Study guide: Mastering Essential Math and English Skills

📋 Course Outline

1. Core English skills for exams
2. Algebra and linear equations foundations
3. Fractions, percentages and decimals
4. Geometry formulas and problem-solving strategies

📖 1. Core English skills for exams

🔑 Key Concepts & Definitions

• English grammar: English grammar : The system of rules that governs word forms, sentence structure, and meaning in English.
• Reading comprehension: Reading comprehension : The ability to understand and extract meaning from written texts.
• Paragraph writing: Paragraph writing : The skill of organizing sentences into a clear, focused paragraph with a main idea.
• Scientific vocabulary: Scientific vocabulary : The set of subject-specific words used to describe ideas accurately in science contexts.

📝 Essential Points

• Use grammar to keep subject–verb agreement and correct tense so your meaning stays clear.
• Answer reading questions by locating evidence in the text, not by guessing from general knowledge.
• Write paragraphs with a clear main idea and supporting sentences that stay on topic.
• Use scientific vocabulary precisely so your explanations sound accurate and exam-ready.
• Manage time by doing quick passes first, then returning to harder questions with remaining minutes.

💡 Memory Hook

Grammar = structure; comprehension = evidence; writing = focus; vocabulary = precision.

📖 2. Algebra and linear equations foundations

🔑 Key Concepts & Definitions

• Algebra: Algebra : A branch of math that uses symbols to represent numbers and solve for unknowns.
• Linear equations: Linear equations : Equations where the highest power of the variable is 1.
• Expanding brackets: Expanding brackets : Distributing multiplication over parentheses to rewrite expressions in simpler form.
• Solving equations step-by-step: Solving equations step-by-step : A method that applies the same operation to both sides to isolate the unknown.

📝 Essential Points

• Solve linear equations by isolating the variable using inverse operations applied to both sides.
• When expanding brackets, multiply every term inside the parentheses by the factor outside.
• Use word problems by translating phrases into algebraic expressions before solving.
• Check your solution by substituting it back into the original equation to confirm equality.
• Avoid common errors like sign mistakes when distributing a negative or forgetting to multiply all terms.

💡 Memory Hook

Step-by-step: do the same thing to both sides until the variable stands alone.

📖 3. Fractions, percentages and decimals

🔑 Key Concepts & Definitions

• Fractions: Fractions : Numbers that represent parts of a whole, written as a numerator over a denominator.
• Percentages: Percentages : A way to express a fraction of 100 as a number followed by %.
• Decimals: Decimals : Numbers written in base 10 using a decimal point to show place value.
• Simplifying fractions: Simplifying fractions : Reducing a fraction to an equivalent form with smaller numerator and denominator.

📝 Essential Points

• Convert between fractions, decimals, and percentages by using the relationships over 100 and place value.
• To convert a percentage to a decimal, divide by 100.
• To convert a decimal to a percentage, multiply by 100.
• Simplify fractions by dividing numerator and denominator by their greatest common factor.
• When comparing or combining values, keep them in the same form before calculating.

💡 Memory Hook

% ↔ decimal: move the decimal point two places (÷100 or ×100).

📖 4. Geometry formulas and problem-solving strategies

🔑 Key Concepts & Definitions

• Basic geometry formulas: Basic geometry formulas : Standard equations for common shapes used to find lengths, areas, or perimeters.
• Basic area formulas: Basic area formulas : Formulas that calculate the area of common 2D shapes such as rectangles and triangles.
• Problem-solving methods: Problem-solving methods : Structured approaches for turning a geometry question into the right calculations.
• Calculator basics: Calculator basics : Knowing how to enter expressions and use basic functions accurately for exam calculations.

📝 Essential Points

• Use the correct area formula by matching the shape (e.g., rectangle vs triangle) before substituting numbers.
• For worded geometry problems, identify given lengths and what quantity the question asks you to find.
• Apply problem-solving methods by writing the formula first, then substituting values, then simplifying.
• Use calculator basics to avoid input errors, especially with brackets and negative numbers.
• Common mistakes include mixing up units and using the wrong formula for the shape.

💡 Memory Hook

Geometry = choose the right formula, then substitute carefully.

⚠️ Common Pitfalls & Confusions

1. Mixing up percentage and decimal conversions by using the wrong direction (×100 vs ÷100).
2. Sign errors when expanding brackets or distributing a negative across parentheses.
3. Skipping the step-by-step isolation in linear equations and losing track of operations.
4. Using an area formula for the wrong shape or forgetting to check units (cm vs m).
5. Guessing in reading comprehension without locating supporting evidence in the text.

✅ Exam Checklist

1. Demonstrate correct English grammar in sentences you write and in answers you interpret.
2. Answer reading comprehension questions using evidence from the text and clear interpretation.
3. Write a focused paragraph with a main idea and supporting sentences that match the prompt.
4. Solve linear equations by isolating the variable with step-by-step inverse operations.
5. Expand brackets correctly by distributing multiplication to every term inside parentheses.
6. Translate word problems into algebraic expressions before solving.
7. Convert between fractions, decimals, and percentages using the correct ×100 or ÷100 relationships.
8. Simplify fractions by reducing numerator and denominator with a common factor.
9. Use basic geometry area formulas by matching the formula to the correct shape.
10. Solve geometry problems by identifying given values, choosing the right formula, substituting, and simplifying.
11. Use calculator basics carefully, especially with brackets and negative numbers.
12. Apply exam strategies such as time management, checking work, and avoiding common mistakes.