## 10 Questions

How can algebraic expressions be manipulated?

Combine like terms, distribute a common factor, collect like terms

What are algebraic expressions composed of?

Variables, constants, and operators

What is the purpose of solving linear equations?

To find the value of the variable(s) that makes the equation true

Why are algebraic expressions considered fundamental in algebra?

They are the building blocks of many algebraic problems

Factor the quadratic expression 6x² + 11x + 5.

(2x + 1)(3x + 5)

Solve the linear inequality 3x - 5 < 12.

x < 5

Combine the following like terms: 2x + 3x + 5x.

10x

Distribute the common factor 3 to each term in the expression 3(x + 2y - 5z).

3x + 6y - 15z

Solve the equation 2x + 3 = 7 for x.

x = 2

Solve the absolute value equation |3x - 5| = 1.

x = 2, x = 4

## Study Notes

## Cracking the 10th Maths Second Revision: Algebraic Expressions

As the exam season nears, it's time to sharpen your pencils and prepare for algebraic expressions on the 10th maths second revision exam papers. Algebraic expressions, a fundamental concept in algebra, are the building blocks of many problems that will undoubtedly appear on your test. Let's delve into the essentials and brush up on this material.

### What are Algebraic Expressions?

Algebraic expressions are made up of variables, constants, and operators. They help to describe a relationship between variables and constants. In simpler terms, they are expressions consisting of letters (variables) and numbers (constants) connected by mathematical operators (+, -, ×, ÷).

### Manipulating Algebraic Expressions

Expressions can be manipulated using various techniques to simplify, combine, or rearrange expressions.

- Combine like terms: Terms containing the same variable(s) raised to the same power(s) can be added or subtracted.
- Distribute a common factor: Multiply each term of an expression by the same factor.
- Collect like terms: Move the terms of the same variable(s) to one side of the equal sign.

### Solving Linear Equations

Solving linear equations involves setting one expression equal to another and then finding the value of the variable(s) that makes the equation true. Use the inverse operations to rewrite one side of the equation until the variable stands alone on one side, and the constants on the other.

### Polynomials and Factoring

Polynomials are expressions made up of variables and constants and are often represented in the form of ax² + bx + c. *Factoring* is the process of breaking down an expression into its factors.

- Factoring a trinomial: Factoring a trinomial of the form ax² + bx + c often involves looking for two binomials whose product is the trinomial and whose sum is the coefficient (b) of the linear term.
- Factoring perfect squares: An expression of the form a² + 2ab + b² can be factored as (a + b)² or (a - b)².

### Linear Inequalities and Absolute Values

Linear inequalities are expressions formed using variables and constants and one of the inequality symbols (<, >, ≤, ≥). Solving linear inequalities often involves isolating the variable in the same way as solving linear equations.

Absolute values are expressions of the form |x|, which represent the distance between a number and zero on a number line. They can be solved by considering two cases: if the expression inside the absolute value is positive or negative.

### Practice Problems

- Combine the following like terms: 2x + 3x + 5x
- Distribute the common factor 3 to each term in the expression 3(x + 2y - 5z):
- Solve the equation 2x + 3 = 7 for x.
- Factor the quadratic expression 6x² + 11x + 5.
- Solve the linear inequality 3x - 5 < 12.
- Solve the absolute value equation |3x - 5| = 1.

Remember to practice, practice, practice! The more you dive into algebraic expressions, the more comfortable you'll become with the material and the less likely you are to lose marks on exam day. Good luck!

Get ready for your 10th Maths Second Revision exam by testing your knowledge on algebraic expressions. This quiz covers manipulating algebraic expressions, solving linear equations, factoring polynomials, dealing with linear inequalities and absolute values. Practice and boost your understanding of these fundamental algebra concepts!

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