Algebra Notes, Quizzes & Revision

Algebra — topic: topic_name_replace

Subject: subject_replace — Notes suited to learners in Kenya (aligned to the Competency-Based Curriculum ideas) for age: age_replace.

What is Algebra?

Algebra is the branch of mathematics that uses letters (like x, y) to represent numbers. It helps us describe patterns, write relationships, and solve problems when some values are unknown.

Core ideas and vocabulary

• Variable: a symbol (e.g. x) that stands for a number.
• Expression: combination of numbers, variables and operations (e.g. 3x + 5).
• Equation: an expression with an equals sign (e.g. 3x + 5 = 20).
• Coefficient: number multiplied by a variable (in 4y, 4 is the coefficient).
• Like terms: terms with the same variable parts (2x and 5x are like terms).
• Solve: find the value of the variable that makes an equation true.

Important rules (brief)

• Addition/Subtraction: do same operation to both sides of an equation.
• Multiplication/Division: you may multiply or divide both sides by the same non-zero number.
• Distributive law: a(b + c) = ab + ac.
• Combining like terms: 2x + 5x = 7x.

Worked examples (step-by-step)

How to form an equation from a word problem

1) Read carefully and choose a variable (e.g. x). 2) Translate phrases into algebra: "total", "sum", "more than", "times", "each". 3) Write the equation. 4) Solve and check by substitution.

Practice exercises

1. Solve: 5x − 10 = 20.
2. Solve: 2(x + 4) = 18.
3. Simplify: 3a + 7 − 2a + 4.
4. Word problem: A bus travels x km in one hour. In 3 hours it travels 75 km. Find x.
5. Word problem (Kenyan market): A trader sold 3 baskets of tomatoes at Ksh x each and got Ksh 600. If one basket costs Ksh 150 more than another item that costs Ksh 50, express and solve for x.

Answers and hints

• 1) 5x − 10 = 20 → 5x = 30 → x = 6.
• 2) 2(x + 4) = 18 → x + 4 = 9 → x = 5.
• 3) 3a + 7 − 2a + 4 = (3a − 2a) + (7 + 4) = a + 11.
• 4) 3x = 75 → x = 25 km per hour.
• 5) If one basket is x and trader sold 3 baskets: 3x = 600 → x = 200. Check relation: one basket costs 150 more than item of 50 → 50 + 150 = 200 ✓.

Checks for understanding

- Can you write an equation for "twice a number plus 6 equals 20"? (Answer: 2x + 6 = 20.)
- When solving an equation, explain why we do the same operation to both sides. (To keep equality true.)

Teaching and study tips (for learners and teachers)

• Use real-life examples (shop prices, distances, school materials) to create equations learners can relate to.
• Encourage showing every step — helps with checking work and exam answers.
• Use simple diagrams or number lines for visual learners (e.g. show subtraction as left moves).

Summary

Algebra uses symbols to represent numbers. Key skills: simplifying expressions, forming equations from words, and solving linear equations. Practice with Kenyan contexts (Ksh, distances between towns, quantities of goods) makes learning meaningful for learners aged age_replace.