Coordinate Geometry and Linear Equations (Class 9)

What this worksheet covers

This is an eighteen-question practice worksheet on coordinate geometry and linear equations in two variables for Class 9, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on coordinate geometry and linear equations in two variables at Class 9 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done on the blank space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Coordinate Geometry and Linear Equations (Class 9) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The point (−3, 5) lies in which quadrant?

   • AQuadrant I
   • BQuadrant IV
   • CQuadrant III
   • DQuadrant IIcorrect
   Solution: A point with a negative abscissa and a positive ordinate lies to the left of the y-axis and above the x-axis, which is Quadrant II. The sign pattern for the four quadrants is (+, +), (−, +), (−, −), (+, −).

2. 2. The cost of a notebook is twice the cost of a pen. Taking the cost of a notebook as ₹x and that of a pen as ₹y, this statement as a linear equation is _______.

   • A2x − y = 0
   • Bx − 2y = 0correct
   • Cx + 2y = 0
   • Dx + y = 2
   Solution: “Notebook = twice the pen” translates directly to x = 2y, which rearranges to x − 2y = 0. The form 2x − y = 0 would say the pen costs twice the notebook, reversing the sentence.

3. 3. How many solutions of the equation 2x + 5y = 20 have both x and y as positive integers?

   • AExactly onecorrect
   • BExactly two
   • CExactly four
   • DInfinitely many
   Solution: Rearranged, 5y = 20 − 2x, so 20 − 2x must be a positive multiple of 5. Since 20 is a multiple of 5, this needs 2x to be a multiple of 5, hence x must be a multiple of 5. Within the range 0 < x < 10 the only such value is x = 5, giving y = 2. (x = 10 gives y = 0, which is not positive.) So there is exactly one such solution, namely (5, 2).