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Form 5 Equations of Straight Lines Practice

Form 5 · 60 practice questions with instant marking and worked solutions.

Equations of Straight Lines is an important part of the Form 5 mathematics curriculum. This topic develops gradient, intercepts, parallel and perpendicular lines and equations. 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 Equations of Straight Lines 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 Equations of Straight Lines; 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 Equations of Straight Lines 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.

Equations of Straight Lines 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
    In Equations of Straight Lines, calculate $y=2x+4,\ x=6$. Choose the correct answer.
  2. 2 Basic
    In Equations of Straight Lines, calculate $y=3x+5,\ x=7$. Give the numerical value only.

  3. 3 Basic
    In Equations of Straight Lines, calculate $y=4x+4,\ x=2$. Show the essential working and give the numerical value.

  4. 4 Basic
    In Equations of Straight Lines, the value of $y=5x+5,\ x=3$ is 21. Is this statement true?
  5. 5 Basic
    A line passes through $A(2,-5)$ and $B(6,-4)$. Find the gradient of $AB$ (as a fraction in lowest terms). Choose the correct answer.
  6. 6 Basic
    A line through $(-2,-5)$ has gradient $-2$. Find its $y$-intercept. Give the answer only.

  7. 7 Basic
    Line $L$ is perpendicular to $-3x-6y+5=0$. Find the gradient of $L$. Show the essential working and give the answer.

  8. 8 Basic
    Consider the line $4x-4y=1$. Its $x$-intercept is -1/4. Is this true?
  9. 9 Basic
    A line passes through $A(1,4)$ and $B(2,8)$. Find the gradient of $AB$. Choose the correct answer.
  10. 10 Basic
    A line through $(2,-2)$ has gradient $\frac{3}{2}$. Find its $y$-intercept. Give the answer only.

  11. 11 Basic
    Line $L$ is perpendicular to $2x-3y+9=0$. Find the gradient of $L$ (as a fraction in lowest terms). Show the essential working and give the answer.

  12. 12 Basic
    Consider the line $3x+2y=-11$. Its $x$-intercept is -11/2. Is this true?
  13. 13 Standard
    In Equations of Straight Lines, calculate $y=1x+7,\ x=4$. Choose the correct answer.
  14. 14 Standard
    In Equations of Straight Lines, calculate $y=2x+8,\ x=5$. Give the numerical value only.

  15. 15 Standard
    In Equations of Straight Lines, calculate $y=3x+7,\ x=6$. Show the essential working and give the numerical value.

  16. 16 Standard
    In Equations of Straight Lines, the value of $y=4x+8,\ x=7$ is 36. Is this statement true?
  17. 17 Standard
    Consider the points $A(-5,4)$ and $B(-1,7)$. Find the length of $AB$. Choose the correct answer.
  18. 18 Standard
    The lines $y=x+2$ and $y=\frac{1}{2}x+\frac{1}{2}$ meet at $P$. Find the $x$-coordinate of $P$. Give the answer only.

  19. 19 Standard
    A line passes through $A(-1,6)$ and $B(2,2)$. Find the gradient of $AB$ (as a fraction in lowest terms). Show the essential working and give the answer.

  20. 20 Standard DSE long question
    $A(1,-4)$ and $B(7,4)$. Answer each part; give the answer only.
    1. (a) Find the gradient of $AB$ (as a fraction in lowest terms).
    2. (b) Find the length of $AB$.
    3. (c) Find the $y$-intercept of the perpendicular bisector of $AB$.
  21. 21 Standard
    Consider the points $A(-2,5)$ and $B(-5,9)$. Find the length of $AB$. Choose the correct answer.
  22. 22 Standard
    The lines $y=x+6$ and $y=4x+18$ meet at $P$. Find the $x$-coordinate of $P$. Give the answer only.

  23. 23 Standard
    A line passes through $A(4,6)$ and $B(0,-7)$. Find the gradient of $AB$ (as a fraction in lowest terms). Show the essential working and give the answer.

  24. 24 Standard DSE long question
    $A(0,3)$ and $B(12,19)$. Answer each part; give the answer only.
    1. (a) Find the gradient of $AB$ (as a fraction in lowest terms).
    2. (b) Find the length of $AB$.
    3. (c) Find the $y$-intercept of the perpendicular bisector of $AB$ (as a fraction in lowest terms).
  25. 25 Advanced
    In Equations of Straight Lines, calculate $y=5x+10,\ x=2$. Choose the correct answer.
  26. 26 Advanced
    In Equations of Straight Lines, calculate $y=1x+11,\ x=3$. Give the numerical value only.

  27. 27 Advanced
    In Equations of Straight Lines, calculate $y=2x+10,\ x=4$. Show the essential working and give the numerical value.

  28. 28 Advanced
    In Equations of Straight Lines, the value of $y=3x+11,\ x=5$ is 27. Is this statement true?
  29. 29 Advanced
    A line through $(3,-6)$ has gradient $2$. Find its $y$-intercept. Choose the correct answer.
  30. 30 Advanced
    Line $L$ is perpendicular to $-2x-5y-5=0$. Find the gradient of $L$ (as a fraction in lowest terms). Give the answer only.

