Linear Equations in One Variable Class 8 important questions with answers PDF download
FAQs on CBSE Important Questions for Class 8 Maths Linear Equations in One Variable - 2025-26
1. Which topics from Chapter 2, Linear Equations in One Variable, are most important for the CBSE Class 8 exams 2025-26?
For the 2025-26 exams, students should focus on the following high-weightage topics from this chapter:
Solving equations with variables on both sides: These questions form the foundation and are frequently asked.
Word problems: This is the most crucial area. Expect questions based on ages, numbers, perimeters, and currency notes. These are often 3-mark or 5-mark questions.
Reducing equations to simpler forms: Questions involving fractions that need to be simplified before solving are considered important as they test multiple algebraic skills.
2. What kind of important questions can be expected from solving linear equations with variables on both sides?
You can typically expect 2-mark or 3-mark questions on this topic. A common format is like: 'Solve and check your result for the equation 5x + 9 = 5 + 3x'. The key steps to solve these are: transposing variables to one side and constants to the other, simplifying the equation, and finally, isolating the variable to find its value. Always remember to check the solution by substituting it back into the original equation.
3. What is a good strategy to score full marks in word problems from this chapter?
To score full marks, follow a systematic approach:
Read Carefully: Read the problem twice to understand the given conditions and what needs to be found.
Assign a Variable: Identify the unknown quantity and assign a variable to it, for example, 'Let the number be x'.
Form the Equation: Translate the statements from the problem into a mathematical linear equation.
Solve Methodically: Solve the equation using the correct transposition and simplification steps.
Verify the Answer: Substitute your answer back into the context of the problem (not just the equation) to ensure it makes logical sense.
4. Are there any specific types of word problems from this chapter that are frequently asked in exams?
Yes, based on previous exam trends, certain types of word problems appear more frequently. For thorough preparation, you should practice important questions based on:
Age Problems: Questions involving the present and future/past ages of people.
Number Problems: Questions about consecutive integers or digits of a two-digit number.
Perimeter Problems: Questions related to the dimensions of rectangles or triangles.
Currency Problems: Questions involving different denominations of notes or coins.
5. What is a common mistake students make when transposing terms in a linear equation, and how can it be avoided?
A very common mistake is confusing the rules for terms that are added/subtracted with terms that are multiplied/divided. For instance, in the equation 3x + 5 = 11, to move the '+5', you subtract 5 from both sides. However, to deal with the '3' in '3x', you must divide both sides by 3, not subtract 3. To avoid this, always remember that transposition involves performing the inverse operation: addition's inverse is subtraction, and multiplication's inverse is division.
6. How can I get better at setting up the correct linear equation from a complex word problem?
Improving this skill involves practice and a clear method. First, break the problem down into smaller parts. Identify the unknown value and represent it with a variable like 'x'. Next, re-read the problem to find relationships between other values and 'x'. For example, if 'Ravi's age is 5 years more than twice Raju's age', and Raju's age is 'x', then Ravi's age is '2x + 5'. Look for the part of the sentence that shows equality (e.g., 'is', 'results in', 'the sum is') to set up the two sides of the equation. This turns the word problem into a solvable mathematical statement.
7. Why is verifying the solution particularly important for word problems in an exam?
Verification is crucial because it serves two purposes. First, it checks for any calculation errors made while solving the equation. Second, and more importantly for word problems, it confirms that the solution is logically possible within the context of the question. For example, if a question asks for a person's age or the length of a side, your final answer cannot be a negative number. Verifying ensures your solution is not just mathematically correct but also makes sense in the real-world scenario described in the problem, helping you secure full marks.
8. How are questions on 'reducing equations to simpler form' considered Higher Order Thinking Skills (HOTS) questions?
These questions are often considered HOTS because they test more than just basic equation solving. They require a student to first handle fractions by finding the LCM (Lowest Common Multiple) of the denominators and then apply the distributive property correctly across the numerators. This multi-step process combines skills from fractions and algebra, testing a student's ability to plan their solution and execute multiple operations in the correct sequence, which is a hallmark of higher-order thinking in mathematics.
