Algebra Notes, Quizzes & Revision
📘 Revision Notes • 📝 Quizzes • 📄 Past Papers available in app
Subject: subject_replace
Topic: topic_name_replace
Subtopic: Algebra — tailored for Kenyan learners aged age_replace
- Understand key terms: variable, coefficient, constant, term, expression, equation.
- Simplify algebraic expressions (collect like terms, use distributive law).
- Evaluate expressions given values of variables.
- Solve simple linear equations (one variable) and set up equations from word problems.
Variable (a symbol like x), coefficient (number multiplied by a variable, e.g., 3 in 3x), constant (fixed number), term (a part of an expression), like terms (same variable power), expression (no =), equation (has = sign).
- Collect like terms: 3x + 4x = 7x; 5 - 2 = 3.
- Distributive property: a(b + c) = ab + ac. Example: 3(x + 2) = 3x + 6.
- To evaluate an expression, replace variables with given numbers and compute.
- To solve an equation, perform the same operation on both sides until the variable is alone.
To solve 2x + 5 = 13, remove 5 from both sides → 2x = 8, divide both sides by 2 → x = 4.
Simplify: 4x + 3x − 7 + 2
Step 1: Combine like terms: 4x + 3x = 7x. Step 2: Combine constants: −7 + 2 = −5. Answer: 7x − 5.
Evaluate: 2a − 3 when a = 5
Substitute a = 5: 2×5 − 3 = 10 − 3 = 7.
Solve: 3(x − 2) = 9
Step 1: Expand: 3x − 6 = 9. Step 2: Add 6 to both sides: 3x = 15. Step 3: Divide by 3: x = 5.
- Mary buys x mangoes at KSh 20 each. She pays KSh 300. Form and solve an equation to find x.
- A matatu fare is KSh 40 per person. Four friends pay a total of 160. If one person paid x, write the equation and find x (check consistency).
- Age problem: Aisha is 3 years older than her brother. If their ages add to 27, find their ages.
Quick solution hints: (1) 20x = 300 → x = 15. (3) Let brother = b, Aisha = b + 3. b + (b + 3) = 27 → 2b + 3 = 27 → 2b = 24 → b = 12, Aisha = 15.
- Simplify: 5y + 2 − 3y + 7.
- Evaluate: 4m + 1 when m = 3.
- Solve: 2x + 7 = 15.
- Solve: (x/2) + 3 = 7.
- Form and solve: A farmer has p baskets. Each basket holds 12 oranges. If total oranges are 180, find p.
- Word problem: A school sells pens at KSh 12 each. If a student buys x pens and pays KSh 96, how many pens did they buy?
- 1 → 5y − 3y + 2 + 7 → 2y + 9.
- 2 → 4×3 + 1 = 13.
- 3 → 2x + 7 = 15 → 2x = 8 → x = 4.
- 4 → (x/2) + 3 = 7 → x/2 = 4 → x = 8.
- 5 → 12p = 180 → p = 15.
- 6 → 12x = 96 → x = 8 pens.
- Write each step clearly; check by substituting your answer back into the original equation.
- Use everyday contexts (money, quantities, ages) to form equations — this helps understanding.
- When collecting like terms, sort terms by variable (e.g., terms with x together, constants together).
- Use a simple balance sketch when solving equations — it helps keep both sides equal.