Mathematics EOYE Full Syllabus
Revision Notes
1. Order of Operations & Number Concepts
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BODMAS: Brackets, Orders (powers/roots), Division, Multiplication, Addition,
Subtraction
Working with Fractions, Decimals, and Integers:
- Add/Subtract: Convert to like denominators.
- Multiply: Multiply numerators and denominators.
- Divide: Flip the second fraction and multiply.
Decimals:
- Terminating: Ends after some digits (e.g., 0.25)
- Recurring: Repeats (e.g., 0.333...)
- Non-Recurring: Doesn’t repeat or end (irrational numbers)
2. Fractions, Decimals & Percentages
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Conversions:
- Fraction to Decimal: Divide numerator by denominator
- Decimal to Percentage: Multiply by 100
- Percentage to Fraction: Write over 100 and simplify
Percentage of Quantity: (percentage/100) × total amount
Express as a Percentage: (part/whole) × 100
Profit & Loss:
- Profit = Selling Price - Cost Price
- Profit % = (Profit / Cost Price) × 100
- Discount = Marked Price - Selling Price
- Discount % = (Discount / Marked Price) × 100
Zakat: 2.5% of total eligible wealth
Ushr:
- 10% for natural irrigation
- 5% for artificial irrigation
3. Sequences and Patterns
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Term-to-Term Rule: How to move from one term to the next
Position-to-Term Rule (nth Term): Formula for the nth term
Example: Sequence: 3, 6, 9, 12 → nth term = 3n
Fibonacci Sequence: Each term = Sum of previous 2 terms
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Finding Terms:
- First few terms: Substitute n = 1, 2, 3, ...
- Finding nth term: Plug into nth term formula
4. Algebraic Expressions & Factorization
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Key Terms:
- Variable: Letter representing a number
- Constant: A fixed value
- Expression: Combination of terms
- Equation: Expression with '=' sign
- Inequality: Uses <, >, ≤, ≥
Simplify Expressions: Combine like terms
Distributive Property: a(b + c) = ab + ac
Expand:
- Monomial × Monomial: Multiply directly
- Monomial × Binomial: Distribute
- Binomial × Binomial (FOIL): First, Outer, Inner, Last
Factorization:
- Common Factors: Take out common term from all
5. Algebraic Equations
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Solving Linear Equations:
- Keep variable on one side
- Balance equation
- Deal with fractions by LCM or cross-multiplying
Example: x/4 = 2 → Multiply both sides by 4 → x = 8
6. Coordinate Geometry
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4 Quadrants: (+,+), (-,+), (-,-), (+,-)
Plotting Points: (x, y)
Graph of Linear Equations:
- y = mx (passes through origin)
- y = mx + c (y-intercept = c)
- Horizontal line: y = a
- Vertical line: x = b
- Finding x & y from graph: Use the graph line values
7. Area, Perimeter, Surface Area & Volume
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2D Shapes
Square: Area = a², Perimeter = 4a
Rectangle: Area = l × w, Perimeter = 2(l + w)
Triangle: Area = 1/2 × b × h
Parallelogram: Area = b × h
Trapezium: Area = 1/2 × (a + b) × h
Circle: Area = πr², Circumference = 2πr
Compound Shapes: Split into basic shapes and add/subtract areas accordingly
3D Shapes
Rectangular Prism: Volume = l × w × h, Surface Area = 2(lw + lh + wh)
Triangular Prism: Volume = 1/2 × b × h × l, Surface Area = Area of triangles + Area of
rectangles
Cylinder: Volume = πr²h, Surface Area = 2πr² + 2πrh, Lateral Area = 2πrh
8. Set Theory
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Descriptive Set: Written in words
Notation: {}, ∈, ∉
Types: Proper/Improper Subset, Equal/Equivalent Sets, Disjoint/Overlapping Sets
Venn Diagrams:
- Union (A ∪ B): All elements in A or B
- Intersection (A ∩ B): Elements common to both
- Complement (A'): Not in A
Number of Subsets: 2ⁿ, Proper Subsets = 2ⁿ - 1
9. Probability
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Basic Probability: P(E) = (favorable outcomes) / (total outcomes)
Complement: P(not E) = 1 - P(E)
Word Problems: Apply logic based on outcomes and total possibilities