Skip to content

Form 6 Inquiry and Mathematical Modelling Practice

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

Inquiry and Mathematical Modelling is an important part of the Form 6 mathematics curriculum. This topic develops defining variables, assumptions, building models and evaluating limitations. 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 Inquiry and Mathematical Modelling 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 Inquiry and Mathematical Modelling; 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. 8 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 Inquiry and Mathematical Modelling 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.

Inquiry and Mathematical Modelling 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.

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 Inquiry and Mathematical Modelling, the value of $7\times 4+7$ is 36. Is this statement true?
  5. 5 Basic
    A hall's charge is modelled by $C=50+18n$ dollars for $n$ hours. The budget is \$337. Find the greatest whole number of hours that can be booked. Choose the correct answer.
  6. 6 Basic
    A shop has fixed monthly costs of \$1200; each item costs \$12 and sells for \$24. Find the number of items needed to break even. Give the answer only.

  7. 7 Basic
    A ball thrown upwards is at height $h=25t-5t^2$ m after $t$ s. Find its greatest height in metres (as a fraction in lowest terms). Show the essential working and give the answer.

  8. 8 Basic
    A bacteria population doubles every 3 hours, starting at 50. The number after 9 hours is 300. Is this true?
  9. 9 Basic
    A hall's charge is modelled by $C=80+12n$ dollars for $n$ hours. The budget is \$249. Find the greatest whole number of hours that can be booked. Choose the correct answer.
  10. 10 Basic
    A shop has fixed monthly costs of \$900; each item costs \$8 and sells for \$20. Find the number of items needed to break even. Give the answer only.

  11. 11 Basic
    A ball thrown upwards is at height $h=20t-5t^2$ m after $t$ s. Find its greatest height in metres. Show the essential working and give the answer.

  12. 12 Basic
    A bacteria population doubles every 4 hours, starting at 50. The number after 12 hours is 300. Is this true?
  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 Inquiry and Mathematical Modelling, the value of $11\times 7+6$ is 83. Is this statement true?
  17. 17 Standard
    The feasible region is the convex quadrilateral with vertices $(0,0)$, $(6,0)$, $(4,8)$, $(0,8)$ (boundary included). Find the maximum value of $P=6x+7y$. Choose the correct answer.
  18. 18 Standard
    A hall's charge is modelled by $C=120+25n$ dollars for $n$ hours. The budget is \$667. Find the greatest whole number of hours that can be booked. Give the answer only.

  19. 19 Standard
    A shop has fixed monthly costs of \$1500; each item costs \$20 and sells for \$35. Find the number of items needed to break even. Show the essential working and give the answer.

  20. 20 Standard DSE long question
    A ball is thrown vertically upwards; its height after $t$ s is $h=50t-5t^2$ m. Answer each part; give the answer only.
    1. (a) Find the time in seconds when the ball returns to the ground.
    2. (b) Find the time in seconds to reach the highest point.
    3. (c) Find the greatest height in metres.
  21. 21 Standard
    The feasible region is the convex quadrilateral with vertices $(0,0)$, $(5,0)$, $(2,4)$, $(0,4)$ (boundary included). Find the maximum value of $P=6x+4y$. Choose the correct answer.
  22. 22 Standard
    A hall's charge is modelled by $C=80+25n$ dollars for $n$ hours. The budget is \$843. Find the greatest whole number of hours that can be booked. Give the answer only.

  23. 23 Standard
    A shop has fixed monthly costs of \$900; each item costs \$12 and sells for \$24. Find the number of items needed to break even. Show the essential working and give the answer.

  24. 24 Standard DSE long question
    A ball is thrown vertically upwards; its height after $t$ s is $h=30t-5t^2$ m. Answer each part; give the answer only.
    1. (a) Find the time in seconds when the ball returns to the ground.
    2. (b) Find the time in seconds to reach the highest point.
    3. (c) Find the greatest height in metres.
  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 Inquiry and Mathematical Modelling, the value of $15\times 10+5$ is 156. Is this statement true?
  29. 29 Advanced
    A ball thrown upwards is at height $h=40t-5t^2$ m after $t$ s. Find its greatest height in metres. Choose the correct answer.
  30. 30 Advanced
    A bacteria population doubles every 4 hours, starting at 100. Find the number after 12 hours. Give the answer only.

  31. 31 Advanced
    The feasible region is the convex quadrilateral with vertices $(0,0)$, $(8,0)$, $(2,7)$, $(0,9)$ (boundary included). The maximum value of $P=2x+4y$ is 36. Is this true?
  32. 32 Advanced DSE long question
    A bacteria count is $N(t)=A\cdot 2^{t/2}$ with $t$ in hours, and $N(0)=200$. Answer each part; give the answer only.
    1. (a) Find $A$.
    2. (b) Find $N(6)$.
    3. (c) Find the time in hours for the count to reach $3200$.
  33. 33 Advanced
    A ball thrown upwards is at height $h=15t-5t^2$ m after $t$ s. Find its greatest height in metres (as a fraction in lowest terms). Choose the correct answer.
  34. 34 Advanced
    A bacteria population doubles every 3 hours, starting at 200. Find the number after 9 hours. Give the answer only.

