(x+a)^2+b. Answer ... Hence, explain why the expression will never be negative. Answer…
  49. 49Find the largest rational number p+q2p + q^2 if −1<p≤1.5-1 < p \le 1.5 and −3≤q≤2-3 \le q \le 2. Answer
  50. 50x2−4x+5=(x−a)2+bx^2 - 4x + 5 = (x - a)^2 + b Find the value of aa and of bb. Answer a = ... b = ... The curve y=x2−4x+5y = x^2 - 4x + 5 is…
  51. 51Jim, his wife and their child visited Hokkaido, Japan. The tables below give information that can be used to work out so…
  52. 52对于实数a、b，定义min{a，b}的含义为：当a＜b时，min{a，b}＝a；当a＞b时，min{a，b}＝b，例如：min{1，﹣2}＝﹣2.已知min{ 30\sqrt[] { 30 } ，a}＝a，min{ 30\sqrt[] { 30 }…
  53. 53Javier and Stella are planning their exercise routines. Javier and Stella have a body mass of 70 kg and 60 kg respective…
  54. 54Express 4 - 2x - x^2 in the form a - (x + b)^2. Answer ... Explain, without solving, why there is no solution of x when…
  55. 55对于有理数aa、bb，定义min⁡{a,b}\min \{a , b\}的含义为：当a<ba < b时，min⁡{a,b}=a\min \{a , b\}=a，例如：min⁡{1,−2}=−2.\min \{1 , -2\}=-2.已知min⁡{30,a}=a\min \{ \sqrt {30} , a\}=a…
  56. 56The cash price of a new motorcycle is $25 120. Jack paid a down payment of 20% of the price of the motorcycle and the b…
  57. 57Solve the inequality x−3≤5−x3<x+12x - 3 \le \dfrac{5 - x}{3} < \dfrac{x + 1}{2}.
  58. 58An event organiser is organising a 3-day Pet Festival for 300 exhibitors. The event organiser charges each exhibitor a r…
  59. 59The nth term of a sequence is given by Tn=6n−53nT_n = \frac{6n-5}{3n}. Use the formula to find T7T_7, giving your answer as an…
  60. 60Solve the equation 2(x−5)=3x−12(x-5)=3x-1. Answer xx = ... Solve the inequality 7−4y>3(y+2)7-4y>3(y+2). Answer ... Given that 1p−12q=13r\dfrac{1}{p}-\dfrac{1}{2q}=\dfrac{1}{3r}…