Math topic中文

Approximation estimation

approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation)

Practice questions

  1. 1On 1st January 2018, Mrs Yeo invests $15000 in an account which pays at a rate of compound interest of RR% per year. O…
  2. 2The curve CC has equation y=x2+x+3x−2y = \frac{x^2 + x + 3}{x - 2}. Without using a calculator, find the set of values that yy…
  3. 3A cuboid has a volume of 250 cm^3, correct to the nearest cubic centimetre. The height of the cuboid is 8.4 cm, correct…
  4. 4The diagram (not drawn to scale) shows the speed-time graph of a vehicle. The vehicle starts from rest and accelerates u…
  5. 5Hamid borrowed a sum of money for 3 years at an interest rate of 3.5% per annum simple interest to pay for his car. If t…
  6. 6The diagram shows the positions of a harbour, H, a lighthouse, L, and two buoys P and Q. HPQ is a straight line. The bea…
  7. 7近似数2.302.30万精确到___位，用科学记数法表示：___.
  8. 8一个自然数的近似数是4亿，这个数最大是 ，最小是 ．
  9. 9A 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…
  10. 10A map has a scale of 1 : 150 000. The length of a road on the map is 6.4 cm. Calculate the actual length, in kilometres,…
  11. 11In the diagram, POR is a quadrant of a circle with radius 6 cm. OR and PQ are parallel. QR is an arc of a circle with ce…
  12. 1223个亿、506个万、9个十组成的数是 ，读作 ，四舍五入到亿位约是 ．
  13. 13The picture shows a model terracotta warrior. The model has height of 15 cm and weighs 20 grammes. A similar terracotta…
  14. 14A circle with centre O has a tangent XY at D. ∠ODC = 70°, ∠BCD = 120° and ∠ODA = 15°. Find ∠CDY. Find ∠DAB. Find ∠OBA. T…
  15. 15一个数四舍五入后是9.0，那么这个数最大是___，最小是___．
  16. 16The marked price of a mobile phone is $1288. After selling the mobile phone at 15% discount, the shop owner still makes…
  17. 17In the diagram, BA and BC are tangents to the circle with centre O. BO meets the circle at D, OA = 10 cm and BC = 28 cm.…
  18. 18The diagram below shows a gift souvenir formed by joining the plane face of a solid hemisphere of radius 3 cm and a soli…
  19. 19Calculate the total surface area of a solid hemisphere with radius 6 cm. Answer ... cm^2
  20. 20In the diagram, PQRS is a vertical rectangular wall of height 2.5 m and length 7.5 m. T is a point on level ground from…
  21. 219.9554保留一位小数是 ，保留三位小数是 ．
  22. 22Mr Johnson has a plot of field that grows dandelion plants. An average of 70 dandelion plants grow on each square metre.…
  23. 23A 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…
  24. 24The figure shows a solid frustum of height 16 cm cut from a right pyramid with square base. The horizontal top surface h…
  25. 25Mr Robert stay in a semi-detached house and is concerned about the rising electricity costs. After reading about solar p…
  26. 26下面的循环小数保留两位小数不正确的是（ ） A. 0.88˙4˙0.8 \dot 8 \dot 4≈0.88 B. 0.6˙0˙0. \dot 6 \dot 0≈0.61 C. 7.9˙7. \dot 9≈8.00 D. 0.8˙4˙0. \dot 8 \dot 4…
  27. 27The 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…
  28. 28估算196×7196×7时，可以把196196看成是___，积大约是___.
  29. 29In triangle ABC, AB = 14.6 cm, BC = 7.6 cm and angle BAC = 31°. Find obtuse angle ACB. Answer ...° area of triangle ABC.…
  30. 30The diagram shows four points P, Q, R and S which lie on level ground in a garden. P is due south of Q. The bearing of S…
