Algebra based Mathematics Notes For CTET Exam : Free PDF

Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts, Facts and Formulae of the Algebra.

To let you make the most of Mathematics section, we are providing important facts related to the Algebra. At least 2-3 questions are asked from this topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

How to Overcome Exam Fever, Especially When You Fear Maths

Algebra

Algebra

It is branch of mathematics that substitutes letters for numbers. Algebra gives different methods of solve equations.

Variables

A variable is represented by either a sign or a letter. Its value may not be the same in every equation.

Example: 2x – 10 = 0; here, will get x = 5

3x – 3 = 0; here, he will get x = 10.

Here, x can have different values in different equations.

Therefore, x is variable

Constants

A constant always has fixed values. Every real number is a constant.

Example: 2, 5, 7 etc.

Expressions

An expression is a combination of constant and/or variables connected to each other by mathematical operators (addition, subtraction, multiplication and division).

Example: 3x + 5, 2y² – 4x 5, etc.

Terms

The parts of an expression are separated from one another by plus or minus sign and are called terms of that expression.

Example: in 3x  + 5, 3x and 5 are both expressions, as they are separated by a plus sign.

In 2y² – 4x + 5, 2y², 4x and 5 are separated by plus and minus signs, Therefore, they all are terms.

Like Terms

Two or more terms are said to be alike if their algebraic factors are the same.

Example: 3x²y, 7x²y and 10x²y are like terms.

In the expression 2xy + 3x – 4y  – 7xy, 2xy and 7xy are like terms.

Unlike Terms

Two or more terms are said to be unalike if their algebraic factors are different

Example: 3x²y, 7xy and 10xy² are unlike terms.

Factors

When numbers and variables multiply to form a product, each quantity is called a factor of the product.

Example: Factors of 3xy are 3, x and y.

Coefficients

The numerical part of term is called its coefficient.

Example: In 6x³, 6 is the coefficient of x³.

Polynomials

The algebraic expression having one or more terms, each of which consists of a constant multiplied by one or more variables raised to a negative integral power, is called a polynomial.

A polynomial can have any finite number of terms.

Monomials, binomials and trinomials are the types of polynomials.

Monomials

The algebraic expression having a single term is called a monomial.

Example: 4x is a monomial expression.

Binomials

The algebraic expression having two terms is called a binomial.

Example: 4x³ + 7x is binomial expression

Trinomials

The algebraic expression having three terms is called a trinomial.

Example: 4x³ + 2y² – x is a trinomial expression.

Addition and subtraction of Algebraic Expressions

The addition or subtraction of algebraic expressions can be simplified by combining the like terms. In this method, coefficient or combined according to their signs, keeping the same algebraic factors.

Example:

= 9x²y + xy²

Multiplication of Algebraic Expressions

By the distributive law, the product of algebraic expressions is calculated.

Example:

1. Find 2x²y × (7x²y – 2xy²).

We have

2x²y × (7x²y – 2xy²)

= 2x²y × 7x²y – 2x²y × 2xy²

= 14x⁴y² – 4x³y³

Fact and Formulae based Mathematics Notes For CTET Exam : Free PDF

Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts, Facts and Formulae.

To let you make the most of Mathematics section, we are providing important facts related to the Facts and Formulae. At least 2-3 questions are asked from this topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

How to Overcome Exam Fever, Especially When You Fear Maths

Facts and Formulae

• 0 is neither a prime number nor a composite number.
• 0 is neither a negative number nor a positive number.
• 1 is the only natural number that is neither a prime number nor a composite number.
• 1 is the smallest natural number.
• -1 is the largest negative integer.
• 2 is the only even prime number.
• The unit’s digit of any perfect square number must be 0,1,4, 5, 6, or 9.
• The unit’s digit of the square of a number whose unit’s digit is 0 will be 0.
• The unit’s digit of the square of a number whose unit’s digit is 1 or 9 will be 1.
• The unit’s digit of the square of a number whose unit’s digit is 2 or 8 will be 4.
• The unit’s digit of the square of a number whose unit’s digit is 3 or 7 will be 9.
• The unit’s digit of the square of a number whose unit’s digit is 4 or 6 will be 6.

Properties of Numbers

• The product of two consecutive numbers is divisible by 2. For example, 4 × 5 = 20, which is divisible by 2.
• The product of three consecutive numbers is divisible by 6. For example, 3 × 4 × 5 = 60, which is divisible by 6.
• The product of four consecutive numbers is divisible by 24. For example, 3 × 4 × 5 × 6 = 360, which is divisible by 24.
• The product of five consecutive numbers is divisible by 120. For example, 3 × 4 × 5 × 6 × 7 = 2520, which is divisible by 120.
• The product of ‘n’ consecutive numbers is divisible by 1 × 2 × 3 × …… × n. For example, the product of ten consecutive numbers will divisible by 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10.
• The difference between the squares of two consecutive numbers is always equal to the sum of both numbers. For example, 16² – 15² = 16 + 15 = 31
• The difference between the square of two consecutive odd numbers is always a multiple of 8. For example, 17² – 15²= 289 – 225 = 64
• The sum of the first ‘n’ odd numbers is the square of ‘n’. For example, the sum of the first five odd numbers = 1 + 3 + 5 + 7 + 9 = 5²= 25

Fractions based Mathematics Notes For CTET Exam : Free PDF

Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts, Facts and Formulae of the Fractions.

