#### Wisdom Education Institute started Mathematics Examination with three goals

• To create a platform to identify students having above-average intelligence by conducting challenging competitive exams and encourage them by giving scholarships.
• To make the subject of Mathematics interesting enough for students having average intelligence and to dissolve the fear that many students have for this subject by helping them understand the basic mathematical concepts. To encourage such students to solve the sums after having understood the sum completely rather than a mechanical or a methodical approach.
• In today’s competitive era, students have to appear for many entrance exams after their H.S.C. to secure admission in their preferred academic field. Mathematics is a compulsory subject in such exams. WEI exams help students to prepare for mathematics subject in such exams at school level.

WE have set the syllabus in WEI textbooks and set the exam question papers in such a way that while studying the textbooks or solving the word problems students have to ‘think’. Thinking helps to get clarity about mathematical concepts. Such clarity helps in solving the sums intelligently rather than mechanically or methodically. The resultant increase in confidence levels about the subject helps average-intelligence students a lot.

#### How & why this activity was started?

At WEI, we thought of starting with this activity for two reasons.
A. The typical Mathematics syllabus at school level does not help in clearing mathematical concepts of students. It contains more numerical problems and a very small no. of word problems. As students get the hang of the method of solving particular type of sums, they go on solving similar sums just mechanically. But if a sum is given in a worded format almost 90% students can not solve it. For ex. If you give a 7th std. student a sum such as
Q. Find the solution set of x2-4x-21=0
Solution: The simple solution involves finding the factors of -21 in such a way that the addition of the factors is -4.
-21=(-7) x (+3) and -7+3 =-4
So you can write the given expression using the factors of -21as
x2-7x+3x-21=0
Make two pairs (underlined) and then take the common factor out.
x(x-7)+3(x-7)=0
Again take out the common factor that is (x-7)
So (x-7)(x+3)=0
When the product of (x-7) and (x+3) is zero, then either
(x-7) =0 or (x+3) = 0
This means
x=7 or x=-3
So,
The solution set of x2-4x-21=0 is {7, -3}.
Once such a method is understood, students can find the solution set of any quadratic equation (a numerical problem). But if these students are given a following problem, even 10% students can’t solve it.

The square of the sum of two consecutive even natural numbers is 1444. Find the smallest of them.
Students can solve such word problems on quadratic equations only when their conceptual mathematical knowledge is strong enough. For example, the above problem can be solved if following concepts are clear in a student’s mind.

• Assumption of the smallest unknown even number.
• Difference between two consecutive even numbers is 2
• Formation of an equation
• Use of identities

Solution: Let the smallest of two even numbers be x.
∴ the greatest of the two consecutive even numbers be x+2
∴ (x + x+2 )2 = 1444
⇒ (2x+2 )2 = 1444
⇒ 4×2 + 8x + 4 =1444
⇒ 4×2 + 8x – 1440=0
⇒ 4(x2 + 2x – 360)=0
⇒ x2 + 20x – 18x – 360=0
x(x+20) – 18(x+20) = 0
(x+20) (x-18) = 0
∴x + 20 = 0 or x – 18 = 0
∴x=-20 or x=18
-20 can not be the answer since the answer should be natural number.