Basic Algebra for Beginners: Civil Service Exam Guide

Introduction to Basic Algebra

Algebra is one of the most fundamental components of the Civil Service Exam (CSE) Numerical Ability section. While many examinees find algebra intimidating, the truth is that most algebra questions on the exam involve simple rules, basic operations, and logical reasoning. By mastering foundational algebraic concepts, you can significantly improve your score and increase your chances of passing.

This guide is designed specifically for beginners who want to strengthen their algebra skills. It covers essential rules, step-by-step explanations, sample problems, and strategies to help you answer questions quickly and accurately.

What Is Algebra?

Algebra is the branch of mathematics that uses letters, symbols, and numbers to represent unknown values and express mathematical relationships. In the Civil Service Exam, algebra commonly appears in questions involving:

• Solving for unknowns (x, y, etc.)

• Simplifying algebraic expressions

• Evaluating expressions

• Translating word problems into equations

• Working with linear equations

Algebra is not just about manipulating symbols—it’s about understanding patterns and relationships.

Key Algebra Terminology

Before solving algebra problems, you need to understand basic vocabulary:

1. Variable

A symbol (usually a letter) that represents an unknown number.
Example: In the equation x + 5 = 12, the variable is x.

2. Constant

A fixed number.
Example: In x + 7, the number 7 is a constant.

3. Coefficient

The number that multiplies a variable.
Example: In 4x, 4 is the coefficient.

4. Expression

A combination of variables, constants, and operations without an equality sign.
Example: 3x + 2

5. Equation

A statement that two expressions are equal.
Example: 2x – 4 = 10

Order of Operations (PEMDAS/BODMAS)

To solve algebra problems correctly, follow the order of operations:

1. Parentheses/Brackets

2. Exponents/Orders

3. Multiplication and Division (left to right)

4. Addition and Subtraction (left to right)

Example:
Solve 3 + 4 × 2
→ Multiply first: 4 × 2 = 8
→ Add: 3 + 8 = 11

Simplifying Algebraic Expressions

Simplifying means combining like terms and reducing expressions.

Like Terms

Terms with the same variable and exponent.

Examples of like terms:

• 3x and 7x

• 5y² and −2y²

Not like terms:

• x and x²

• y and xy

Example: Simplify the expression

5x + 3x − 7 + 2

Combine like terms:

• Combine 5x + 3x = 8x

• Combine constants: −7 + 2 = −5

Final Answer:
8x − 5

Solving Basic Algebraic Equations

The goal is to isolate the variable.

Example 1: Solve for x

x + 9 = 20

Subtract 9 on both sides:
x = 20 − 9
x = 11

Example 2: Solve for x

3x = 15

Divide both sides by 3:
x = 5

Example 3: Solve for x

2x + 4 = 18

Step 1: Subtract 4 → 2x = 14
Step 2: Divide by 2 → x = 7

Working with Linear Equations

A linear equation is written in this form:

y = mx + b

Where:

• m = slope

• b = y-intercept

For the Civil Service Exam, you mainly solve simple equations such as:

y = 3x + 4
or
2x − y = 10

The focus is usually on solving for one variable or evaluating the expression.

Translating Word Problems into Algebra

A major challenge in the Civil Service Exam is converting sentences into algebraic equations.

Here are common phrases and their algebra meanings:

Example Word Problem

“A number increased by 7 is 25. What is the number?”

Let the number = x

Equation:
x + 7 = 25

Solve:
x = 18

Common Types of Algebra Questions in the CSE

You will typically encounter:

1. Simplifying Expressions

Example:
Simplify 2x + 5 − x + 3
→ x + 8

2. Solving Linear Equations

Example:
Solve 4x − 8 = 12
→ Add 8: 4x = 20
→ Divide: x = 5

3. Evaluating Expressions

Given x = 3, find the value of 2x² − x + 1.

Substitute:
→ 2(9) − 3 + 1
→ 18 − 3 + 1 = 16

4. Basic Word Problems

Example:
“The sum of a number and twice the number is 21.”
Equation: x + 2x = 21
Solve: 3x = 21 → x = 7

Strategies for Answering Algebra Questions Quickly

1. Always isolate the variable step-by-step

Do not skip steps—simple mistakes cause lost points.

2. Check your answer

Plug the value back into the equation.

3. Use estimation when needed

Eliminate wrong choices quickly.

4. Translate word problems into equations immediately

Look for key operational words.

5. Practice mental math

Many questions must be solved in under 30 seconds.

Sample Problems for Practice (With Explanations)

Problem 1

Simplify: 7x − 3 + 2x + 8

Combine like terms:
→ 7x + 2x = 9x
→ −3 + 8 = 5

Final Answer: 9x + 5

Problem 2

Solve: 2x − 5 = 11

Add 5: 2x = 16
Divide 2: x = 8

Problem 3

If x = 4, evaluate 3x² − 2x + 1

→ 3(16) − 8 + 1
→ 48 − 8 + 1 = 41

Problem 4 (Word Problem)

“Three times a number decreased by 4 is 26.”

