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Form 6 Paper 2 Multiple-choice Questions Practice

Form 6 · 60 practice questions with instant marking and worked solutions.

Paper 2 Multiple-choice Questions is an important part of the Form 6 mathematics curriculum. This topic develops recognising topics, connecting multi-step methods, clear working and checking answers. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.

A reliable approach to Paper 2 Multiple-choice Questions has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.

The 60 original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Paper 2 Multiple-choice Questions; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample. 4 of them are DSE Paper 1 style structured questions answered in parts (a), (b), (c), where later parts build on earlier ones.

Effective revision is more than recording a score. After completing the Paper 2 Multiple-choice Questions set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.

Paper 2 Multiple-choice Questions should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.

This batch adds 20 questions, bringing the topic to 60. The new questions cover controlled variations of different concepts, with paired bilingual conditions, hints, worked solutions and reproducible checks.

All 20 new questions in this batch are multiple-choice questions; existing formats are retained.

Start practising

  1. 1 Basic
    A situation has 5 groups of 8, plus a fixed 4. Form a model and find the total. Choose the correct answer.
  2. 2 Basic
    A situation has 4 groups of 9, plus a fixed 5. Form a model and find the total. Give the numerical value only.

  3. 3 Basic
    A situation has 5 groups of 10, plus a fixed 6. Form a model and find the total. Show the essential working and give the numerical value.

  4. 4 Basic
    In Paper 2 Multiple-choice Questions, the value of $7\times 4+7$ is 36. Is this statement true?
  5. 5 Basic
    Consider the quadratic equation $x^{2}-5x-8=0$. Find the value of the discriminant $\Delta$. Choose the correct answer.
  6. 6 Basic
    Without using a calculator, find the value of $\log_{32} 8$ (as a fraction in lowest terms). Give the answer only.

  7. 7 Basic
    An infinite geometric series has first term $15$ and common ratio $\frac{2}{3}$. Find the sum to infinity. Show the essential working and give the answer.

  8. 8 Basic
    From 8 different students, 3 are chosen to fill 3 different posts. The number of ways is 56. Is this true?
  9. 9 Basic
    Consider the quadratic equation $x^{2}+6x-12=0$. Find the value of the discriminant $\Delta$. Choose the correct answer.
  10. 10 Basic
    Without using a calculator, find the value of $\log_{4} 32$ (as a fraction in lowest terms). Choose the correct answer.
  11. 11 Basic
    An infinite geometric series has first term $3$ and common ratio $-\frac{1}{3}$. Find the sum to infinity (as a fraction in lowest terms). Choose the correct answer.
  12. 12 Basic
    From 9 different students, 4 are chosen to fill 4 different posts. Find the number of ways. Choose the correct answer.
  13. 13 Standard
    A situation has 8 groups of 12, plus a fixed 3. Form a model and find the total. Choose the correct answer.
  14. 14 Standard
    A situation has 7 groups of 13, plus a fixed 4. Form a model and find the total. Give the numerical value only.

  15. 15 Standard
    A situation has 8 groups of 14, plus a fixed 5. Form a model and find the total. Show the essential working and give the numerical value.

  16. 16 Standard
    In Paper 2 Multiple-choice Questions, the value of $11\times 7+6$ is 83. Is this statement true?
  17. 17 Standard
    Consider the data 11, 12, 22, 33, 34, 36, 41, 55. Find the interquartile range (as a fraction in lowest terms). Choose the correct answer.
  18. 18 Standard
    Line $L$ is perpendicular to $-5x-5y=0$. Find the gradient of $L$. Give the answer only.

  19. 19 Standard
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=82^\circ$. Find $\angle ADC$ in degrees. Show the essential working and give the answer.

  20. 20 Standard DSE long question
    Let $\log_2 M=5$ and $\log_2 N=3$. Answer each part; give the answer only.
    1. (a) Find $\log_2(MN)$.
    2. (b) Find $\log_2\frac{M}{N}$.
    3. (c) Find $\log_2(M^2\sqrt{N^2})$.
    4. (d) Find $M$.
  21. 21 Standard
    Consider the data 11, 13, 15, 18, 24, 28, 34, 47. Find the interquartile range. Choose the correct answer.
  22. 22 Standard
    Line $L$ is perpendicular to $-x+4y+4=0$. Find the gradient of $L$. Choose the correct answer.
  23. 23 Standard
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=130^\circ$. Find $\angle ADC$ in degrees. Choose the correct answer.
  24. 24 Standard
    Solve $x^4-29x^2+100=0$. Find the largest real root. Choose the correct answer.
  25. 25 Advanced
    A situation has 11 groups of 16, plus a fixed 7. Form a model and find the total. Choose the correct answer.
  26. 26 Advanced
    A situation has 10 groups of 17, plus a fixed 3. Form a model and find the total. Give the numerical value only.

  27. 27 Advanced
    A situation has 11 groups of 18, plus a fixed 4. Form a model and find the total. Show the essential working and give the numerical value.

