5-quadratic equation using identity

                    
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perimeter STD V

Circle STD VIII

Circle STD VIII

trignometry STD VIII

Counting STD IV

Count The number of Doughnuts

magic box method for solving problems on percentage STD VII

Are problems on “percentage” a cause of concern for you? You may wish to try out this magic box. It may take away your trouble?

I will illustrate the concept with an example;

Say, Nanu sells a pen at a profit of 20%.

It means if Nanu were to buy the pen at Rs 100, then the selling price will be Rs 120.

Say, vegetable prices have gone up by 15%.

It means that vegetables which were earlier costing Rs 100, can now be purchased for Rs 115.

Rain fall in 2013 was 30% above average in Mumbai.

It means that if the average rainfall in Mumbai is 100 mm, then in the year 2013 the rainfall is 130 mm.

Lata’s has scored 10% more than Suresh in the Maths exam.

It means if Suresh has secured 100 in maths, then Lata has got 110.

Similarly,

Say, Nanu sells a pen at a loss of 20%.

It means if Nanu were to buy the pen at Rs 100, then the selling price will be Rs 80.

Say, vegetable prices have gone down by 15%.

It means that vegetables which were earlier costing Rs 100, can now be purchased for Rs 85.

Rain fall in 2013 was 30% below average in Mumbai.

It means that if the average rainfall in Mumbai is 100 mm, then in the year 2013 the rainfall is 70mm.

Lata’s has scored 10% less than Suresh in the Maths exam.

It means if Suresh has secured 100 in maths, then Lata has got 90.

If this concept has got ingrained in you, then we will move to the next step.

Cost of cabbage was $ 2 per kg last week. This week the prices have gone up by 14%. What is the per kg cost of cabbage this week?

Let us construct our magic box:

	Last week	This week
Cabbage cost  based on %	100	114
Actual cabbage cost	$ 2	?  (say, x)

Now, note this step carefully,

 Ratio in the first row = ratio in the second row.

So, 100/ 114 = 2/x

You could also write

114/100 = x/2, and you will still not make a mistake.

So, if 100/ 114 = 2/x

Or, 100x = 2 x 114

Or, x = 2 x 114/100 = 2.28

The present cabbage cost is $ 2.28.

General rule:

	Event 1	Event 2
Comparison based on %	100	A1
actual	B1	C1

Rule:

 A1/100 = C1/B1,

You could also write 100/A1 = B1/C1.

Then solve for the missing entity.

Let us take another example:

The rainfall in Mumbai for the year 2013 is 30% more than the average rainfall of Mumbai. The average rain fall is 250mm.What is the rainfall in 2013.

	Average	2013
Rainfall based on %	100	130
Actual	250	? let us say, x

     

Now, write, 

100/130 = 250/x

Or, x = 250 x 130 / 100 =  325 mm

We will take it forward in the next lesson.

Mirror images STD IV

                                                          
mirror image of 3,4, 5 and 6.
every single point of the number will be at equal distance on the other side of mirror. So, mark the corner points (points where two lines meet). Take an approximate measure of distance from the mirror. Now mark a  point on the opposite side of the mirror at the same distance. Do it for all the corner points and then join the points. You will get the mirror image.

Problems on Remainder theorem

If  2x³ +ax² - 13x + b is divisible by x² -x - 6, then find the value of “a” and “b”.

Answer:

Factorizing x² - x -6 we get,

= x² - 3x + 2x -6

= x(x - 3) + 2(x - 3)

= (x- 3)(x + 2)

if F(x) = 2x³ +ax² - 13x + b

Now according to remainder theorem,  F(3) = 0 and F(-2) = 0 for complete divisibility.

Substituting x = 3 we get

9a + b + 15 = 0     -------------(1)

Similarly substituting x = -2, we get

4a + b + 10 = 0  ---------(2)

Solving Equation 1 and 2 we get,

“a” = -1

“b” = -6