Let the number = x

Equation: 3x − 4 = 26
Add 4 → 3x = 30
Divide → x = 10

Advanced Tips for CSE Takers

1. Memorize Common Algebra Patterns

Examples:

• (a + b)(a − b) = a² − b²

• (a + b)² = a² + 2ab + b²

Though rarely used, they help speed up simplification.

2. Avoid Math Anxiety

Most algebra questions on the exam are easier than typical high school questions.

3. Focus on accuracy over speed

A wrong answer wastes more time than a slow but correct solution.

Conclusion

Algebra is a crucial skill for the Civil Service Exam, but mastering it does not require advanced mathematical knowledge. By learning the basic rules, practicing simplification, solving equations, and understanding word problems, you can confidently handle all algebra-related questions on the test.

With consistent practice, what once felt intimidating will soon feel simple and familiar. Strengthen your math foundation, build your confidence, and move one step closer to passing the Civil Service Exam.

Problem Sets

Part A: Simplifying Algebraic Expressions

1. Simplify: 5x + 3x − 7
2. Simplify: 4y − 2y + 9
3. Simplify: 7a + 2 − 3a + 5
4. Simplify: 6m − 4 + 2m − 1
5. Simplify: 10x − 3 + 2 − 4x

Part B: Solving One-Step and Two-Step Equations

6. Solve for x: x + 9 = 20
7. Solve for x: 3x = 21
8. Solve for x: 2x − 5 = 11
9. Solve for x: 4x + 3 = 31
10. Solve for x: 18 − x = 7

Part C: Evaluating Expressions

11. If x = 3, find the value of 2x + 5.
12. If x = 4, find the value of 3x² − 2.
13. If y = −2, find the value of y² + 4y + 1.
14. If a = 5, find the value of 2a − 3a + 4.
15. If x = −1, find the value of 4x² + x.

Part D: Word Problems (Translate and Solve)

16. The sum of a number and 7 is 19. What is the number?
17. Three times a number is 27. What is the number?
18. A number decreased by 6 is equal to 11. Find the number.
19. Twice a number increased by 5 is 29. What is the number?
20. The sum of a number and twice the number is 36. What is the number?

Answer Key

Part A: Simplifying Algebraic Expressions

1. 5x + 3x − 7 = 8x − 7
2. 4y − 2y + 9 = 2y + 9
3. 7a + 2 − 3a + 5 = 4a + 7
4. 6m − 4 + 2m − 1 = 8m − 5
5. 10x − 3 + 2 − 4x = 6x − 1

Part B: Solving One-Step and Two-Step Equations

6. x + 9 = 20
   → x = 20 − 9 = 11
7. 3x = 21
   → x = 21 ÷ 3 = 7
8. 2x − 5 = 11
   → 2x = 11 + 5 = 16
   → x = 16 ÷ 2 = 8
9. 4x + 3 = 31
   → 4x = 31 − 3 = 28
   → x = 28 ÷ 4 = 7
10. 18 − x = 7
    → −x = 7 − 18 = −11
    → x = 11

Part C: Evaluating Expressions

11. x = 3, 2x + 5
    → 2(3) + 5 = 6 + 5 = 11
12. x = 4, 3x² − 2
    → 3(4²) − 2 = 3(16) − 2 = 48 − 2 = 46
13. y = −2, y² + 4y + 1
    → (−2)² + 4(−2) + 1
    → 4 − 8 + 1 = −3
14. a = 5, 2a − 3a + 4
    → (2 × 5) − (3 × 5) + 4
    → 10 − 15 + 4 = −1
15. x = −1, 4x² + x
    → 4(−1)² + (−1)
    → 4(1) − 1 = 3

Part D: Word Problems (Translate and Solve)

16. “The sum of a number and 7 is 19.”
    Let the number be x.
    Equation: x + 7 = 19
    x = 19 − 7 = 12
17. “Three times a number is 27.”
    Let the number be x.
    Equation: 3x = 27
    x = 27 ÷ 3 = 9
18. “A number decreased by 6 is equal to 11.”
    Let the number be x.
    Equation: x − 6 = 11
    x = 11 + 6 = 17
19. “Twice a number increased by 5 is 29.”
    Let the number be x.
    Equation: 2x + 5 = 29
    2x = 29 − 5 = 24
    x = 24 ÷ 2 = 12
20. “The sum of a number and twice the number is 36.”
    Let the number be x.
    Equation: x + 2x = 36
    3x = 36
    x = 36 ÷ 3 = 12

Civil Service Exam Philippines: Complete Preparation and Passing Guide