  31. 31果园选购1919棵树苗，每棵树苗5050元，大约要付___元钱。
  32. 32An industrial mixer is made up of an open cylinder connected to a cone. The height of the cylinder and the cone is 1.2 m…
  33. 33估算49×72所得的积是 ，准确的积是 ．
  34. 34近似数54.24精确到___，近似数0.027有___个有效数字，5.748≈___（保留两个有效数字）
  35. 35城市公园了有一个直径20米的大喷泉，沿着喷泉的周边每隔3米安装一个喷水管，共要安装多少个喷水管？（得数保留整数）
  36. 36The following stem-and-leaf diagram shows the marks obtained by 20 pupils in a class test that has a total mark of 50. S…
  37. 37A cargo ship has an average fuel consumption of 0.000 892 kilometres per litre. Write this consumption in litres per kil…
  38. 38The force, F units, between two objects is inversely proportional to the square of the distance, d units, between them.…
  39. 39In the diagram, ABCDEFGH is a cuboid with dimensions 8 cm by 6 cm by 15 cm. V is the centre of the rectangular base. Sho…
  40. 40The diagram shows a right circular cone cut from a solid steel sphere. Point O is the centre of the sphere with radius 1…
  41. 41The figure above shows a solid. The cross-section of the solid is a sector of a circle of radius 5 cm and angle 30°. The…
  42. 42Mrs Boey deposited $20 000 in a bank that pays 0.8% per annum compound interest compounded half-yearly. Find the total…
  43. 43The 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…
  44. 44估算572÷8时，把572看作 ， 商大约是 ．
  45. 45Solve 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}…
  46. 46The waiting time, t in minutes, for 40 customers at two phone service shops, Shop A and Shop B, are as follows. Calculat…
  47. 47The diagram shows a parallelogram ABCD on horizontal ground where AC is a path. AB = 15 m and BC = 8 m. The bearing of B…
  48. 48Complete the table of values for y=x−4x2y = x - \frac{4}{x^2}. Values are given to one decimal place where appropriate. Compl…
  49. 49一个两位小数取近似值是 0.6 ，这个小数在取近似值前最大是 （ ___ ） ，最小是 （ ___ ） 。
  50. 50Electricity tariffs are regulated by the Energy Market Authority (EMA) of Singapore and revised quarterly to reflect the…
  51. 51In the diagram, A(1, 2), B(8, 5), C(13, 7) and D(13, 2) are four points. Show that AB+BC=13.0AB + BC = 13.0, correct to 3 signif…
  52. 52Town P and Town Q are 40 km apart. A car is travelling from Town P to Town Q at an average speed of x km/h. During its r…
  53. 53The diagram above shows a park ABCDABCD that is on horizontal ground, crossed by a straight path ACAC. Point BB is due no…
  54. 549.99649.9964保留一位小数是___，精确到百分位是___.
  55. 55Calculate −(−11.8)−(−11)2−7×16×(−40)2×16\dfrac{-(-11.8)-\sqrt{(-11)^2-7\times16\times(-40)}}{2\times16}. Answer ... There are 800 people in an audit…
  56. 56The temperatures of eighteen girls in a class on a particular day are shown in the stem-and-leaf diagram. (Stem-and-leaf…
  57. 57成人的一般的步行速度大约是每分钟60米～70米，张家港港区到市区大约24千米，请你估计一下，一个成人从港区步行到市区大约需要（ ）小时．（中途不休息） A. 40 B. 4 C. 0.4 D. 6
  58. 58The diagram shows the positions of 3 points A, B, and C, at sea level. AB = 4.83 km and BC = 7.24 km. The bearing of B f…
  59. 59由四舍五入得到的地球半径约为6.4×103km6.4×10^{3}km；精确到()() A. 1000km1000km B. 100km100km C. 0.1km0.1km D. 0.01km0.01km
  60. 60Figure I shows a piece of wood is in the form of a right circular cone with a base diameter of 18 cm. The curved surface…