ZIMSEC O Level · Mathematics · Form 1
Numbers are grouped into sets. Knowing which set a number belongs to helps you choose the right method.
- Natural numbers: 1, 2, 3, … Whole numbers add 0.
- Integers: …, −2, −1, 0, 1, 2, … (positive and negative whole numbers).
- Rational numbers can be written as a fraction a/b (b ≠ 0), e.g. 3/4, 0.5, −2. Irrational numbers cannot, e.g. √2 and π.
- A prime number has exactly two factors, 1 and itself: 2, 3, 5, 7, 11, 13, … (1 is not prime).
Factors, multiples, HCF and LCM
Write each number as a product of prime factors. The HCF uses the common primes with the lowest powers; the LCM uses every prime with the highest powers.
Worked example: Find the HCF and LCM of 36 and 60.
36 = 2² × 3² and 60 = 2² × 3 × 5
HCF = 2² × 3 = 12
LCM = 2² × 3² × 5 = 180
Directed numbers and order of operations
Same signs multiply or divide to give a positive answer; different signs give a negative answer: (−4) × (−3) = 12, (−12) ÷ 3 = −4.
Work in the order Brackets, Indices (powers), Division and Multiplication, Addition and Subtraction (BODMAS).
Worked example: Evaluate 18 − 3 × (2 + 4)².
Brackets: 2 + 4 = 6. Index: 6² = 36. Multiply: 3 × 36 = 108. Subtract: 18 − 108 = −90.
Check yourself
- Express 84 as a product of prime factors.
- Find the LCM of 12, 18 and 30.
- Evaluate (−5)² − 2 × (−3).
Show answers
- 84 = 2² × 3 × 7
- 180
- 25 + 6 = 31
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