Maths Revision

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Pythagoras' Theorem

The formula for Pythagoras' Theorem is a2+b2=c2. Pythagoras' Theorem proves that by making the sides of right angled triangles squares, the sum of the area of the squares of the shorter sides equal the area of the hypotenuse's square. This theorem can be used to calculate the length of the hypotenuse.

Hypotenuses:

The hypotenuse is the longest side of a right-angled triangle. It is never next to the actual right angle, but opposite it.

Examples:

Another diagram which also proves that Pythagoras' Theorem is correct is Perigal's Dissection, which put the smallest of the two small squares in the centre of the hypotenuse's square and cut the larger square of the short sides into four triangles. Common numbers used with triangles to demonstrate Pythagoras' Theorem include 3, 4 and 5, and 5, 12 and 13.

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Circles:

"A circle is a curve that is the locus of a point that moves from a fixed point at a fixed distance."

Arc: a part of the circumference. The major arc is the longer arc and the minor arc is the shorter arc.

Circumference: the perimeter of a circle whose length is equal to 2πr.

Chord: a straight segment which joins two points on a circle.

Diameter: a chord which runs across the centre of a circle.

Radius: the distance between the centre of a circle and any point on the circumference.

Sector: a region in a circle between two radii and any part of the arc they cut off.

Segment: a region in a circle between a chord and the arc the chord cuts off. It can be divided into two segments: the minor segment which is the region between the chord and the minor arc and the major segment which is the region between the chord and the major arc.

Tangent: a line which touches the outside of the circle at one point (the point of contact.)

Formulae:

Circumference: πd

Area: πr2

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Probability:

Probability is predicting whether an event is certain to happen or impossible (or inbetween; likely, unlikely etc.)

Mutually Exclusive Outcomes: events that can't happen at the same time.

Independent Events: events that aren't affected by previous events.

Rules:

The 'OR' Rule: P(A or B) = P(A) + P(B). This means: the probability of A or B is equal to the probability of A plus the probability of B. This is only true when the events are mutually exclusive. If they aren't, this rule can't work as some probabilities get counted twice.

The 'AND' Rule: P(A and B) = P(A) + P(B). This means: the probability of A and B TOGETHER is equal to the probability of A multiplied by the probability of B. This only works if the events are independent. An example of this is P (Heads + Black Card) = 1/2 * 1/2 = 1/4.

Set Notation:

A Intersection: members in BOTH A and B. Symbol - ∩

A Union B: members in A and B (or either). Symbol - U

A Complement: members NOT in A. Symbol - '

Union = Or

Intersection = And

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Percentages:

Quick Calc: 1 lot of start value multiplied by 0.(*insert percentage*)

Quick Calc (Decrease): n (start value) x 0.(*difference between percentage and 100*)

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Data Handling:

Types of Data:

Discrete: countable data. Only CERTAIN values. (e.g: number of white cars on road)

Continuous: measurable data. (e.g: height)

Quantitative: numerical data. (e.g: length)

Qualitative: non-numerical. (e.g: eye colour)

Stem and Leaf:

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Transformation:

Rotation: