MATHEMATICS PREPARATORY TEST SOLUTION..!!!

SECTION A

10 Easy Arithmetic Tricks!!.

Math can be terrifying for many people. This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head.

1. The 11 Times Trick

We all know the trick when multiplying by ten – add 0 to the end of the number, but did you know there is an equally easy trick for multiplying a two digit number by 11? This is it:

Take the original number and imagine a space between the two digits (in this example we will use 52:

5_2

Now add the two numbers together and put them in the middle:

5_(5+2)_2

That is it – you have the answer: 572.

If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first:

9_(9+9)_9

(9+1)_8_9

10_8_9

1089 – It works every time.

2. Quick Square

If you need to square a 2 digit number ending in 5, you can do so very easily with this trick. Multiply the first digit by itself + 1, and put 25 on the end. That is all!

25² = (2x(2+1)) & 25

2 x 3 = 6

625

3. Multiply by 5

Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex – or does it? This trick is super easy.

Take any number, then divide it by 2 (in other words, halve the number). If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works everytime:

2682 x 5 = (2682 / 2) & 5 or 0

2682 / 2 = 1341 (whole number so add 0)

13410

Let’s try another:

5887 x 5

2943.5 (fractional number (ignore remainder, add 5)

29435

3. Multiply by 5

Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex – or does it? This trick is super easy.

Take any number, then divide it by 2 (in other words, halve the number). If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works everytime:

2682 x 5 = (2682 / 2) & 5 or 0

2682 / 2 = 1341 (whole number so add 0)

13410

Let’s try another:

5887 x 5

2943.5 (fractional number (ignore remainder, add 5)

29435

4. Multiply by 9

This one is simple – to multiple any number between 1 and 9 by 9 hold both hands in front of your face – drop the finger that corresponds to the number you are multiplying (for example 9×3 – drop your third finger) – count the fingers before the dropped finger (in the case of 9×3 it is 2) then count the numbers after (in this case 7) – the answer is 27.

5. Multiply by 4

This is a very simple trick which may appear obvious to some, but to others it is not. The trick is to simply multiply by two, then multiply by two again:

58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232

6. Calculate a Tip

If you need to leave a 15% tip, here is the easy way to do it. Work out 10% (divide the number by 10) – then add that number to half its value and you have your answer:

15% of $25 = (10% of 25) + ((10% of 25) / 2)

$2.50 + $1.25 = $3.75

7. Tough Multiplication

If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:

32 x 125, is the same as:
16 x 250 is the same as:
8 x 500 is the same as:
4 x 1000 = 4,000

8. Dividing by 5

Dividing a large number by five is actually very simple. All you do is multiply by 2 and move the decimal point:

195 / 5

Step1: 195 * 2 = 390
Step2: Move the decimal: 39.0 or just 39

2978 / 5

step 1: 2978 * 2 = 5956
Step2: 595.6

9. Subtracting from 1,000

To subtract a large number from 1,000 you can use this basic rule: subtract all but the last number from 9, then subtract the last number from 10:

1000
-648

step1: subtract 6 from 9 = 3
step2: subtract 4 from 9 = 5
step3: subtract 8 from 10 = 2

answer: 352

10. Assorted Multiplication Rules

Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 6: Sometimes multiplying by 3 and then 2 is easy.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number (which is obvious from the first step).
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).
Multiply by 45: Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number.

Source :-

http://listverse.com/2007/09/17/10-easy-arithmetic-tricks/

MATHS TRICKS FOR FASTER AND ACCURATE CALCULATIONS ..!!!!

Visit the following link for amazing tricks for calculations :) :)
http://www.glad2teach.co.uk/fast_maths_calculation_tricks.htm

7 Tips To Finish Your Maths Paper Before Time !!..

Many students, even some really intelligent and talented ones, have a strange enemy. They often find it difficult to finish the paper within the allotted time. They are forced to leave a few questions just because they run out of time and often it has been found that the questions they leave are those which they otherwise could do very easily. It can be very disappointing if you are forced to skip such easy questions.

But how can you avoid a situation like this? Many people suggest a single tablet for this "Time management". But how to manage time and how to stop it from running out is a difficult proposition, especially for an average 14-15-year-old tenth grader.

