Perfect square of a trinomial

Perfect square of a trinomial:

If all the terms of the polynomial have a common factor, we take out the common factor and factorise.
If the polynomial can be expressed as the difference of two squares,
we use a² - b² = (a + b) (a - b).

• If all the terms of the polynomial have a common factor, we take out the common factor and factorise .
• If all the terms of the polynomial have a common factor, we take out the common factor and factorise .

• If the polynomial can be expressed as the difference of two squares,

we use a² - b² = (a + b) (a - b)

• Quadratic trinomials of the form x² + ax + b can be factorised using the identity. (x + a) (x + b) = x² + x(a + b) + ab.

• When the trinomial is ax² + bx + c and , we follow the following steps. We find two factors whose sum is b, and whose product is a x c.

We split the middle term using these two factors and factorise by grouping the terms.

• If the polynomial can be expressed as the sum or difference of two cubes we use the following identities.

a³ + b³ = (a + b) (a² - ab + b²)
a³ - b³ = (a - b) (a² + ab + b²)

What are equal and parallel line?

What are equal and parallel line?


If two parallel lines are cut by a transverse, the alternate angles are equal.

and
These are two pairs of alternate angles.



A transversal intersects two lines. If the alternate angles are equal, then the lines are parallel.
If or then AB is parallel to CD.

Divisibility rules

Divisibility rules:

• Numbers ending with 0‚ 2‚ 4‚ 6 or 8 are divisible by 2
• If the sum of the digits of a given number is divisible by 3, the number is divisible by 3.
• If the number formed by the end two digits of a given number is divisible by 4‚ then the number will be divisible by 4.
• Numbers ending with 0 or 5 are divisible by 5
• If the number formed by the end three digits of a given number is divisible by 8‚ then the number will be divisible by 8.
• If the sum of the digits of a number is divisible by 9, the number is divisible by 9.
• Numbers ending with 0 are divisible by 10
• If the difference of the sums of the digits in alternate places is divisible by 11, the number is divisible by 11.

Addition Rule of Probability

The Addition Rule:

Probability is the probably that event will happen – how likely the event will happen. The addition rule for probability: a statistical property that states the probability of one and/or two events occurring at the same time is equal to the probability of the first event occurring, plus the probability of the second event occurring, minus the probability that both events occur at the same time.
If events A and B are mutually exclusive or disjoint, then P(A U B) = P(A) + P(B)
Otherwise, P(A U B) = P(A) + P(B) – P(A ∩ B).

Quadrants

Quadrants:




Let X'OX and Y'OY perpendicular coplanar lines intersecting each other at O. We refer X'OX as x-axis and Y'OY as y-axis. It is clear from the adjoining figure, that these two lines divide the plane into four equal parts, each part is called a Quadrant.
The four Quadrants are:
XOY - first Quadrant
YOX' - second Quadrant
X'OY' - third Quadrant
Y'OX - fourth Quadrant

Trigonometry Heights and Distances

Trigonometry Heights and Distances:

• The word "Trigonometry" is derived from the two Greek words meaning measurements or solution of triangles. Trigonometry which is a branch of mathematics that deals with the ratio between the sides of a right triangle and its angles.
• Trigonometry is the study about relationships between the sides and angles of a triangle.
• Trigonometry is used in surveying and to determine Heights and Distances, in navigation it is to determine the location and the distances, and in the fields like nondestructive testing for determining things such as the angle for reflection or refraction of an ultrasound wave.

Types of Angles

Types of angles: