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#### Numbers

• Natural numbers are used for counting purposes. They are made up of all possible rational and irrational numbers.
• An integer is a whole number.
• A prime number is a number that is divisible only by itself and one. 1 is not a prime number.
• A rational number is a number that can be written as a fraction.
• An irrational number is a number that cannot be written as a fraction. E.g. Any recurring decimals; π, 3.3333333⋅⋅⋅
##### HCF and LCM
• Highest Common Factor and Lowest Common Multiple: From the Venn diagram above:

• HCF = Product of common factors of x and y.
• LCM = Product of all items in the Venn diagram.
• Prime Factorization
• This is just finding prime numbers that multiply together to make the original number.
• For example: • ∴ 48 = 2 × 2 × 2 × 2 × 3
##### SETS
• Definition of sets. For example:
• A = {x: x is a natural number}
• B = {(x, y): y = mx + c}
• C = {x: a ≤ x ≤ b}
• D = {a, b, c, …}
• Notations:
• n(A) = Number of elements in A
• ∈ = is an element of
• ∉ = is not an element of
• A’ = Compliment set of A
• Ø or {} = Empty set
• ξ or U = Universal set
• A ∪ B = Union of A and B
• A ∩ B = Intersection of A and B
• A ⊆ B = A is a subset of B
• A ⊂ B = A is a proper subset of B
• A ⊄ B = A is not a subset of B
• Set Representations:
• A ∩ B (the darker shade) • A ∪ B • ⊂ ‘is a subset of’ • b ∈ X • ξ = {a, b, c, d, e}  • Standard Form:
• 104 = 10000
• 103 = 1000
• 102 = 100
• 101 = 10
• 100 = 1
• 10-1 = 0.1
• 10-2 = 0.01
• 10-3 = 0.001
• 10-4 = 0.0001
• 10-5 = 0.00001
##### RATIO & PROPORTION
• Ratio is used to describe a fraction. E.g. 3 : 1
• Foreign exchange: Money changed from one currency to another using proportion. For example:
• Convert \$22.50 to Dinars
• \$1 : 0.30KD
• \$22.50 : 6.75KD
• Map Scales: Using proportion to work out map scales. For example:
• 1 km = 1000 m
• 1 m = 100 cm
• 1 cm = 10 mm
• Direct Variation
• y is proportional to x
• y ∝ x
• ∴ y = kx
• Inverse Variation
• y is inversely proportional to x
• y ∝ 1/x
• ∴ y = k/x
• Percentage
• This is a convenient way to express fractions.
• Per cent means per 100
• Percentage increase/decrease = Actual increase/decrease/Original Amount
• Simple Interest:
• I = PRT/100
• where P is Principal
• R is Rate
• T is Time
• Compound Interest:
• A = P(1 + R/100)n
• where P is Principal
• R is Rate
• T is Time
• A is Amount
• Speed, Distance, & Time
• Speed = Distance/Time
• Average Speed = Total Distance/Total Time
• ———–
• Units of speed: km/hr, m/s
• Units of distance: km, m
• Units of time: hr, mins, secs
• ———–
• 1 km/hr × 5/18 = m/s
• 1 m/sec × 18/5 = km/hr
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