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.
