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Form 6 Paper 1 Structured Questions Practice

Form 6 · 60 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 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 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. 24 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.

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 structured questions; existing formats are retained.

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  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 Basic DSE long question
    It is given that $f(x)=x^2+bx+c$, where the roots of $f(x)=0$ are $-1$ and $6$. Answer each part; give the answer only.
    1. (a) Find $b$.
    2. (b) Find $c$.
    3. (c) Find $f(4)$.
    4. (d) Find the minimum value of $f(x)$ (as a fraction in lowest terms).
  10. 10 Basic DSE long question
    An arithmetic sequence has first term $3$ and fifth term $7$. Answer each part; give the answer only.
    1. (a) Find the common difference.
    2. (b) Find the 10th term.
    3. (c) Find the sum of the first 10 terms.
  11. 11 Basic DSE long question
    A bag has 5 red and 3 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).
  12. 12 Basic DSE long question
    Circle $C$ has equation $x^2+y^2-2x-10y-143=0$. 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 $P(6,17)$ to the centre of $C$.
  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 1 Structured Questions, the value of $11\times 7+6$ is 83. Is this statement true?
  17. 17 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.
  18. 18 Standard
    Circle $C$ has equation $x^2+y^2+12x+12y+36=0$. Find the radius of $C$. Give the answer only.

  19. 19 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.

  20. 20 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).
  21. 21 Standard DSE long question
    The line $L:y=-x+3$ meets the parabola $\Gamma:y=x^{2}-6x+3$ at $A$ and $B$ ($A$ to the left of $B$). Answer each part; give the answer only.
    1. (a) Find the $x$-coordinate of $B$.
    2. (b) Find the $y$-coordinate of $B$.
    3. (c) Find the sum of the $y$-coordinates of $A$ and $B$.
  22. 22 Standard DSE long question
    \$20000 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.
  23. 23 Standard DSE long question
    $A(-2,1)$ and $B(4,3)$; a moving point $P$ satisfies $PA=PB$. Answer each part; give the answer only.
    1. (a) Find the $y$-coordinate of the midpoint of $AB$.
    2. (b) Find the gradient of $AB$ (as a fraction in lowest terms).
    3. (c) Find the gradient of the locus of $P$.
    4. (d) Find the $y$-intercept of the locus.
  24. 24 Standard DSE long question
    Cuboid $ABCDEFGH$ has base $ABCD$ measuring 7 cm by 24 cm and height 60 cm. Answer each part; give the answer only.
    1. (a) Find the base diagonal $AC$ in cm.
    2. (b) Find the space diagonal $AG$ in cm.
    3. (c) Find the tangent of the angle between $AG$ and the base (as a fraction in lowest terms).
  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 1 Structured Questions, the value of $15\times 10+5$ is 156. Is this statement true?
  29. 29 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.
  30. 30 Advanced
    Solve $x^{2}+2x-15=0$. Find the larger root. Give the answer only.

  31. 31 Advanced
    Consider the quadratic function $y=3x^{2}-12x+8$. The minimum value of $y$ is -4. Is this true?
  32. 32 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.
  33. 33 Advanced DSE long question
    It is given that $f(x)=x^2+bx+c$, where the roots of $f(x)=0$ are $1$ and $5$. Answer each part; give the answer only.
    1. (a) Find $b$.
    2. (b) Find $c$.
    3. (c) Find $f(5)$.
    4. (d) Find the minimum value of $f(x)$.
  34. 34 Advanced DSE long question
    An arithmetic sequence has first term $9$ and fifth term $25$. Answer each part; give the answer only.
    1. (a) Find the common difference.
    2. (b) Find the 26th term.
    3. (c) Find the sum of the first 26 terms.
  35. 35 Advanced DSE long question
    A bag has 6 red and 5 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).
  36. 36 Advanced DSE long question
    Circle $C$ has equation $x^2+y^2-8x+8y-257=0$. 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 $P(12,11)$ to the centre of $C$.
  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 1 Structured Questions, the value of $19\times 13+4$ is 251. Is this statement true?
  41. 41 Challenging
    An arithmetic sequence has first term $9$ and common difference $4$. Find the sum of the first 10 terms. Choose the correct answer.
  42. 42 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.

  43. 43 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?
  44. 44 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).
  45. 45 Challenging DSE long question
    The line $L:y=3x+4$ meets the parabola $\Gamma:y=x^{2}+x-4$ at $A$ and $B$ ($A$ to the left of $B$). Answer each part; give the answer only.
    1. (a) Find the $x$-coordinate of $B$.
    2. (b) Find the $y$-coordinate of $B$.
    3. (c) Find the sum of the $y$-coordinates of $A$ and $B$.
  46. 46 Challenging DSE long question
    \$20000 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.
  47. 47 Challenging DSE long question
    $A(-1,1)$ and $B(1,7)$; a moving point $P$ satisfies $PA=PB$. Answer each part; give the answer only.
    1. (a) Find the $y$-coordinate of the midpoint of $AB$.
    2. (b) Find the gradient of $AB$.
    3. (c) Find the gradient of the locus of $P$ (as a fraction in lowest terms).
    4. (d) Find the $y$-intercept of the locus.
  48. 48 Challenging DSE long question
    Cuboid $ABCDEFGH$ has base $ABCD$ measuring 6 cm by 8 cm and height 24 cm. Answer each part; give the answer only.
    1. (a) Find the base diagonal $AC$ in cm.
    2. (b) Find the space diagonal $AG$ in cm.
    3. (c) Find the tangent of the angle between $AG$ and the base (as a fraction in lowest terms).
  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 1 Structured Questions, the value of $23\times 16+3$ is 372. Is this statement true?
  53. 53 Elite
    Circle $C$ has equation $x^2+y^2+10x+6y+30=0$. Find the radius of $C$. Give the answer only.

  54. 54 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.

  55. 55 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?
  56. 56 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 $C$.
  57. 57 Elite DSE long question
    It is given that $f(x)=x^2+bx+c$, where the roots of $f(x)=0$ are $1$ and $3$. Answer each part; give the answer only.
    1. (a) Find $b$.
    2. (b) Find $c$.
    3. (c) Find $f(4)$.
    4. (d) Find the minimum value of $f(x)$.
  58. 58 Elite DSE long question
    An arithmetic sequence has first term $12$ and fifth term $20$. Answer each part; give the answer only.
    1. (a) Find the common difference.
    2. (b) Find the 11th term.
    3. (c) Find the sum of the first 11 terms.
  59. 59 Elite DSE long question
    A bag has 3 red and 2 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).
  60. 60 Elite DSE long question
    Circle $C$ has equation $x^2+y^2+4x+6y-276=0$. 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 $P(6,12)$ 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.

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