CBSE Class 9 Maths Mid-Term 2026: Top 15 Questions & Key Concepts From the PW Marathon

Maths mid-term preparation can become difficult when you remember a formula but are unsure where to apply it, or when a small calculation error changes the final answer. You need to revise the concept behind each method along with practising questions where that concept is actually used.

The PW Class 9 CBSE Maths Mid-Term Marathon approaches revision through questions covering different parts of the syllabus. The marathon contains many more questions, while the selected set below focuses on some of the important, repeated, and concept-based questions discussed during the session.

What Maths Topics and Concepts Can You Revise With the PW Class 9 CBSE Maths Mid-Term Marathon?

The marathon moves through different types of Maths problems rather than limiting revision to formulas alone. While solving the questions, you get to work with concepts such as:

• Coordinate Geometry: Coordinates, points on axes, distance, midpoint, and collinearity

• Number Systems: Rational and irrational numbers, decimal expansions, and representation on the number line

• Patterns: Linear growth and decay, matchstick patterns, and forming expressions

• Algebra: Polynomial values, algebraic identities, and factorisation

• Application-Based Problems: Ages, charges, population changes, and other situations that can be represented algebraically

• Geometry: Triangle properties and angle relationships

• Circles: Circumference, chords, cyclic quadrilaterals, semicircles, and arc length

As you move through these topics, pay attention to the step where you choose a formula or property. That is often more important than simply reaching the final answer.

Top 15 Maths Questions From the PW Class 9 CBSE Maths Mid-Term Marathon

The complete PW Class 9 CBSE Maths Mid-Term Marathon covers questions that focus on coordinate geometry, quadrants, distance formula, midpoint formula, collinearity, and application-based problems. The set includes both direct concept questions and calculation-based problems to help you revise different types of questions that may appear in the mid-term exam.

Try solving each question independently before checking the answer. Pay particular attention to coordinates, distance and midpoint problems, as these concepts are used across several questions in the marathon.

Q1. If a door starting point D1 is at (8,0), how far is D1 from the y-axis?

Answer:

The distance of a point from the y-axis is given by the absolute value of its x-coordinate.

• Distance = |8| = 8 units

Result: D1 is 8 units from the y-axis.

Q2. How far is the point D1 = (8,0) from the x-axis?

Answer:

The y-coordinate of D1 is 0. Therefore, the point lies directly on the x-axis.

Result: Its distance from the x-axis is 0 units.

Q3. What are the coordinates of a point that is 8 units to the right of the y-axis and lies on the x-axis?

Answer:

• x-coordinate = 8 (8 units right of the y-axis)

•  

• y-coordinate = 0 (lies on the x-axis)

•  

Result: Coordinates = (8, 0)

Q4. If D1 = (8,0) and R1 = (11.5,0) are the endpoints of a door, find the width of the door.

Answer:

Width = Difference in x-coordinates

• Width = 11.5 - 8 = 3.5 units

•  

Result: The width of the door is 3.5 units.

Q5. A bathroom door has endpoints at (0,1.5) and (0,4). Find its width. Is it narrower or wider than a door of width 3.5 units?

Answer:

• Width of bathroom door = 4 - 1.5 = 2.5 units

•  

• Comparison: 2.5 units < 3.5 units

•  

Result: The bathroom door is 2.5 units wide, which makes it narrower than the 3.5-unit door.

Q6. Three vertices of a rectangular study table are (8,9), (11,9), and (11,7). Find the coordinates of the fourth vertex.

Answer:

The missing vertex must share the x-coordinate of (8,9) and the y-coordinate of (11,7).

• x-coordinate = 8

•  

• y-coordinate = 7

•  

Result: Fourth vertex = (8, 7)

Q7. Using the vertices (8,9), (11,9), (11,7), and (8,7), find the dimensions of the rectangular table.

