Skip to content

Form 6 Further Applications Practice

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

Further Applications 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 Further Applications 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 Further Applications; 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 Further Applications 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.

Further Applications 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 Further Applications, the value of $7\times 4+7$ is 36. Is this statement true?
  5. 5 Basic
    \$8000 is deposited at 10% p.a. compounded yearly. Find the amount after 3 years in dollars. Choose the correct answer.
  6. 6 Basic
    A machine costs \$40000 and depreciates by 25% each year. Find its value after 2 years in dollars. Give the answer only.

  7. 7 Basic
    An item's price rises by 25% and then falls by 20%. Find the overall percentage change (as a percentage; a decrease is negative). Show the essential working and give the answer.

  8. 8 Basic
    An item costs \$400 and sells for \$520. The percentage profit is -30. Is this true?
  9. 9 Basic
    \$20000 is deposited at 4% p.a. compounded yearly. Find the amount after 2 years in dollars. Choose the correct answer.
  10. 10 Basic
    A machine costs \$40000 and depreciates by 10% each year. Find its value after 2 years in dollars. Give the answer only.

  11. 11 Basic
    An item's price rises by 50% and then falls by 20%. Find the overall percentage change (as a percentage; a decrease is negative). Show the essential working and give the answer.

  12. 12 Basic
    An item costs \$150 and sells for \$210. The percentage profit is -40. 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 Further Applications, the value of $11\times 7+6$ is 83. Is this statement true?
  17. 17 Standard
    $y$ varies directly as $x^{2}$. If $x$ increases by 50%, find the percentage increase in $y$ (as a percentage; give the number only). Choose the correct answer.
  18. 18 Standard
    \$8000 is deposited at 5% p.a. compounded yearly. Find the amount after 3 years in dollars. Give the answer only.

  19. 19 Standard
    A machine costs \$250000 and depreciates by 10% each year. Find its value after 3 years in dollars. Show the essential working and give the answer.

  20. 20 Standard DSE long question
    \$50000 is deposited at 20% p.a. compounded yearly. Answer each part; give the answer only.
    1. (a) Find the amount after 2 years in dollars.
    2. (b) Find the amount after 3 years in dollars.
    3. (c) Find the interest earned in the 3rd year in dollars.
  21. 21 Standard
    \$10000 is deposited at 2% p.a. compounded yearly. Find the amount after 3 years in dollars. Choose the correct answer.
  22. 22 Standard
    \$8000 is deposited at 5% p.a. compounded yearly. Find the amount after 2 years in dollars. Give the answer only.

  23. 23 Standard
    A machine costs \$80000 and depreciates by 25% each year. Find its value after 2 years in dollars. Show the essential working and give the answer.

  24. 24 Standard DSE long question
    \$50000 is deposited at 5% p.a. compounded yearly. Answer each part; give the answer only.
    1. (a) Find the amount after 2 years in dollars.
    2. (b) Find the amount after 3 years in dollars.
    3. (c) Find the interest earned in the 3rd year in dollars.
  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 Further Applications, 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
    \$5000 is deposited at 20% p.a. compounded yearly. Find the amount after 2 years in dollars. Give the answer only.

  31. 31 Advanced
    $y$ varies directly as $x^{2}$. If $x$ increases by 10%, the percentage increase in $y$ is 21. Is this true?
  32. 32 Advanced DSE long question
    $z$ varies directly as $x$ and inversely as $y^2$. When $x=5$ and $y=3$, $z=\frac{10}{9}$. Answer each part; give the answer only.
    1. (a) Find the constant $k$ (where $z=\frac{kx}{y^2}$).
    2. (b) Find $z$ when $x=6$ and $y=4$ (as a fraction in lowest terms).
    3. (c) If $x$ increases by 25% and $y$ decreases by 20%, find the percentage change in $z$ (as a percentage; a decrease is negative).
  33. 33 Advanced
    An item costs \$120 and sells for \$156. Find the percentage profit (as a percentage; a loss is negative). Choose the correct answer.
  34. 34 Advanced
    An item costs \$150 and sells for \$187.5. Find the percentage profit (as a percentage; a loss is negative). Give the answer only.

