Skip to content
QuizQuip
Sign up
Back to Chapter 6
Mark schemePDF

Chapter 6 Practice Paper: Coordinate Geometry and Circles — question paper

QuizQuipPractice Series
QQ/S3AM/CH6

Secondary 3 · Additional Mathematics (G3)

Chapter 6 Practice Paper

Coordinate Geometry and Circles

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.
  • 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 Additional Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 6 (G2 Coordinate geometry: lines, area, circles).

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 unless told otherwise.

  1. 1

    The line L₁ has equation 3x − y + 7 = 0, and the line L₂ passes through the points (1, 4) and (5, 16).

    1. (a)

      Find the gradient of each line.

      gradients =[2]
    2. (b)

      Explain why L₁ and L₂ are parallel.

      [1]
    3. (c)

      Find the equation of the line through (0, −1) that is perpendicular to L₂, giving your answer in the form ax + by = c.

      [2]
  2. 2

    A quadrilateral has vertices O(0, 0), A(7, 1), B(8, 5) and C(1, 4), in that order.

    1. (a)

      Show, by splitting the quadrilateral into two triangles along OB, that the area can be found from the triangles OAB and OBC.

      [2]
    2. (b)

      Find the areas of triangles OAB and OBC.

      [3]
    3. (c)

      Hence state the area of the quadrilateral.

      area =[1]
  3. 3

    The equation x² + y² − 4x + 6y − 12 = 0 represents a circle C.

    1. (a)

      Determine the centre and the radius of C.

      [4]
    2. (b)

      Find the coordinates of the two points where C crosses the x-axis.

      [2]
  4. 4

    The circle x² + y² = 45 has centre O. The point P(a, 3), where a > 0, lies on the circle.

    1. (a)

      Find the value of a.

      [2]
    2. (b)

      State the gradient of the radius OP.

      gradient =[1]
    3. (c)

      Find the equation of the tangent to the circle at P, giving your answer in the form ax + by = c.

      [2]
    4. (d)

      Determine whether the point (3, 8) lies inside or outside the circle.

      [1]
  5. 5

    The line y = 2x + c intersects the circle (x − 1)² + (y − 3)² = 20, where c is a constant.

    1. (a)

      Show that the x-coordinates of any intersection point satisfy 5x² + (4c − 14)x + (c² − 6c − 10) = 0.

      [3]
    2. (b)

      Given that the line is a tangent to the circle, form an equation in c.

      [1]
    3. (c)

      Find the two possible values of c.

      c =[3]

— End of paper —