ALGEBRA Notes, Quizzes & Revision
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ALGEBRA โ topic: topic_name_replace
Subject: subject_replace | Target age: age_replace | Designed to match Kenyan classroom examples (e.g., Ksh currency, local contexts).
Overview
Algebra helps us use letters (called variables) to stand for numbers. In these notes you will learn how to read and write algebraic expressions, simplify them, expand and factor simple expressions, and solve basic linear equations used in everyday Kenyan contexts (shopping, sharing, measurement).
Learning objectives
- Understand what a variable is and identify terms, coefficients and constants.
- Simplify algebraic expressions by collecting like terms.
- Expand and factor simple linear expressions (single bracket).
- Solve one-step and two-step linear equations and check answers in context.
Key vocabulary
Variable: a letter (e.g., x, y) that represents a number. Term: a number, a variable, or a number multiplied by a variable (e.g., 3, x, 5x). Coefficient: the number in front of a variable (in 5x, coefficient = 5). Constant: a number without a variable (e.g., 7).
1. Writing and reading expressions
Examples:
3x means 3 times a number x.
x + 7 means an unknown number plus 7.
2p + 5q has two different variables p and q.
2. Simplifying by collecting like terms
Only terms with the same variable part are like terms (e.g., 4x and -2x). Add coefficients to combine.
Example 1: Simplify 3x + 5x - 2
Example 2: Simplify 7y - 2y + 4
3. Expanding and factoring (single bracket)
Use the distributive rule: a(b + c) = ab + ac
Expand: 2(x + 3) = 2x + 6
Factor: 6x + 9 = 3(2x + 3) because both terms share factor 3.
Tip: To factor, find the highest common factor (HCF) of numeric coefficients and common variable powers.
4. Solving linear equations (one-step and two-step)
An equation shows equality. We do the same operation on both sides to isolate the variable.
One-step (add/sub): x + 5 = 12 โ x = 12 - 5 = 7
One-step (mul/div): 4x = 20 โ x = 20 รท 4 = 5
Two-step: 3x + 4 = 16 โ 3x = 16 - 4 = 12 โ x = 12 รท 3 = 4
A matatu fare for a trip is Ksh x. If 4 friends share the fare and each pays Ksh 120, then 4x = 480 so x = 120. Thus a single fare is Ksh 120.
5. Worked examples with step-by-step boxes
Step 2: Calculate: 2x + 10
Final answer: 2x + 10
Step 2: Subtract 10 from both sides: 2x = 8
Step 3: Divide both sides by 2: x = 4
Check: 2(4 + 5) = 2 ร 9 = 18 โ
6. Visual: Number-line check for solutions
We can place the solution on a simple number line to show where x lies.
7. Practice questions
- Simplify: 5x - 2x + 9
- Expand: 3(y + 4)
- Factor: 8x + 12
- Solve: x/4 + 3 = 10
- Word problem: A packet of maize costs Ksh x. If 5 packets cost Ksh 850, find x.
Answers (click to reveal)
Common mistakes & tips
- Never combine unlike terms (e.g., x and 3 are not like terms).
- When expanding, multiply every term inside the bracket.
- When solving, do inverse operations in reverse order of operations: undo addition/subtraction then multiplication/division.
- Always check your solution by substituting back into the original equation.