Skip to content

Form 6 Paper 1 Structured Questions Practice

Form 6 · 40 practice questions with instant marking and worked solutions.

Paper 1 Structured 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 1 Structured 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 forty 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 1 Structured 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. Four 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 1 Structured 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 1 Structured 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.

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 1 Structured Questions, the value of $7\times 4+7$ is 36. Is this statement true?
  5. 5 Basic
    Solve $x^{2}+5x+4=0$. Find the larger root. Choose the correct answer.
  6. 6 Basic
    Consider the quadratic function $y=x^{2}+10x+32$. Find the minimum value of $y$. Give the answer only.

  7. 7 Basic
    An arithmetic sequence has first term $2$ and common difference $-3$. Find the sum of the first 14 terms. Show the essential working and give the answer.

  8. 8 Basic
    A bag has 7 red and 4 blue balls. Two are drawn at random without replacement. The probability that they are of different colours is 49/121. Is this true?
  9. 9 Standard
    A situation has 8 groups of 12, plus a fixed 3. Form a model and find the total. Choose the correct answer.
  10. 10 Standard
    A situation has 7 groups of 13, plus a fixed 4. Form a model and find the total. Give the numerical value only.

  11. 11 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.

  12. 12 Standard
    In Paper 1 Structured Questions, the value of $11\times 7+6$ is 83. Is this statement true?
  13. 13 Standard
    A circle has radius 26 cm and chord $AB$ is 10 cm from the centre $O$. Find the length of $AB$ in cm. Choose the correct answer.
  14. 14 Standard
    Circle $C$ has equation $x^2+y^2+12x+12y+36=0$. Find the radius of $C$. Give the answer only.

  15. 15 Standard
    \$5000 is deposited at 4% p.a. compounded yearly. Find the amount after 2 years in dollars. Show the essential working and give the answer.

  16. 16 Standard DSE long question
    It is given that $f(x)=x^2+bx+c$, where the roots of $f(x)=0$ are $0$ and $7$. Answer each part; give the answer only.
    1. (a) Find $b$.
    2. (b) Find $c$.
    3. (c) Find $f(-1)$.
    4. (d) Find the minimum value of $f(x)$ (as a fraction in lowest terms).
  17. 17 Advanced
    A situation has 11 groups of 16, plus a fixed 7. Form a model and find the total. Choose the correct answer.
  18. 18 Advanced
    A situation has 10 groups of 17, plus a fixed 3. Form a model and find the total. Give the numerical value only.

  19. 19 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.

  20. 20 Advanced
    In Paper 1 Structured Questions, the value of $15\times 10+5$ is 156. Is this statement true?
  21. 21 Advanced
    A moving point $P$ is equidistant from $A(-5,-1)$ and $B(-3,3)$. Find the $y$-intercept of the locus of $P$ (a straight line). Choose the correct answer.
  22. 22 Advanced
    Solve $x^{2}+2x-15=0$. Find the larger root. Give the answer only.

  23. 23 Advanced
    Consider the quadratic function $y=3x^{2}-12x+8$. The minimum value of $y$ is -4. Is this true?
  24. 24 Advanced DSE long question
    An arithmetic sequence has first term $9$ and fifth term $5$. Answer each part; give the answer only.
    1. (a) Find the common difference.
    2. (b) Find the 16th term.
    3. (c) Find the sum of the first 16 terms.
  25. 25 Challenging
    A situation has 14 groups of 20, plus a fixed 6. Form a model and find the total. Choose the correct answer.
  26. 26 Challenging
    A situation has 13 groups of 21, plus a fixed 7. Form a model and find the total. Give the numerical value only.

  27. 27 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.

  28. 28 Challenging
    In Paper 1 Structured Questions, the value of $19\times 13+4$ is 251. Is this statement true?
  29. 29 Challenging
    An arithmetic sequence has first term $9$ and common difference $4$. Find the sum of the first 10 terms. Choose the correct answer.
  30. 30 Challenging
    A bag has 3 red and 5 blue balls. Two are drawn at random without replacement. Find the probability that both are red (as a fraction in lowest terms). Show the essential working and give the answer.

  31. 31 Challenging
    A circle has radius 15 cm and chord $AB$ is 9 cm from the centre $O$. The length of $AB$ in cm is 12. Is this true?
  32. 32 Challenging DSE long question
    A bag has 3 red and 4 blue balls. Two are drawn without replacement. Answer each part; give the answer only.
    1. (a) Find the probability that the first is red (as a fraction in lowest terms).
    2. (b) Find the probability that both are red (as a fraction in lowest terms).
    3. (c) Find the probability of at least one blue ball (as a fraction in lowest terms).
  33. 33 Elite
    A situation has 17 groups of 24, plus a fixed 5. Form a model and find the total. Choose the correct answer.
  34. 34 Elite
    A situation has 16 groups of 25, plus a fixed 6. Form a model and find the total. Give the numerical value only.

  35. 35 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.

  36. 36 Elite
    In Paper 1 Structured Questions, the value of $23\times 16+3$ is 372. Is this statement true?
  37. 37 Elite
    Circle $C$ has equation $x^2+y^2+10x+6y+30=0$. Find the radius of $C$. Give the answer only.

  38. 38 Elite
    \$5000 is deposited at 20% p.a. compounded yearly. Find the amount after 2 years in dollars. Show the essential working and give the answer.

  39. 39 Elite
    A moving point $P$ is equidistant from $A(3,3)$ and $B(5,9)$. The $y$-intercept of the locus of $P$ (a straight line) is 22/3. Is this true?
  40. 40 Elite DSE long question
    Circle $C$ has equation $x^2+y^2+8x-273=0$. Answer each part; give the answer only.
    1. (a) Find the $x$-coordinate of the centre.
    2. (b) Find the $y$-coordinate of the centre.
    3. (c) Find the radius.
    4. (d) Find the distance from the point $P(4,15)$ to the centre of $C$.

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

Common mistakes

Common mistakes in Paper 1 Structured 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.

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