Math Portion Daily These questions repeat in PST test

 Math Portion Daily These questions repeat in PST test.

Mathematics Notes

zero is neither positive nor negative.

Zero is an even number.

Whole number starts with zero.

Negative numbers are numbers that are smaller than zero, and positive numbers are numbers that are bigger than zero.

Zero is not a natural number.

Natural numbers start with 1.

Natural numbers are called counting numbers and cardinal numbers.

1 is a Natural Number.

1 is the cardinal number.

1 is an odd number.

1 is the whole number.

Number 1 is not a prime number.

1 is not a composite number.

One is the only positive integer (whole number) which is neither prime (exactly two factors: one and itself) nor composite (more than two factors).

The smallest prime Number is  2.

Smallest composite number is 4.

In Maths, integers are the numbers which can be positive, negative or zero, but cannot be a fraction or decimal.

Digits 10 symbols .

Numeral : group of digits.

Place Value : Local value due to place

Face value : Actual value of digit

Types of Numbers

Natural Numbers 

Counting numbers , cardinal numbers.

1,2,3,3,4,5,6,7,8,9

Ordinal numbers : in order

First, second ,third, eleventh, twenty first 

Whole Numbers : zero , all natural Numbers

0,1,2,3,4,5,6,7,8,9

Integers : natural Number , positive numbers, whole Number, negative numbers. Not decimals and not fractions.

Non negative integers : 0,1,2,2

Non Positive integers 0,-1,-2,-3,

Prime Number : factor 1 and itself

Smallest prime : 2

2,3,5,7,11

Composite Numbers : More than two factors ,not prime 

Smallest composite : 4

4,6,8,9,10,12,14

Even number : divisible by 2

Odd number : not divisible by 2

Co Prime : Highest Common factor 1

Angle

Straight line 180

Straight angle 180

Triangle all angles 180

Circle 360

Square 360

Rectangle 360

Complete angle 360

Acute angle smaller than 90 

Right Angle equal to 90

Obtuse angle bigger than 90 smaller than 180

Reflex bigger than 180 smaller than 360

Triangle all angles 180

Triangle

All angles equal 180

Types on Side based:

Equilateral all sides equal size

Isosceles two sides equal

Scalene all sides and angles unequal

Types of Angle based 

Acute angle triangle : every angle smaller than 90

Right angle triangle = one angle 90

Obtuse angle triangle = angles bigger than 90

Complementary angles are pair angles with the sum of 90 degrees.

Two angles are called supplementary when their measures add up to 180 degrees.

Thus two angles are said to be adjacent angles, if they have a vertex, a common arm.

The side opposite the right angle is called the hypotenuse. 

What is the meaning of a right angle triangle?

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.

Line

Set of infinite points.

Line segment

a part of a line which has two endpoints called the line segment.

Vertex (of an angle) The vertex of an angle is the common endpoint of two rays that form the angle.

The circumference is the distance measured around a circle.

380 degrees

Diameter is the distance from one side to the other crossing center.

Diameter x pi = Circumference

Pi is the ratio of circumference and diameter.

Circumference divided by diameter= pi

Diameter = 2r (Radius)

Circumference = Pi x D

= Pi x 2r 

= Pi 2r 

If the radius of the circle is 4cm then find its circumference.

Given: Radius = 4cm

Circumference = 2πr

= 2 x 3.14 x 4

= 25.12 cm

What is a quadrilateral shape?

A quadrilateral is a polygon that has exactly four sides. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.)

A quadrilateral should be a closed shape with 4 sides. All the internal angles of a quadrilateral sum up to 360°.

Properties of a Quadrilateral:

A quadrilateral has 4 sides, 4 angles and 4 vertices.

A quadrilateral can be regular or irregular.

The sum of all the interior angles of a quadrilateral is 360°.

Square.

All  the  four  sides  are  equal .

Opposite sides parallel.

 Each angle is of 90.

Rectangle

All  the  four  sides  are  equal .

Opposite sides parallel.

 Each angle is of 90.

Parallelogram

Opposite sides equal

 Opposite sides are parallel 

Opposite angles are equal.

 None of the angles measure 90

Rhombus

Four equal sides 

Opposite sides are parallel.

Opposite angles are equal.

None of the angles measure 90.

Trapezium

Only one pair of opposite parallel sides.

Kite

Two pairs of adjacent equal sides.

Here one pair of equal angles.

Perimeter of a circle is called circumference.

Perimeter is the boundary distance of shapes, square, rectangle etc.

Perimeter 

Sum all sides

If area is given

2 (L + B )

Area 

Consist of square units.

