Mathematics Standard Class X: Sample Paper 05 Solved
Preparing for Class X board examinations requires consistent practice with various question patterns. This document provides a comprehensive look at Sample Paper 05, focusing on key concepts, logical reasoning, and step-by-step solutions to ensure clarity for students.
Overview of the Paper
Mathematics Standard is designed to test a student's conceptual depth, calculation speed, and analytical skills. Sample Paper 05 covers topics including Real Numbers, Polynomials, Quadratic Equations, Arithmetic Progressions, Coordinate Geometry, Trigonometry, and Statistics. Below are selected solved problems from different sections of the paper.
Section A: Objective Type Questions
65 = 5 13
117 = 9 13
HCF = 13.
Step 2: Equate 65m - 117 = 13.
65m = 130
m = 2.
x(x - 5) + 2(x - 5) = 0
(x + 2)(x - 5) = 0
Roots are x = -2 and x = 5.
Section B: Short Answer Questions
Eq 1: a + 9d = 21
Eq 2: a + 19d = 41
Subtracting Eq 1 from Eq 2:
10d = 20 ⇒ d = 2
Substitute d=2 into Eq 1:
a + 9(2) = 21 ⇒ a + 18 = 21 ⇒ a = 3.
The first term is 3 and the common difference is 2.
By Pythagoras theorem, AB + BC = AC.
Divide by AC: (AB/AC) + (BC/AC) = 1.
Since AB/AC = cos and BC/AC = sin (relative to angle C),
cos + sin = 1.
Section C: Long Answer Questions
Volume of cylinder = Rh = * (6) * h
Equating volumes:
(4/3) * (4.2 * 4.2 * 4.2) = 36 * h
h = (4 * 74.088) / (3 * 36)
h = 2.744 cm.
Conclusion
The key to mastering Mathematics lies in understanding the logic behind every step. Sample Paper 05 focuses heavily on the application of formulas rather than rote memorization. Students are advised to practice these problems repeatedly, paying close attention to unit conversions and sign conventions, which are common areas where mistakes occur. Regular revision of these solved examples will significantly improve your confidence and performance in the final examination.
Mathematics Standard X Sample Paper 01 Solved and Reference File Download Link
Mathematics Standard X Sample Paper 05 Solved and Reference File Download Link
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