Pre IB Math

Natural Numbers, ℕ

Positive integers starting from 1, used for counting and ordering objects. do not include 0, fractions, decimals, or negative numbersExample: 1, 2, 3, 4...

Intergers, ℤ

all positive numbers, negative numbers, and 0. They can never be a fraction or decimal.

rationals, ℚ

The set of numbers that can be expressed as a ratio of two integers. It includes fractions, terminating decimals, and repeating decimals. Rational numbers can be expressed as a ratio between two integers. The rational numbers include all the integers because any integer z can be expressed as the ratio z/1.

Irrationals

Numbers that cannot be expressed as a simple fraction, with an infinite decimal expansion that neither repeats nor terminates. Example: √2.

Real numbers, ℝ

The set of numbers that contain all of the rational numbers and all of the irrational numbers. The real numbers are "all the numbers" on the number line. There are infinitely many real numbers, just as there are infinitely many numbers in each of the other sets of numbers.

relationship in the number system

Système International Mass

1kg = 1000g. 1g = 1000mg. 1mg = 1000μg

Système International Time

1min = 60s. 1h = 3600s.

Système International Length

1km = 1000m. 1m = 100cm. 1cm = 10mm. 1mm = 1000µm. 1µm = 1000nm

Système International Area

square meter (m²) the amount of surface a two-dimensional shape can cover. 1m² = 10,000cm². 1km² = 1,000,000m².

Système International Volume

the amount of three-dimensional space an object occupies. Cubic Meter (m³). 1m³ = 1,000,000cm³. 1L = 1,000cm³

Speed

m/s

Absolute Error

|Measured Value - True Value|

Percentage Error

(|Measured Value - True Value|/True Value) x 100

Factors

A number that divides exactly into another number without a remainder. It is often helpful to write them in pairs. Ex: for 20: 1, 2, 4, 5, 10, 20

Multiples

The result of multiplying a number by and integer. It is the times table of a number. Multiples of 4: 4, 8, 12, 16, 20

Prime number

number that has only two factors which are 1 and itself. 2, 3, 5, 7, 11, 13

Pythagoras theorem

c² = a² + b²

if the square of the length of the longest side of a triangle is _____ to the sum of the squares of the other two sides, then the triangle is a right triangle

equal

midpoint formula

((x₁ + x₂) / 2, (y₁ + y₂) / 2)

distant between two points

√[(x2 - x1)^2 + (y2 - y1)^2]

triangle sum theorem

the sum of all three angles in triangle equals 180 degrees