  35. 35 Advanced
    $y$ varies directly as $x^{2}$. If $x$ increases by 30%, the percentage increase in $y$ is 69. Is this true?
  36. 36 Advanced DSE long question
    $z$ varies directly as $x$ and inversely as $y^2$. When $x=6$ and $y=2$, $z=\frac{9}{2}$. Answer each part; give the answer only.
    1. (a) Find the constant $k$ (where $z=\frac{kx}{y^2}$).
    2. (b) Find $z$ when $x=6$ and $y=4$ (as a fraction in lowest terms).
    3. (c) If $x$ decreases by 10% and $y$ decreases by 50%, find the percentage change in $z$ (as a percentage; a decrease is negative).
  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 Further Applications, the value of $19\times 13+4$ is 251. Is this statement true?
  41. 41 Challenging
    \$2000 is deposited at 10% p.a. compounded yearly. Find the amount after 3 years in dollars. Choose the correct answer.
  42. 42 Challenging
    A machine costs \$80000 and depreciates by 10% each year. Find its value after 2 years in dollars. Show the essential working and give the answer.

  43. 43 Challenging
    An item's price rises by 10% and then falls by 10%. The overall percentage change is 0. Is this true?
  44. 44 Challenging DSE long question
    \$10000 is deposited at 10% p.a. compounded yearly. Answer each part; give the answer only.
    1. (a) Find the amount after 2 years in dollars.
    2. (b) Find the amount after 3 years in dollars.
    3. (c) Find the interest earned in the 3rd year in dollars.
  45. 45 Challenging
    \$5000 is deposited at 10% p.a. compounded yearly. Find the amount after 3 years in dollars. Choose the correct answer.
  46. 46 Challenging
    A machine costs \$40000 and depreciates by 10% each year. Find its value after 3 years in dollars. Show the essential working and give the answer.

  47. 47 Challenging
    An item's price rises by 40% and then falls by 25%. The overall percentage change is 15. Is this true?
  48. 48 Challenging DSE long question
    \$10000 is deposited at 20% p.a. compounded yearly. Answer each part; give the answer only.
    1. (a) Find the amount after 2 years in dollars.
    2. (b) Find the amount after 3 years in dollars.
    3. (c) Find the interest earned in the 3rd year in dollars.
  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 Further Applications, the value of $23\times 16+3$ is 372. Is this statement true?
  53. 53 Elite
    An item costs \$200 and sells for \$160. Find the percentage profit (as a percentage; a loss is negative). Give the answer only.

  54. 54 Elite
    $y$ varies directly as $x^{2}$. If $x$ increases by 20%, find the percentage increase in $y$ (as a percentage; give the number only). Show the essential working and give the answer.

  55. 55 Elite
    \$10000 is deposited at 2% p.a. compounded yearly. The amount after 3 years in dollars is 10612.08. Is this true?
  56. 56 Elite DSE long question
    $z$ varies directly as $x$ and inversely as $y^2$. When $x=5$ and $y=3$, $z=\frac{10}{9}$. Answer each part; give the answer only.
    1. (a) Find the constant $k$ (where $z=\frac{kx}{y^2}$).
    2. (b) Find $z$ when $x=9$ and $y=1$.
    3. (c) If $x$ increases by 25% and $y$ decreases by 20%, find the percentage change in $z$ (as a percentage; a decrease is negative).
  57. 57 Elite
    An item costs \$120 and sells for \$144. Find the percentage profit (as a percentage; a loss is negative). Give the answer only.

  58. 58 Elite
    $y$ varies directly as $x^{3}$. If $x$ increases by 20%, find the percentage increase in $y$ (as a percentage; give the number only). Show the essential working and give the answer.

  59. 59 Elite
    \$8000 is deposited at 8% p.a. compounded yearly. The amount after 2 years in dollars is 9331.2. Is this true?
  60. 60 Elite DSE long question
    $z$ varies directly as $x$ and inversely as $y^2$. When $x=2$ and $y=3$, $z=\frac{8}{9}$. Answer each part; give the answer only.
    1. (a) Find the constant $k$ (where $z=\frac{kx}{y^2}$).
    2. (b) Find $z$ when $x=6$ and $y=1$.
    3. (c) If $x$ increases by 25% and $y$ decreases by 20%, find the percentage change in $z$ (as a percentage; a decrease is negative).

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

Common mistakes

Common mistakes in Further Applications

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.

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