  35. 35 Advanced
    The feasible region is the convex quadrilateral with vertices $(0,0)$, $(8,0)$, $(6,4)$, $(0,4)$ (boundary included). The maximum value of $P=2x+6y$ is 36. Is this true?
  36. 36 Advanced DSE long question
    A bacteria count is $N(t)=A\cdot 2^{t/4}$ with $t$ in hours, and $N(0)=200$. Answer each part; give the answer only.
    1. (a) Find $A$.
    2. (b) Find $N(8)$.
    3. (c) Find the time in hours for the count to reach $1600$.
  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 Inquiry and Mathematical Modelling, the value of $19\times 13+4$ is 251. Is this statement true?
  41. 41 Challenging
    A hall's charge is modelled by $C=50+30n$ dollars for $n$ hours. The budget is \$821. Find the greatest whole number of hours that can be booked. Choose the correct answer.
  42. 42 Challenging
    A ball thrown upwards is at height $h=30t-5t^2$ m after $t$ s. Find its greatest height in metres. Show the essential working and give the answer.

  43. 43 Challenging
    A bacteria population doubles every 2 hours, starting at 50. The number after 6 hours is 300. Is this true?
  44. 44 Challenging DSE long question
    A ball is thrown vertically upwards; its height after $t$ s is $h=20t-5t^2$ m. Answer each part; give the answer only.
    1. (a) Find the time in seconds when the ball returns to the ground.
    2. (b) Find the time in seconds to reach the highest point.
    3. (c) Find the greatest height in metres.
  45. 45 Challenging
    A hall's charge is modelled by $C=120+12n$ dollars for $n$ hours. The budget is \$383. Find the greatest whole number of hours that can be booked. Choose the correct answer.
  46. 46 Challenging
    A shop has fixed monthly costs of \$900; each item costs \$5 and sells for \$17. Find the number of items needed to break even. Show the essential working and give the answer.

  47. 47 Challenging
    A ball thrown upwards is at height $h=25t-5t^2$ m after $t$ s. Its greatest height in metres is 5/2. Is this true?
  48. 48 Challenging DSE long question
    A ball is thrown vertically upwards; its height after $t$ s is $h=40t-5t^2$ m. Answer each part; give the answer only.
    1. (a) Find the time in seconds when the ball returns to the ground.
    2. (b) Find the time in seconds to reach the highest point.
    3. (c) Find the greatest height in metres.
  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 Inquiry and Mathematical Modelling, the value of $23\times 16+3$ is 372. Is this statement true?
  53. 53 Elite
    A bacteria population doubles every 5 hours, starting at 100. Find the number after 15 hours. Give the answer only.

  54. 54 Elite
    The feasible region is the convex quadrilateral with vertices $(0,0)$, $(9,0)$, $(6,4)$, $(0,4)$ (boundary included). Find the maximum value of $P=3x+6y$. Show the essential working and give the answer.

  55. 55 Elite
    A hall's charge is modelled by $C=300+15n$ dollars for $n$ hours. The budget is \$835. The greatest whole number of hours that can be booked is 35. Is this true?
  56. 56 Elite DSE long question
    A bacteria count is $N(t)=A\cdot 2^{t/2}$ with $t$ in hours, and $N(0)=500$. Answer each part; give the answer only.
    1. (a) Find $A$.
    2. (b) Find $N(8)$.
    3. (c) Find the time in hours for the count to reach $16000$.
  57. 57 Elite
    A bacteria population doubles every 2 hours, starting at 50. Find the number after 6 hours. Give the answer only.

  58. 58 Elite
    The feasible region is the convex quadrilateral with vertices $(0,0)$, $(4,0)$, $(2,7)$, $(0,7)$ (boundary included). Find the maximum value of $P=3x+8y$. Show the essential working and give the answer.

  59. 59 Elite
    A hall's charge is modelled by $C=300+12n$ dollars for $n$ hours. The budget is \$578. The greatest whole number of hours that can be booked is 23. Is this true?
  60. 60 Elite DSE long question
    A bacteria count is $N(t)=A\cdot 2^{t/3}$ with $t$ in hours, and $N(0)=400$. Answer each part; give the answer only.
    1. (a) Find $A$.
    2. (b) Find $N(6)$.
    3. (c) Find the time in hours for the count to reach $3200$.

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

Common mistakes

Common mistakes in Inquiry and Mathematical Modelling

This topic needs particular care with defining variables, assumptions, building models and evaluating limitations. 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.

More Form 6 topics

Form 6 mixed revision → My mistakes →

Keep missing the same type?

Repeating the same mistake usually means an earlier concept never landed. We find that step in the trial lesson.

Book a Trial WhatsApp us
WhatsApp