  28. 28 Advanced
    In Paper 2 Multiple-choice Questions, the value of $15\times 10+5$ is 156. Is this statement true?
  29. 29 Advanced
    An item's price rises by 40% and then falls by 25%. Find the overall percentage change (as a percentage; a decrease is negative). Choose the correct answer.
  30. 30 Advanced
    Solve $x^4-20x^2+64=0$. Find the largest real root. Give the answer only.

  31. 31 Advanced
    Consider the quadratic equation $x^{2}+5x-9=0$. The value of the discriminant $\Delta$ is 61. Is this true?
  32. 32 Advanced DSE long question
    A geometric sequence has first term $81$ and common ratio $-\frac{1}{2}$. Answer each part; give the answer only.
    1. (a) Find the 4th term (as a fraction in lowest terms).
    2. (b) Find the sum of the first 4 terms (as a fraction in lowest terms).
    3. (c) Find the sum to infinity.
  33. 33 Advanced
    Solve $x^4-10x^2+9=0$. Find the largest real root. Choose the correct answer.
  34. 34 Advanced
    Consider the quadratic equation $x^{2}+2=0$. Find the value of the discriminant $\Delta$. Choose the correct answer.
  35. 35 Advanced
    Without using a calculator, find the value of $\log_{4} 8$ (as a fraction in lowest terms). Choose the correct answer.
  36. 36 Advanced
    An infinite geometric series has first term $9$ and common ratio $\frac{3}{4}$. Find the sum to infinity. Choose the correct answer.
  37. 37 Challenging
    A situation has 14 groups of 20, plus a fixed 6. Form a model and find the total. Choose the correct answer.
  38. 38 Challenging
    A situation has 13 groups of 21, plus a fixed 7. Form a model and find the total. Give the numerical value only.

  39. 39 Challenging
    A situation has 14 groups of 22, plus a fixed 3. Form a model and find the total. Show the essential working and give the numerical value.

  40. 40 Challenging
    In Paper 2 Multiple-choice Questions, the value of $19\times 13+4$ is 251. Is this statement true?
  41. 41 Challenging
    Without using a calculator, find the value of $\log_{16} 32$ (as a fraction in lowest terms). Choose the correct answer.
  42. 42 Challenging
    An infinite geometric series has first term $3$ and common ratio $\frac{3}{4}$. Find the sum to infinity. Show the essential working and give the answer.

  43. 43 Challenging
    From 9 different students, 4 are chosen to fill 4 different posts. The number of ways is 126. Is this true?
  44. 44 Challenging DSE long question
    Consider the data 13, 17, 18, 34, 52, 59, 64, 65. Answer each part; give the answer only.
    1. (a) Find the median.
    2. (b) Find the range.
    3. (c) Find the interquartile range.
  45. 45 Challenging
    From 6 different students, 2 are chosen to fill 2 different posts. Find the number of ways. Choose the correct answer.
  46. 46 Challenging
    Consider the data 11, 19, 20, 24, 29, 42, 51, 53. Find the interquartile range. Choose the correct answer.
  47. 47 Challenging
    Line $L$ is perpendicular to $-x-3y-10=0$. Find the gradient of $L$. Choose the correct answer.
  48. 48 Challenging
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=58^\circ$. Find $\angle ADC$ in degrees. Choose the correct answer.
  49. 49 Elite
    A situation has 17 groups of 24, plus a fixed 5. Form a model and find the total. Choose the correct answer.
  50. 50 Elite
    A situation has 16 groups of 25, plus a fixed 6. Form a model and find the total. Give the numerical value only.

  51. 51 Elite
    A situation has 17 groups of 26, plus a fixed 7. Form a model and find the total. Show the essential working and give the numerical value.

  52. 52 Elite
    In Paper 2 Multiple-choice Questions, the value of $23\times 16+3$ is 372. Is this statement true?
  53. 53 Elite
    Consider the data 21, 23, 30, 31, 35, 39, 40, 51. Find the interquartile range. Give the answer only.

  54. 54 Elite
    Line $L$ is perpendicular to $-2x+4y-8=0$. Find the gradient of $L$. Show the essential working and give the answer.

  55. 55 Elite
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=115^\circ$. $\angle ADC$ in degrees is 65. Is this true?
  56. 56 Elite DSE long question
    The feasible region is the convex quadrilateral with vertices $(0,0)$, $(9,0)$, $(4,5)$ and $(0,5)$. $P=8x+6y$. Answer each part; give the answer only.
    1. (a) Find $P$ at $(9,0)$.
    2. (b) Find $P$ at $(4,5)$.
    3. (c) Find the maximum value of $P$.
  57. 57 Elite
    Solve $x^4-17x^2+16=0$. Find the largest real root. Choose the correct answer.
  58. 58 Elite
    Solve $x^4-25x^2+144=0$. Find the largest real root. Choose the correct answer.
  59. 59 Elite
    Consider the quadratic equation $3x^{2}-4x-7=0$. Find the value of the discriminant $\Delta$. Choose the correct answer.
  60. 60 Elite
    Without using a calculator, find the value of $\log_{25} 125$ (as a fraction in lowest terms). Choose the correct answer.

The report lists what you got wrong and why. Only you can see it.

Common mistakes

Common mistakes in Paper 2 Multiple-choice Questions

This topic needs particular care with recognising topics, connecting multi-step methods, clear working and checking answers. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.

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