1. Understand your exam
The most important thing is to understand the examination you are about to take. In the class X mathematics paper, there are 30 questions in four sections A, B, C and D and we have 180 minutes to answer these questions. Here, a rough calculation is that we get about six minutes to answer a question. But that is not the fact.

The question paper contains 'very short answer' type, 'short answer' type and 'long answer' type questions and the time requirement for each type is different. An ideal allotment for the four sections is as shown below:

2. Use the first 15 minutes effectively

You get a good 15 minutes in the beginning to read the question paper -- use this time to do just that, READ. Read all the 30 questions in 15 minutes. While reading, mark the questions into categories viz easy, manageable and tough. This is done to have an overall idea about the questions and make a rough plan.

3. Don't worry about the tough ones

The moment you find that there are a few tough questions; it is natural that you start worrying about them. This is not required and will only harm your performance.

The fact is that they may look a bit tough on the surface, but when you actually work on them you will find most of them to be much easier than they seemed. So be happy about the easy ones and don't get unduly worried about the tougher lot.

4. Prioritise your attempt

Always attempt the easy questions first and then move on to the manageable ones and ensure that you complete them before taking on the difficult ones. This will ensure that you are not leaving any question that you know.

Once you successfully attempt all the easy and manageable questions, your confidence will grow and you will be mentally ready to take on the more challenging questions.

5. Ensure speed and accuracy

Use quicker methods in calculations to ensure that you are not wasting time and your answers are correct. Mostly, we take a lot of time to solve a problem if we happen to make some error in the process.

For example, if you make an error in the sign of a term (+/-), you may not be able to solve questions involving quadratic equations or linear equations. Therefore avoiding silly mistakes is very important to save time. Always follow the tricks we discussed in speed strategies.

6. Keep an eye on your watch

Keeping an eye on your watch is of course not to increase your stress. This is just to see that you are broadly adhering to the time allocation we discussed in the beginning. A minor variation is not at all a reason to worry.

7. Avoid thinking too much about a question
Thinking about the questions before you attempt them is essential; but not to such an extent that you waste a lot of time on one question.

Also you need not write a very lengthy answer to a question just because the question is easy and you know it very well. Remember, you need to just answer the question and nothing more. Any over-attempt will be a mere waste of time.

Additionally, you must practice the habit of finishing samples papers in 140-150 minutes. This will help you simulate and exercise examination pressures better.

Source :- http://cbse-sample-papers.blogspot.in

Dear Readers this was just to increase your knowledge about attempting your Maths examination and helping you in sorting out the problem of time management in mathematics paper.

Fast Math Trick

Math Study Skills

Preparing for a Math Test

Your success on a math test can be maximized by proper preparation.

1. Practice good study techniques throughout the semester.

   Read the section on study techniques for mathematics. for details.
   

2. Begin studying for the test at least one week ahead of time.

3. Work out all practice tests in the textbook and those given by your instructor.

4. Review your study lists.

5. Find out from your instructor:

   • on which topics or objectives you will be tested.
   • what materials are needed for the test: calculators, rulers, etc.
   • what materials are prohibited from the tests: calculators, cell-phones, etc.

6. Prepare yourself physically

   
   
   • Get proper exercise weekly.
   • Eat properly prior to the test.
     • Avoid overeating just before the test.
     • Eat a good breakfast and/or lunch before the test.
     • Do not drink too much before the test: you do not want to have to use the restroom during the test.
     • Avoid too much caffinated beverages before the test; this may cause nervousness.
     • Do not use alcohol or recreational drugs before the test. These will impair your concentration and brain functioning.
     • If you are taking prescribed medications, be aware of their effects on your concentration and thinking. Adjust your intellectual activity accordingly.
   • Get a good night sleep before the test. Staying up late cramming is not productive and can reduce your mental sharpness.
7. Read the section on doing well on a math test so you know what to do once the test has started.
8. Do not study the day of the test. Relax and be confident that you have done your best to prepare. Additional studying will only make you more nervous and reducde your confidence. Before the test, take a nice walk around the campus and think positive thoughts.

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TRY THESE OUT !!.....

