ZIMSEC O-Level Mathematics (4004)

Number, Fractions and Estimation: notes

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Types of Number

Prime number: a number with exactly two factors, 1 and itself. 2, 3, 5, 7, 11 are prime. 1 is not prime.
Factor and multiple: 3 is a factor of 12; 12 is a multiple of 3.
HCF: the highest common factor, the biggest number that divides both. HCF of 12 and 18 is 6.
LCM: the lowest common multiple, the smallest number both divide into. LCM of 4 and 6 is 12.
Prime factorisation: write a number as a product of primes. 60 = 2 x 2 x 3 x 5.

BODMAS: Brackets, Orders (powers), Division and Multiplication, Addition and Subtraction. 2 + 3 x 4 = 14, not 20.
Directed numbers: minus times minus is plus. (-3) x (-2) = 6. Subtracting a negative adds: 5 - (-2) = 7.
Adding fractions: make the denominators the same first. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Dividing by a fraction: flip it and multiply. 3 divided by 1/2 = 3 x 2 = 6.

Decimal places: count digits after the point. 3.476 to 2 d.p. is 3.48.
Significant figures: count from the first non-zero digit. 0.004572 to 2 s.f. is 0.0046.
Estimate: round each number to 1 s.f. first. 48 x 21 is about 50 x 20 = 1000.
Bounds: a length of 6 cm to the nearest cm lies from 5.5 cm up to (not including) 6.5 cm.