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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}
    • A’ is shaded
  • 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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