ALGEBRA Notes, Quizzes & Revision
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SUBTOPIC: ALGEBRA
Topic: topic_name_replace | Subject: subject_replace
Context: Kenyan examples · Target age: age_replace
1. What is Algebra?
Algebra uses letters (like x, y) to stand for numbers. It helps us write and solve rules about numbers.
Example: 2x + 3 means "two times a number x, plus three".
2. Why learn Algebra?
- To solve everyday problems (money, measurements, sharing).
- To build skills for science, engineering, business.
- It appears in KCSE/KCPE style problems (logical steps, unknowns).
3. Key ideas
Variable: a letter that stands for a number (e.g. x).
Expression: combination of numbers, letters and operations (e.g. 3x + 5).
Equation: statement that two expressions are equal (e.g. 3x + 5 = 20).
Like terms: terms that have the same variable part (2x and 5x are like terms).
4. Simplifying expressions (basic)
Steps:
- Collect like terms: add or subtract coefficients of same variable.
- Do multiplications and divisions first (if present).
- Write the expression in simplest form.
5. Solving simple linear equations (one step at a time)
Rule: Do the same operation to both sides until the variable is alone.
Worked example:
Solve 2x + 5 = 17.
Step 1: Subtract 5 from both sides: 2x + 5 - 5 = 17 - 5 โ 2x = 12.
Step 2: Divide both sides by 2: x = 12 รท 2 = 6.
Answer: x = 6.
Step 2: Divide both sides by 2: x = 12 รท 2 = 6.
Answer: x = 6.
6. Kenyan context example (using Ksh)
Problem: A matatu fare for a short town trip is Ksh (x) and a student gets a discount of Ksh 30. If the student pays Ksh 70, find x.
Equation: x - 30 = 70 โ x = 70 + 30 = 100.
So the normal fare is Ksh 100.
So the normal fare is Ksh 100.
7. Expanding brackets (use distributive law)
Rule: a(b + c) = ab + ac.
Example: 3(x + 4) = 3x + 12.
8. Practice questions
- Simplify: 5x + 2x - 4.
- Solve: x + 12 = 25.
- Solve: 4x = 28.
- Expand: 2(x + 5).
- If the cost of a loaf of bread is Ksh x and you buy 3 loaves for Ksh 270, find x.
- Simplify: 6y - 2y + 8.
9. Answers
1) 7x - 4
2) x = 13
3) x = 7
4) 2x + 10
5) 3x = 270 โ x = 90 (so one loaf costs Ksh 90)
6) 4y + 8
2) x = 13
3) x = 7
4) 2x + 10
5) 3x = 270 โ x = 90 (so one loaf costs Ksh 90)
6) 4y + 8
10. Tips & common mistakes
- Always do the same thing to both sides of an equation.
- Combine like terms only (do not add x and 2 or x and y).
- Keep steps neat โ useful during exams (KCSE/KCPE style marking).
- Check your answer by substituting back into the original equation.
Quick reference:
- Like terms: 2x and 5x โ add coefficients.
- Distributive: a(b + c) = ab + ac.
- To solve ax + b = c: subtract b, then divide by a.
- Distributive: a(b + c) = ab + ac.
- To solve ax + b = c: subtract b, then divide by a.
Practice more with real Kenyan prices (Ksh) and simple word problems to build confidence. Good luck!