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Chapter 1 Practice Paper: Coordinate Geometry — question paper

QuizQuipPractice Series
QQ/S4EM/CH1

Secondary 4 · Elementary Mathematics (G2 / G3)

Chapter 1 Practice Paper

Coordinate Geometry

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 1 (G6 Coordinate Geometry: distance, midpoint, gradient, y = mx + c, geometric problems).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures.

  1. 1

    The points O(0, 0) and P(6, 8) are given.

    1. (a)

      Find the length OP.

      [2]
    2. (b)

      Write down the midpoint of OP.

      [1]
  2. 2

    A line passes through the points (−2, 1) and (4, −5).

    1. (a)

      Find the gradient of the line.

      [2]
    2. (b)

      Find the equation of the line, in the form y = mx + c.

      [2]
  3. 3

    A line has equation 2y = 4x − 6.

    1. (a)

      Write the equation in the form y = mx + c and state its gradient and y-intercept.

      [2]
    2. (b)

      Write down the coordinates of the x-intercept.

      [2]
  4. 4

    The points A(1, 1) and B(5, 4) are given.

    1. (a)

      Find the length AB.

      [2]
    2. (b)

      Find the midpoint of AB.

      [2]
  5. 5

    Two lines have equations y = 2x − 3 and x + y = 6.

    1. (a)

      Find the coordinates of their point of intersection.

      [3]
    2. (b)

      Verify that the point satisfies both equations.

      [2]
  6. 6

    The vertices of a triangle are A(0, 0), B(4, 0) and C(4, 3).

    1. (a)

      Show that the triangle is right-angled.

      [3]
    2. (b)

      Find the area of the triangle.

      [2]
  7. 7

    The points P(1, 2) and Q(7, 10) are given.

    1. (a)

      Find the gradient of PQ.

      [2]
    2. (b)

      Find the equation of PQ in the form y = mx + c.

      [2]
    3. (c)

      Determine whether the point (10, 14) lies on PQ.

      [1]

— End of paper —