Class 10 Mathematics Model Paper – Unit Test 2025

📘 Class 10 Mathematics Model Paper – Unit Test 2025

🔍 Presented by Digital Pipal Academy

As the Unit Test Examination 2025 approaches, it's the perfect time for students to practice and polish their preparation. This Model Question Paper for Class 10 Mathematics is designed to help students understand the exam pattern, improve speed and accuracy, and build confidence.

This paper covers all important concepts from the first part of the syllabus and follows the SEBA/NCERT-style pattern.

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📝 Model Question Paper

Subject: Mathematics
Class: 10
Examination: Unit Test 2025
Maximum Marks: 50
Time: 1½ Hours

Chapters Included:

• Real Numbers

• Polynomials

• Pair of Linear Equations in Two Variables

• Quadratic Equations

• Arithmetic Progressions

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General Instructions:

• Attempt all questions.

• Show all necessary steps.

• Use graph paper wherever needed.

• Ensure clarity in calculations and presentation.

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Section A – Very Short Answer Questions (1 mark each)

Find the HCF of 36 and 120 using prime factorisation.
Find the zeroes of the polynomial: $x^2 - 9$.
Write the general form of a pair of linear equations in two variables.
Solve the linear equation: $2x - 3 = 7$.
Write the nth term formula of an arithmetic progression (A.P.).

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Section B – Short Answer Type I (2 marks each)

Show that $\sqrt{3}$ is irrational.
Divide $2x^2 + 3x + 1$ by $x + 1$.
Solve the system: $x + y = 5$, $x - y = 1$.
The sum of the first three terms of an A.P. is 27. If the common difference is 3, find the first term.
Find the roots of the quadratic equation: $x^2 - 5x + 6 = 0$.

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Section C – Short Answer Type II (3 marks each)

Prove that there are infinitely many rational numbers between 1 and 2.
Find the zeroes of the polynomial: $x^2 - 2x - 8$ and verify the relationship between zeroes and coefficients.
Solve the pair of equations: $2x + 3y = 12$ and $x - y = 2$.
Find the 20th term and the sum of the first 20 terms of the A.P. 5, 8, 11, …

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Section D – Long Answer Type (4 marks each)

The sum of the squares of two consecutive odd numbers is 290. Find the numbers.
Factorise: $4x^2 - 12x + 9$.
Draw the graphs of the equations: $x + y = 6$ and $x - y = 2$. Find their point of intersection.
If the 7th term of an A.P. is 21 and the 13th term is 39, find the first term and common difference of the A.P.

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✅ Tips for Preparation:

• Focus on solving step-by-step and showing clear working.

• Practice graph plotting with accuracy.

• Revise formulas for polynomials and quadratic equations.

• Solve a variety of word problems on A.P. and equations.

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