Construction for Xth Class

Construction for class Xth students

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1. Construction of Tangents to a circle
2. Construction of Tangent to a circle without using centre
3. Construction of Circumcircle
4. Construction of Incircle
5. Construction of Similar Tiangles
6. Construction of triangle in which base, vertical angle and Median is given
7. Construction of triangle in which base, vertical angle and altudide is given

Solution of Puzzle

 

 

 

 

 

BASIC PROPORTIONALITY THEOREM

Video : Relation Between circumference of circle and diameter

  

 

Note: Pie is an  irrational number and this actvity is to understand that pie is very near to 22/7

Video:Divisibility Test of 11

Factorization (Learning by Doing )

Puzzle

Try Yourself

How many squares, of any size, can you find on this chess board that do not contain a Rook?

 

Answer: There are 116 squares without a rook.

1 x 1 : 61 squares.

2 x 2 : 37 squares.
3 x 3 : 15 squares.
4 x 4 :   3 squares.

 

Multiplication of 2 two-digit numbers

Multiplication of 2 two-digit numbers where the first digit of both the numbers are same and the last digit of the two numbers sum to 10

Example

 To calculate 56 x 54

Multiply 5 by 5+1. So, 5 x 6 = 30. Write down 30.

 Multiply together the last digits: 6 x 4 = 24. Write down 24.

 The product of 56 and 54 is thus 3024.

 

Multiplication of two numbers that differ by 2

 (This trick only works if you have memorized or can quickly calculate the squares of numbers.

When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1.

Example

 18 x 20 =( 19 x 19) - 1 = 361 - 1 = 360

 25 x 27 = (26 x 26) - 1 = 676 - 1 = 675

 49 x 51 = (50 x 50 ) - 1 = 2500 - 1 = 2499

 

 

Multiplication of two numbers that differ by 4

(This trick only works if you have memorized or can quickly calculate the squares of numbers.

 If two numbers differ by 4, then their product is the square of the number in the middle (the average of the two numbers) minus 4.

 Example

 22 x 26 = (24 x 24 ) - 4 = 572

 98 x 102 = ( 100 x 100) - 4 = 9996

 148 x 152 = (150 x 150) - 4 = 22496

 

Multiplication of two numbers that differ by 6

(This trick only works if you have memorized or can quickly calculate the squares of numbers.

 If the two numbers differ by 6 then their product is the square of their average minus 9.

 Example

 10 x 16 = (13 x 13) - 9 = 160

 22 x 28 = (25 x 25) - 9 = 616

Activity : Sum of all angles of quadrilateral is 360

·         Draw a Quadrilateral ABCD on colour chart Sheet .
·         Cut such four Quadrilaterals on four different sheets.
·         Mark ÐA as Ð1 ,  ÐB as Ð2 , ÐC as Ð3 and ÐD as Ð4 on each quadrilateral as shown in fig .
·         Arrange all four angles of quadrilateral one from each colour at one point.
·         What you observe ?
·         It forms a complete angle i.e 360⁰
·         This shows that sum of all angles of quadrilateral is 360⁰

 

 

Squaring by shortcut

Squaring

 

Let us take advantage of  algebraic identity.

A² = (A - d)(A + d) + d²

Naturally, this formula works for any value of d, but we should choose d to be the distance to a number close to A that is easy to multiply.

Examples. To square the number 23, we let d = 3 to get

23² = 20 x 26 + 3² = 520 + 9 = 529:

 

To square 48, let d = 2 to get

48² = 50 x 46 + 2² = 2300 + 4 = 2304:

 With just a little practice, it's possible to square any two-digit number in a matter of seconds. Once you have mastered those, we can quickly square three-digit numbers by rounding up and down to the nearest hundred.

Examples. 223² = 200 x 246 + 23²= 49;200 + 529 = 49;729

952² = 1000 x 904 + 48² = 904;000 + 2;304 = 906;304:

To do mental calculations of this size, one needs to be quick at multiplying 2-digit and 3-digit numbers by 1-digit numbers, generating the answer from left to right.