  31. 31 Advanced
    Consider the line $-2x+3y=-9$. Its $x$-intercept is 9/2. Is this true?
  32. 32 Advanced DSE long question
    $A(2,2)$ and $B(8,4)$; 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.
  33. 33 Advanced
    A line through $(-2,-5)$ has gradient $4$. Find its $y$-intercept. Choose the correct answer.
  34. 34 Advanced
    Line $L$ is perpendicular to $x-2y-10=0$. Find the gradient of $L$. Give the answer only.

  35. 35 Advanced
    Consider the line $5x+y=-4$. Its $x$-intercept is -4/5. Is this true?
  36. 36 Advanced DSE long question
    $A(-2,0)$ and $B(2,6)$; 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 $P$ (as a fraction in lowest terms).
    4. (d) Find the $y$-intercept of the locus.
  37. 37 Challenging
    In Equations of Straight Lines, calculate $y=4x+13,\ x=6$. Choose the correct answer.
  38. 38 Challenging
    In Equations of Straight Lines, calculate $y=5x+14,\ x=7$. Give the numerical value only.

  39. 39 Challenging
    In Equations of Straight Lines, calculate $y=1x+13,\ x=2$. Show the essential working and give the numerical value.

  40. 40 Challenging
    In Equations of Straight Lines, the value of $y=2x+14,\ x=3$ is 20. Is this statement true?
  41. 41 Challenging
    Consider the points $A(4,-2)$ and $B(-4,4)$. Find the length of $AB$. Choose the correct answer.
  42. 42 Challenging
    The lines $y=x+8$ and $y=4x+23$ meet at $P$. Find the $x$-coordinate of $P$. Show the essential working and give the answer.

  43. 43 Challenging
    A line passes through $A(-1,3)$ and $B(1,7)$. The gradient of $AB$ is 1/2. Is this true?
  44. 44 Challenging DSE long question
    $A(-3,1)$ and $B(13,31)$. Answer each part; give the answer only.
    1. (a) Find the gradient of $AB$ (as a fraction in lowest terms).
    2. (b) Find the length of $AB$.
    3. (c) Find the $y$-intercept of the perpendicular bisector of $AB$ (as a fraction in lowest terms).
  45. 45 Challenging
    Consider the points $A(-1,-4)$ and $B(-22,16)$. Find the length of $AB$. Choose the correct answer.
  46. 46 Challenging
    The lines $y=3x+2$ and $y=4x+3$ meet at $P$. Find the $x$-coordinate of $P$. Show the essential working and give the answer.

  47. 47 Challenging
    A line passes through $A(-4,1)$ and $B(6,-4)$. The gradient of $AB$ is -2. Is this true?
  48. 48 Challenging DSE long question
    $A(-3,-2)$ and $B(13,28)$. Answer each part; give the answer only.
    1. (a) Find the gradient of $AB$ (as a fraction in lowest terms).
    2. (b) Find the length of $AB$.
    3. (c) Find the $y$-intercept of the perpendicular bisector of $AB$ (as a fraction in lowest terms).
  49. 49 Elite
    In Equations of Straight Lines, calculate $y=3x+16,\ x=4$. Choose the correct answer.
  50. 50 Elite
    In Equations of Straight Lines, calculate $y=4x+17,\ x=5$. Give the numerical value only.

  51. 51 Elite
    In Equations of Straight Lines, calculate $y=5x+16,\ x=6$. Show the essential working and give the numerical value.

  52. 52 Elite
    In Equations of Straight Lines, the value of $y=1x+17,\ x=7$ is 25. Is this statement true?
  53. 53 Elite
    A line through $(2,0)$ has gradient $-2$. Find its $y$-intercept. Give the answer only.

  54. 54 Elite
    Line $L$ is perpendicular to $-3x+3y-6=0$. Find the gradient of $L$. Show the essential working and give the answer.

  55. 55 Elite
    Consider the line $5x-y=-11$. Its $x$-intercept is -11/5. Is this true?
  56. 56 Elite DSE long question
    $A(-4,2)$ and $B(2,4)$; 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.
  57. 57 Elite
    A line through $(3,-2)$ has gradient $-1$. Find its $y$-intercept. Give the answer only.

  58. 58 Elite
    Line $L$ is perpendicular to $4x+4y+9=0$. Find the gradient of $L$. Show the essential working and give the answer.

  59. 59 Elite
    Consider the line $-3x-4y=-12$. Its $x$-intercept is 4. Is this true?
  60. 60 Elite DSE long question
    $A(-2,-3)$ and $B(2,3)$; 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 $P$ (as a fraction in lowest terms).
    4. (d) Find the $y$-intercept of the locus.

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

Common mistakes

Common mistakes in Equations of Straight Lines

This topic needs particular care with gradient, intercepts, parallel and perpendicular lines and equations. 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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