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Topic 11 Practice Paper: Coordinate geometry — question paper

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QQ/IGCSE-MATHS/T11

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 11 Practice Paper

Coordinate geometry

Duration: 40 minutes
Total: 30 marks
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Class:
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READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 11: gradients from two points, midpoints and lengths of segments, equations of straight lines and their intercepts, parallel and perpendicular lines, and perpendicular bisectors.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    Joining (2, 3) to (6, 11), the line’s gradient works out as

    1. A1⁄2
    2. B4
    3. C2
    4. D3
    ( )
  2. 2

    Halving the segment from (1, 2) to (7, 10) lands on

    1. A(4, 6)
    2. B(8, 12)
    3. C(3, 5)
    4. D(4, 8)
    ( )
  3. 3

    How long is the stretch from (0, 0) to (5, 12)?

    1. A11
    2. B17
    3. C60
    4. D13
    ( )
  4. 4

    The line with gradient −1 through (0, 4) is

    1. Ay = x − 4
    2. By = −x + 4
    3. Cy = −x − 4
    4. Dy = x + 4
    ( )
  5. 5

    The line through the origin parallel to y = 3x − 2 is

    1. Ay = 3x
    2. By = −3x
    3. Cy = 3x − 2
    4. Dy = x + 3
    ( )
  6. 6

    A line perpendicular to a gradient of −3⁄4 has gradient

    1. A−4⁄3
    2. B3⁄4
    3. C4⁄3
    4. D−3⁄4
    ( )
  7. 7

    The x-intercept of y = 4x − 12 is at

    1. Ax = 12
    2. Bx = −3
    3. Cy = −12
    4. Dx = 3
    ( )
  8. 8

    Rearranged, the slope of 2x − y = 5 comes to

    1. A−2
    2. B2
    3. C1⁄2
    4. D5
    ( )
  9. 9

    One of these pairs sits on y = 2x + 3 — which?

    1. A(3, 5)
    2. B(1, 4)
    3. C(5, 13)
    4. D(2, 6)
    ( )
  10. 10

    Cutting the segment from (−2, 0) to (4, 0) in half at right angles gives the line

    1. Ax = 1
    2. By = 1
    3. Cy = x
    4. Dx = 3
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show all your working.

  1. 11

    A(−2, 1) and B(4, 9). (Extended)

    1. (a)

      Work out the gradient of the segment AB.

      [2]
    2. (b)

      Write down the coordinates of the midpoint of AB.

      [1]
    3. (c)

      Calculate the length of AB.

      [2]
  2. 12

    With a slope of 2 and running through (3, 5), the line is fixed.

    1. (a)

      Determine the equation of this line.

      [2]
    2. (b)

      State the y-intercept as a coordinate.

      [1]
    3. (c)

      Determine whether the point (10, 19) lies on the line.

      [1]
    4. (d)

      Write down the equation of the parallel line through (0, 2).

      [1]
  3. 13

    Line l₁ is y = ½x + 3. (Extended)

    1. (a)

      State the gradient that any line perpendicular to l₁ must have.

      [1]
    2. (b)

      Line l₂ runs through (5, 7) at right angles to l₁. Find its equation.

      [3]
    3. (c)

      Find the x-coordinate of the point where l₁ and l₂ meet.

      [1]
  4. 14

    P(2, 1) and Q(6, 9). (Extended)

    1. (a)

      Find the midpoint of PQ.

      [1]
    2. (b)

      Find the gradient of PQ.

      [1]
    3. (c)

      Write down the gradient of the perpendicular bisector of PQ.

      [1]
    4. (d)

      Find the equation of the line that bisects PQ at right angles.

      [2]

— End of paper —