Study guide: Mastering Algebra and Geometry Fundamentals

📋 Course Outline

1. Algebraic expressions and equations
2. Fractions, ratio and geometry

📖 1. Algebraic expressions and equations

🔑 Key Concepts & Definitions

• Algebraic expressions: An expression is a combination of numbers, variables, and operations that can be simplified or factorised.
• Equations with the unknown on both sides: An equation can have the variable term on both sides, so you must rearrange to isolate it.

📖 2. Fractions, ratio and geometry

🔑 Key Concepts & Definitions

• Mixed numbers: A mixed number combines a whole number with a fraction, often converted for calculations.
• Volume of a prism: A prism’s volume is found by multiplying the area of its cross-section by its length (height) between the faces.

⚠️ Common Pitfalls & Confusions

1. For equations with the unknown on both sides, sign errors can stop the variable from isolating correctly.
2. For mixed numbers, converting to improper fractions incorrectly leads to wrong fraction calculations.
3. For prism volume, mixing up which length to use (cross-section area versus prism length) gives the wrong scale.

✅ Exam Checklist

1. Simplify algebraic expressions.
2. Factorise algebraic expressions.
3. Solve equations where the unknown appears on both sides.
4. Expand double brackets.
5. Find the volume of a prism.
6. Solve money problems involving area.
7. Carry out calculations with mixed numbers.
8. Solve fractions and ratio problem-solving questions.