#### 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

- A ∩ B (the darker shade)

- Standard Form:
- 10
^{4}= 10000 - 10
^{3}= 1000 - 10
^{2}= 100 - 10
^{1}= 10 - 10
^{0}= 1 - 10
^{-1}= 0.1 - 10
^{-2}= 0.01 - 10
^{-3}= 0.001 - 10
^{-4}= 0.0001 - 10
^{-5}= 0.00001

- 10

**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

- I =

- Compound Interest:
- A = P(1 +
^{R}/_{100})^{n} - where P is Principal
- R is Rate
- T is Time
- A is Amount

- A = P(1 +

- 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

- Speed =