Math
Algebra - Use of letters for numbers, factors of algebraic expressions. Value of the polynomial and operations on them
MCQ

Introduction

Algebra is a branch of mathematics where we use letters or symbols to represent unknown numbers. These letters are called variables because their value can change depending on the problem.

 

 

 

 

Visual representation of how variables and constants form an expression.

Explanation Step by Step

1. Identify the unknown value in a story or problem. 2. Assign a letter (like a, b, x, y) to that value. 3. Form an expression or equation based on the given conditions.

Sub-topics

Use of letters for numbers

We use letters to state mathematical properties and formulas in a general way. For example, the area of a rectangle is length (l) × breadth (b).

Examples

Example 1: Real-life scenario
If one pen costs 10 rupees, what is the cost of 'n' pens?
Total cost = 10n
Tricky Example
Think of a number, double it, and subtract the original number. What is the expression?
2x - x (which simplifies to x).

Factors of algebraic expressions

Factoring is the process of breaking down an expression into a product of simpler expressions or numbers.

Examples

Example 1
Find the factors of 12ab.
2 × 2 × 3 × a × b

Tricks and Shortcuts

* When multiplying a number and a letter, we don't need a multiplication sign (e.g., 5 × x = 5x). * To find common factors, always look for the highest number that divides all coefficients.

Common Mistakes

* Adding unlike terms: Students often write 3x + 2y = 5xy. This is wrong! They stay separate. * Confusing 2x (multiplication) with x² (power).

Practice Questions

Easy Questions

  1. Write an expression: 5 more than a number 'x'.
  2. What are the factors of 7pqr?
  3. (Tricky) If x = 0, what is the value of 100x?

Medium Questions

  1. The side of a square is 's'. Write the formula for its perimeter.
  2. Factorize the expression 18xy².
  3. (Real-life Tricky) You have 50 rupees. You bought 'k' candies for 2 rupees each. How much money is left?

Hard Questions

  1. Write an algebraic expression for: "Half of a number added to 10".
  2. Find the common factors of 24a²b and 36ab².
  3. (Tricky) If a = 2 and b = 3, is 2a + 3b the same as 3a + 2b? Prove it.

Revision Summary

Letters represent numbers in Algebra. Variables allow us to write general rules. Factoring helps in simplifying complex expressions by breaking them into products.

If x = -1, what is the value of 2x³ - 3x² + 4x - 5?
A
-14
B
-10
C
4
D
-12
Explanation
2(-1)³ - 3(-1)² + 4(-1) - 5
= 2(-1) - 3(1) - 4 - 5 = -2 - 3 - 4 - 5 = -14
Correct 1 Wrong 1