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Practice questions

  1. 1Mrs Ang runs a small tuition centre for secondary school students. The tables provide information on the cost of running…
  2. 2On 1st January 2018, Mrs Yeo invests $15000 in an account which pays at a rate of compound interest of RR% per year. O…
  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. 4Hamid 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…
  5. 5The diagram shows the positions of a harbour, H, a lighthouse, L, and two buoys P and Q. HPQ is a straight line. The bea…
  6. 6A 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…
  7. 7The diagram below shows the speed-time graph of a bus journey. The bus accelerated from rest at 1.25 m/s^2 to a speed of…
  8. 8已知α是锐角，且cosα=0.9794，下列各值中，与α最接近的是（ ） A. 73°33′ B. 73°27′ C. 11°37′ D. 11°45′
  9. 9A 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,…
  10. 10In 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…
  11. 11A circle with centre O has a tangent XY at D. ∠ODC = 70°, ∠BCD = 120° and ∠ODA = 15°. Find ∠CDY. Find ∠DAB. Find ∠OBA. T…
  12. 12The diagrams show the speed-time graph and the corresponding distance-time graph of a car. The car travelled from a poin…
  13. 13The marked price of a mobile phone is $1288. After selling the mobile phone at 15% discount, the shop owner still makes…
  14. 14The diagram below shows a gift souvenir formed by joining the plane face of a solid hemisphere of radius 3 cm and a soli…
  15. 15In 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…
  16. 16Elva invested a sum of money in an account paying compound interest at 4% per year. After 3 years, there was $89 989.12…
  17. 17Mr Johnson has a plot of field that grows dandelion plants. An average of 70 dandelion plants grow on each square metre.…
  18. 18A 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…
  19. 19The figure shows a solid frustum of height 16 cm cut from a right pyramid with square base. The horizontal top surface h…
  20. 20On every weekday, a bakery delivers chicken pies and apple pies to four cafes. On every weekend, it delivers double the…
  21. 21The 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…
  22. 22In triangle ABC, AB = 14.6 cm, BC = 7.6 cm and angle BAC = 31°. Find obtuse angle ACB. Answer ...° area of triangle ABC.…
  23. 23The 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…
  24. 24The variables x and y are connected by the equation y=2x3−21x2+54xy = 2x^3 - 21x^2 + 54x. Some corresponding values of x and y are g…
  25. 25The volume of an Olympic size swimming pool is 660 000 gallons. 1 gallon is approximately 3790 cm^3. Convert 660 000 gal…
  26. 26Mr Faizal stays in a terrace house in the east of Singapore. He is considering installing solar panel at his home. He wa…
  27. 27A cargo ship has an average fuel consumption of 0.000 892 kilometres per litre. Write this consumption in litres per kil…
  28. 28In 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…
  29. 29The masses of 20 bags, in kg, are measured. The results are shown on the stem-and-leaf diagram. Find the mean mass of th…
  30. 30A bag contains some green counters, some orange counters and some yellow counters. The probability of picking a green co…
  31. 31The diagram shows a right circular cone cut from a solid steel sphere. Point O is the centre of the sphere with radius 1…
  32. 32Find the area of a regular hexagon with each side 7 cm. Answer ... cm^2 Find the interior angle of a regular 15-sided po…
  33. 33Mrs Boey deposited $20 000 in a bank that pays 0.8% per annum compound interest compounded half-yearly. Find the total…
  34. 34Write 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…
  35. 35The 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…
  36. 36Solve 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}…
  37. 37The waiting time, t in minutes, for 40 customers at two phone service shops, Shop A and Shop B, are as follows. Calculat…
  38. 38The diagram shows a parallelogram ABCD on horizontal ground where AC is a path. AB = 15 m and BC = 8 m. The bearing of B…
  39. 39A factory prints posters for corporate events. The prices of printing posters of different sizes are listed below. The f…
  40. 40Part of the graph of a quadratic function is shown below. The graph passes through the point A (1, 15) and it cuts the x…
  41. 41In 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…
  42. 42Town 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…
  43. 43The diagram above shows a park ABCDABCD that is on horizontal ground, crossed by a straight path ACAC. Point BB is due no…
  44. 44Calculate −(−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…
  45. 45The 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…
  46. 46A, B and C are points (6, 10), (6,6) and (q, 2) respectively. The area of triangle ABC is 16 square units. Show that q =…
  47. 47The air resistance, RR newtons, is directly proportional to the square of the speed, VV m/s, of an object when it is f…
  48. 48On 6 June 2020, Elijah invested some money in a bank which pays a simple interest at a rate of 3.5% per annum. He receiv…
  49. 49John owns a cleaning company that cleans office blocks. The number of employees in his company and their salaries in 202…
  50. 50Given that 0<x<1800 < x < 180, find the possible values of xx for sin⁡x∘=0.985\sin x^{\circ} = 0.985. Give your answers correct to 1 d…
  51. 51The diagram shows two open containers, a right cylinder and an inverted frustum. The right cylinder has a base radius of…
  52. 52The diagram shows a cardboard in the shape of a major sector, centre O and radius 15 cm. The total area of the major sec…
  53. 53Gino can paint 6 fence panels in 4 hours, while Danish can paint 7 fence panels in 5 hours. Gino and Danish work togethe…
  54. 54Mr Smith plans to invest his money in unit trust with a bank. His target is to earn an interest of $10,000 after 5 year…
  55. 55A new housing estate is represented by an area of 200 cm^2 on a Map A drawn to a scale of 1 : n. Given that the actual a…
  56. 56A company sells chocolate muffins and banana muffins. These muffins are sold across three different outlets, which are O…
  57. 57Alan drove a distance of xx km and his car used 7.5 litres of fuel. Write down an expression, in terms of xx, for the…
  58. 58The table shows the currency exchange rate between Singapore dollars ($) and Thai Baht (THB) at a money changer. Before…
  59. 59The table below shows the price board displayed at a petrol station on 12 April 2023. Pump price refers to the price bef…
  60. 60The masses of 20 bags, in kg, are measured. The results are shown on the stem-and-leaf diagram. Find the mean mass of th…