To let you make the most of Mathematics section, we are providing important facts related to the Fractions. At least 2-3 questions are asked from this topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

How to Overcome Exam Fever, Especially When You Fear Maths

FRACTIONS

Shapes And Spatial Understanding- Mathematics Notes For CTET Exam : Free PDF

Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts and properties of the Shapes And Spatial Understanding.

To let you make the most of Mathematics section, we are providing important facts related to the Shapes And Spatial Understanding.At least 2-3 questions are asked from geometry topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

How to Overcome Exam Fever, Especially When You Fear Maths

SHAPES AND SPATIAL UNDERSTANDING

This unit can help young children build maths skills by encouraging them to explore and compare shapes and spatial relationships.

SPATIAL RELATIONSHIPS

Spatial Relationships explore the concept of where objects are in relationship to something else. Some spatial concepts are:

(a) Above, below
(b) Before, after
(c) High, low
(d) Small, big
(e) Outside, inside
(f) On top of, under
(g) Near, far
(h) In front of, in back of, behind

If we see above group (a), (b), (c) and (d) carefully, then we get the following results:
(a) a is bigger than b.
(b) a is inside and b is outside
(c) b is above and a is below.
(d) b is between a and c and a is far from c and is near to be.

OPEN AND CLOSED CURVES

A curve with end points or the ends didn’t join up is called open curve.
A curve that joins up so there are no end point is called closed curve.

Polygon: A closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex.
Some Polygons are-

Polygon Parts:
Side- one of the line segments that’s make up the polygon.
Vertex- point where two sides meet. Two or more of these.
Diagonal- a line connecting two vertices that is not a side.
Interior angle- Angle formed by two adjacent sides inside the polygon.
Exterior Angle- Angled formed by two adjacent sides outside the polygon.

Example: Which one of the following figure is an open curve?

SOLID AROUND US
We live in a three-dimensional world. Every object you can see or touch has three dimensions that can be measured: length, width, and height.
Rectangular Room: The room you are sitting in can be described by these three dimensions such as L, B and H.
Dice: In a game of ludo, dice is in shape of cube.
Soccer ball: A soccer ball is a shape of sphere.
Conical Cape: A magician person or birthday cap are of conical shape.
Example: If Ram have three marbles of radius. If all marbles are same in colour and size, then total volume will be
(a) 4πr³ cubic unit
(b) 4/3 πr³ cubic unit
(c) 3πr² cubic unit
(d) ¾ πr³d cubic unit

Mathematics Formulae notes For CTET Exam : Free PDF

Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts, Facts and Formulae of the Arithmetic.

To let you make the most of Mathematics section, we are providing important facts related to the Percentage, Profit and Loss etc. At least 5-6 questions are asked from these topics in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

How to Overcome Exam Fever, Especially When You Fear Maths

Math’s Formulae

PERCENTAGE

• When a value is determined in comparison with hundred, it is called percentage.
• Example: if profit on Rs 100 is 12, it will be called 12% profit.
• If a person faces the loss of Rs 30 on Rs 200, it means he faces the loss of Rs 15 on Rs 100. So, it is 15% loss.
• When percentage is converted into fraction, it is divided by 100.

PROFIT –LOSS

• When a person runs a business, he/she either face loss or gets profit.

Cost price (C.P.)

• Cost price is the price at which a person purchases a product.

Selling price (S.P)

• Selling price is the price at which a person sells a product.

Market price (M.P.)

• It is the price that is marked on an article or commodity. It is also known as list price or tag price. If there is no discount on the marked price, then selling price is equal to the marked price.
• If there is some discount on the marked price, then S.P. =M.P. – discount

Profit

• When a person sells a product at higher rate than he/she purchased at, the difference between both amounts is called profit.

Loss

• When a person sells a product at lower rate than he/she purchased at, the difference between both amounts is called loss.

Formulae

• Profit = S.P. – C.P.
• Loss = C.P. –S.P.
• Discount = M.P. –S.P.

SIMPLE INTEREST

• When an amount of money is lent or borrowed and fixed interest is added to the principal after every interval, the total amount that is added is called simple interest.
• Principal = P
• Rate of interest = r%
• Time duration = t
• Interest, I =
• Amount = P + l

COMPOUND INTEREST

• It is the interest calculated on initial principal and also on the interest accumulated of previous periods of deposit or loan.
• Principal = P
• Rate of = r%
• Number of time interval = n
• Interest, I = A- P
• If compounding is done k times in n years, then

TIME, DISTANCE AND SPEED

• The speed of any object is the distance covered by it per unit time.
• Distance = Time × Speed
• Speed is measured in kilometer per hour (km/h) or meter per second (m/s).
• Time is measured in hours or seconds.
• Distance is measured in kilometer or meters.
• To convert a speed in km/h into m/s, multiply the speed with 5/18.
• To convert a speed in m/s into km/h, multiply the speed with 18/5.
• If a body travels a distance at a speed of x km/h and then returns to its original position at a speed of y km/h, then its average speed for the entire journey is km/h.