Area of Rectangle

Area = length x width

Area of circle

A = π r ²

Find perimeter and area

L 5.3 cm

W 5.3

P = 2 (l+b)

= 2 ( 5.3 + 5.3)

= 21.2 cm

Area = l x w

5.3 x 5.3

28.09 cm²

Perimeter and area of rectangle shape

Perimeter 

2 (l + b )

Area = l x width

Perimeter and area of Square shape

Perimeter = 4 x side

Or 

a + a + a + a

Solved Problems Using Perimeter of Square Concept

Question 1: Find the perimeter of a square whose side is 5 cm.

Solution:

Given:

Side, s = 5 cm

The formula to find the perimeter of a square is given by:

The perimeter of Square = 4s units

Substitute the value of ‘s’ in the perimeter formula,

P= 4 × 5 cm

P = 20 cm

Therefore, the perimeter of square = 20 cm

Question 2: Calculate the perimeter of a square having a side of 16 cm.

Solution:

Given,

Side of the square = a = 16 cm

Perimeter of a Square = 4a

= 4 × 16

= 64 cmSolved Problems Using Perimeter of Square Concept

Question 1: Find the perimeter of a square whose side is 5 cm.

Solution:

Given:

Side, s = 5 cm

The formula to find the perimeter of a square is given by:

The perimeter of Square = 4s units

Substitute the value of ‘s’ in the perimeter formula,

P= 4 × 5 cm

P = 20 cm

Therefore, the perimeter of square = 20 cm

Question 2: Calculate the perimeter of a square having a side of 16 cm.

Solution:

Given,

Side of the square = a = 16 cm

Perimeter of a Square = 4a

= 4 × 16

= 64 cm

Solved Problems Using Perimeter of Square Concept

Question 1: Find the perimeter of a square whose side is 5 cm.

Solution:

Given:

Side, s = 5 cm

The formula to find the perimeter of a square is given by:

The perimeter of Square = 4s units

Substitute the value of ‘s’ in the perimeter formula,

P= 4 × 5 cm

P = 20 cm

Therefore, the perimeter of square = 20 cm

Question 2: Calculate the perimeter of a square having a side of 16 cm.

Solution:

Given,

Side of the square = a = 16 cm

Perimeter of a Square = 4a

= 4 × 16

= 64 cm

Area of square

Side x side = Side ²

Area = a²

Perimeter of circle

Circumference of circle

π x d

Or 

31.4 x d

Area of circle

A = π r²

How to Calculate the Perimeter of a Triangle?

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c

Let us consider some of the examples on the perimeter of a triangle:

Example 1: Find the perimeter of a polygon whose sides are 5 cm, 4 cm and 2 cm.

Solution: Let,

a = 5 cm

b = 4 cm

c = 2 cm

Perimeter = Sum of all sides = a + b + c = 5 + 4 + 2 = 11

Therefore, the answer is 11 cm.

Example 2: Find the perimeter of a triangle whose each side is 10 cm.

Solution: Since all three sides are equal in length, the triangle is an equilateral triangle.

i.e. a = b = c = 10 cm

Perimeter = a + b + c

= 10 + 10 + 10

= 30

Perimeter = 30 cm. 

Area of triangle

Base and height given

1/2bh

3 sides given Heron's formula

Rational numbers

All integers are Rational numbers.

Means that can be written in ratio or fraction form or decimal.

P/Q 

P and Q integers.

Q, Denominator is not equal to zero.

Rational numbers can be written in fractions and decimals.

Irrational numbers can't be written in fractions but can be written in decimals.

All rational numbers can be written in decimals.

All irrational numbers can be written in decimals.

Irrational numbers can't be written in fractions.

All Real numbers can be written in decimals.

Real numbers can be written in fractions except irrational numbers.

Real numbers

 are simply the combination of rational and irrational numbers, in the number system

Real numbers =

Whole Numbers

Natural Numbers

Integers

Rational numbers

Irrational numbers.

Class 5

HCF

LCM

Percentage

Class 6

Ratio Proportion

Linear equation

Class 7

Decimals

Exponents

Square Root

Ratio proportion Direct Indirect

Algebra

Linear equation

Class 8

Real numbers

Number System

Polynomials

Factorization

Simultaneous equation

Sets

PST SAMPLE PAPER

Line number

Algebra subtraction

JEST SAMPLE PAPER

Sets

Logarithms

JEST PAST PAPER IBA

Equation properties

Line number

Irrational numbers

Charts questions

Equations

Angle measurements

Area of right triangle

A = b x h/2

Base x height both divided by 2 

Fahrenheit to Celsius

1 Minus 32

2 Multiply 5/9

Celsius to Fahrenheit

C x 9/5 + 32

Part / whole percentage

Part / whole = part given / whole

Cross multiply

16/100 = 32/whole

16/100 = 32/x

16x= 3200

= 3200/16

= 200

Rational numbers = Perfect squares + Terminating decimals + Repeating decimals

·         Irrational numbers = Surds + Non-repeating decimals

Simply all integers are Rational numbers.