Answer:

• Horizontal length = 11 - 8 = 3 units

•  

• Vertical width = 9 - 7 = 2 units

•  

Result: Dimensions = 3 units × 2 units

Q8. A bathroom door is 2.5 units wide and a wardrobe is 3 units away from its hinge. Will the door hit the wardrobe when opened?

Answer:

• Available clearance = 3 units - 2.5 units = 0.5 units

•  

Result: The door will not hit the wardrobe. It leaves a clearance gap of 0.5 units.

Q9. What are the coordinates of the point where the x-axis and y-axis intersect?

Answer:

The x-axis and y-axis intersect at the origin.

Result: Coordinates = (0, 0)

Q10. A point has an x-coordinate of -5. In which quadrants can it lie?

Answer:

A negative x-coordinate places the point on the left side of the y-axis.

• If y is positive, it lies in Quadrant II.

•  

• If y is negative, it lies in Quadrant III.

•  

Result: Quadrant II and Quadrant III

Q11. What is the distance formula for two points A(x1, y1) and B(x2, y2)?

Answer:

The distance AB between two points is given by:

• AB = √[(x2 - x1)² + (y2 - y1)²]

•  

(Note: Because terms are squared, reversing the order of subtraction yields the same result.)

Q12. Find the distance between the points A(1, 2) and B(4, 6).

Answer:

Using the distance formula:

1. AB = √[(4 - 1)² + (6 - 2)²]

2.  

3. AB = √[3² + 4²]

4.  

5. AB = √[9 + 16]

6.  

7. AB = √25 = 5

8.  

Result: AB = 5 units

Q13. What is the midpoint formula for the line segment joining A(x1, y1) and B(x2, y2)?

Answer:

The coordinates of midpoint M are:

• M = [ (x1 + x2) / 2 , (y1 + y2) / 2 ]

Q14. The midpoint of AB is M(-7, 1). If A = (3, -4), find the coordinates of B.

Answer:

Let B = (x, y).

Finding x-coordinate:

• (3 + x) / 2 = -7

•  

• 3 + x = -14

•  

• x = -17

•  

Finding y-coordinate:

• (-4 + y) / 2 = 1

•  

• -4 + y = 2

•  

• y = 6

•  

Result: Coordinates of B = (-17, 6)

Q15. Points M, A, and G satisfy MA = 5 units, AG = 10 units, and MG = 15 units. Are the three points collinear?

Answer:

For three points to be collinear with A lying between M and G, the sum of segment lengths must equal the total length:

• MA + AG = MG

•  

• 5 + 10 = 15

•  

• 15 = 15

•  

Result: Yes, points M, A, and G are collinear.

After completing these 15 Maths questions, review the ones where you made calculation or concept-based mistakes. You can return to the complete PW Maths Mid-Term Marathon for more questions and explanations on coordinate geometry, distance, midpoint, quadrants, and other important mid-term concepts.

Important Class 9 CBSE Maths Formulas and Rules to Revise

Instead of memorising a long formula list, revise the formulas and properties alongside the types of questions where you need them.

How Can You Use the PW Class 9 CBSE Maths Mid-Term Marathon for Final Revision?

You can use the marathon differently depending on what happens when you attempt these questions:

• Attempt first, then check: Pause before the solution and try to complete the question independently.

• Compare the method: Even when your final answer is correct, check whether you used the formula or property correctly.

• Mark the reason for each mistake: Separate calculation errors, formula errors, sign errors, and concept gaps.

• Reattempt difficult questions: Solve them again without looking at your earlier steps.

• Return to the explanation when needed: If you cannot decide which formula or theorem applies, revisit that concept in the marathon instead of memorising the completed solution.

• Practise beyond these 20 questions: The complete PW Maths Mid-Term Marathon contains additional questions and explanations, so you can continue with the relevant section once you identify a topic that needs more practice.

The PW Class 9 CBSE Maths Mid-Term Marathon can help you bring formulas, concepts, and question practice into the same revision session. Use the 20 questions above to check where you can choose the right method independently, then return to the complete marathon for the topics where you still need more practice before the mid-term.