SAT MATHS REVISION NOTES
PART 1 – Numbers & Arithmetic
1. Integers
Concept: Whole numbers, their negatives, and zero.
Key Points
• Positive (>0), Negative (<0), Zero
• Even numbers are divisible by 2.
• Odd numbers are not divisible by 2.
• Consecutive integers differ by 1.
• Opposite numbers have equal absolute value.
Example
• −5, −2, 0, 3, 8
2. Factors & Multiples
Concept: Factors divide a number exactly; multiples are obtained by multiplying.
Key Points
• Every number has at least 1 and itself as factors.
• Multiples continue infinitely.
• Factors are always less than or equal to the number.
• Multiples can be larger than the number.
Example
• Factors of 12 → 1, 2, 3, 4, 6, 12
• Multiples of 12 → 12, 24, 36...
,3. Prime Numbers
Concept: Numbers with exactly two factors.
Key Points
• 2 is the only even prime.
• 1 is neither prime nor composite.
• Composite numbers have more than two factors.
• Prime factorization expresses a number as a product of primes.
Example
• Prime: 2, 3, 5, 7, 11
• Composite: 4, 6, 8, 9
4. GCF & LCM
Concept
• GCF = Largest common factor.
• LCM = Smallest common multiple.
Key Points
• Use prime factorization for large numbers.
• GCF is used for simplifying.
• LCM is used for common denominators and repeating events.
Example
• GCF(18, 24) = 6
• LCM(18, 24) = 72
5. Divisibility Rules
Key Points
, • 2: Last digit even
• 3: Sum of digits divisible by 3
• 4: Last 2 digits divisible by 4
• 5: Ends in 0 or 5
• 6: Divisible by 2 and 3
• 8: Last 3 digits divisible by 8
• 9: Sum of digits divisible by 9
• 10: Ends in 0
6. Fractions
Concept: Represents part of a whole.
Key Points
• Simplify before solving.
• Common denominator needed for addition/subtraction.
• Multiply numerators and denominators directly.
• Divide by multiplying by the reciprocal.
Example
• 2/3 + 1/6 = 5/6
7. Decimals
Key Points
• Line up decimal points when adding/subtracting.
• Multiply normally, then place decimal.
• Move decimal when multiplying/dividing by powers of 10.
• Convert between fractions and decimals when useful.
8. Percentages
Concept: Per hundred.
Key Points
, • 50% = 1/2
• 25% = 1/4
• 20% = 1/5
• 10% = divide by 10
• Percent can be converted to decimal or fraction.
Example
• 15% of 80 = 12
9. Ratios & Proportions
Concept
PART 1 – Numbers & Arithmetic
1. Integers
Concept: Whole numbers, their negatives, and zero.
Key Points
• Positive (>0), Negative (<0), Zero
• Even numbers are divisible by 2.
• Odd numbers are not divisible by 2.
• Consecutive integers differ by 1.
• Opposite numbers have equal absolute value.
Example
• −5, −2, 0, 3, 8
2. Factors & Multiples
Concept: Factors divide a number exactly; multiples are obtained by multiplying.
Key Points
• Every number has at least 1 and itself as factors.
• Multiples continue infinitely.
• Factors are always less than or equal to the number.
• Multiples can be larger than the number.
Example
• Factors of 12 → 1, 2, 3, 4, 6, 12
• Multiples of 12 → 12, 24, 36...
,3. Prime Numbers
Concept: Numbers with exactly two factors.
Key Points
• 2 is the only even prime.
• 1 is neither prime nor composite.
• Composite numbers have more than two factors.
• Prime factorization expresses a number as a product of primes.
Example
• Prime: 2, 3, 5, 7, 11
• Composite: 4, 6, 8, 9
4. GCF & LCM
Concept
• GCF = Largest common factor.
• LCM = Smallest common multiple.
Key Points
• Use prime factorization for large numbers.
• GCF is used for simplifying.
• LCM is used for common denominators and repeating events.
Example
• GCF(18, 24) = 6
• LCM(18, 24) = 72
5. Divisibility Rules
Key Points
, • 2: Last digit even
• 3: Sum of digits divisible by 3
• 4: Last 2 digits divisible by 4
• 5: Ends in 0 or 5
• 6: Divisible by 2 and 3
• 8: Last 3 digits divisible by 8
• 9: Sum of digits divisible by 9
• 10: Ends in 0
6. Fractions
Concept: Represents part of a whole.
Key Points
• Simplify before solving.
• Common denominator needed for addition/subtraction.
• Multiply numerators and denominators directly.
• Divide by multiplying by the reciprocal.
Example
• 2/3 + 1/6 = 5/6
7. Decimals
Key Points
• Line up decimal points when adding/subtracting.
• Multiply normally, then place decimal.
• Move decimal when multiplying/dividing by powers of 10.
• Convert between fractions and decimals when useful.
8. Percentages
Concept: Per hundred.
Key Points
, • 50% = 1/2
• 25% = 1/4
• 20% = 1/5
• 10% = divide by 10
• Percent can be converted to decimal or fraction.
Example
• 15% of 80 = 12
9. Ratios & Proportions
Concept