Q1. 17 cards numbered 1 to 17 are put in abox and mixed . Find the probability that anumber on card is odd , a prime , divisible by 3 .




Q2. The king , queen and jack of clubs are removed from a deck of 52 playing cards and well - shuffled . One card is selected from remaining cards . Find the probability of getting heart , king , and club.




Q3. A bag contains 5 red balls and some blue balls . If the probability of drawing a blue ball is double that of ared ball , find the number of blue balls in a bag.




Q4. Cards marked from numbers 2 to 101 are placed in a box and mixed thoroughly. Find the probability that a number on a card is an even number , a number less than 14 , a number which is a perfect square and a prime number less than 20.




Q5. A jar contains 54 marbles each of which is blue , green and white . The probability of selecting a blue marble at random from jar is 1 / 3 , and the probability of selecting a green marble at random is 4 / 9 . How many white marbles does the jar contain?

Try these questions and share your solutions..............
Feel free to ask about any query.............

SOME IMPORTANT QUESTIONS !!...

Q1. Find the probability that a leap year selected at random will contain 366 Sundays.

366 days = 52 weeks and 2 days.

therefore , leap year = 52 sundays.

the remaining two days can be :-

sunday and monday , monday and tuesday , tuesday and wednesday , wednesday and thursday ,
thursady and friday , friday and saturday , saturday and sunday.

total elementary events = 7 and favourable are 2

Therefore required probability = 2 / 7



Q2. Tickets numbered from 1 to 20 are mixed together . What is a probability that a ticket has
a number which is multiple of 3 or 7 ?

Here , total favourable outcomes = 3 , 6 , 7 , 9 , 12 , 14 , 15 and 18.

required probability = 8 / 20 = 2 / 5.



Q3. A bag contain 6oo pens out of which 12 are defective . What is probability for non - defective
pens ?

Total pens = 6oo
defective = 12
therefore , non - defective = 600 - 12 = 588

So , required probability = 588 / 600 = 49 / 50 = 0.98.



Q4. A letter is chosen at random from the letters of word 'ASSASSINATION' . Find the
probability that letter chosen is (i) vowel (ii) consonant.

Total letters = 13

(i) favourable for vowel = 6 (A , A , I , A , I , O )
SO , required probability = 6 / 13

(ii) probability for consonants = 1 - 6 / 13 = 7 / 13.



Q5. If x is chosen at random from the numbers -1 , 0 , 1 ,2 . What is a probability that x is
less than 2 ?

Total elementary outcomes = 5
favourable = 3 (-1 , 0 , 1)

So , required probability = 3 / 5.



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Feel free to ask about queries and clear your doubts !!!........

PROBABILITY

Probability : p = no.of favourable outcomes/Total number of possible outcomes
                   q(not happening) = 1 - p

Sample space when:
(i) A coin is tossed, S = {H,T}
(ii) When two coins are tossed simultaneously = {HH,HT,TH,TT}
(iii) When three coins are tossed simultaneously = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT)

Sample space of throwing a die:

(i) When a die is thrown once = {1,2,3,4,5,6}

(ii) When two dice are thrown simultaneously
             { (1,1) , (1,2) , (1,3) ,......, (1,6)
                (2,1) , (2,2) , (2,3), .......,(2,6)
                (3,1) , (3,2) , (3,3),........,(3,6)
                (4,1) , (4,2) , (4,3),.........,(4,6)
                (5,1) , (5,2) , (5,3),..........,(5,6)
                (6,1) , (6,2) , (6,3),...........(6,6)

Geometric Probability: If the total number of outcomes of a trial in a random experiment is infinite, then the definition of probability is not sufficient to find the probability of an event.In such cases, the definition of probability is modified and probability so obtained is called geometric probability. The geometric probability p of an event is given by
            p = measure of the specified part of the region/measure of the whole region
                      (measure means length,area,volume of the region etc.)

Playing cards consists of 52 cards which are divided into four suits of 13 cards each. Each suit consists of one king, one queen, one jack, one ace, and nine other cards numbered from 2 to 10. The four suits are named as spade, club, heart, and diamond.
       
                                       If you are having any doubt in this chapter then feel free to ask here..!!!

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