
Difficult Problems in Mathematics From post utme (UI 2006)
Mathematics
Chima Sunday (Tutor)
01042016 15:43:00 +0000As rightly said that 'it is not over until its over' Note that the aim of this app is to see you celebrate your MATRICULATION, So in our own way in this room is to review some questions asked in some prominent schools that most people that attempted it failed it.
About 80% of student that attempted this questions failed it. Try it and proof that you are not an element in this set
Question 13 Factorize 3a^{2}  11a + 6
Option A (3a2)(a3)
Option B (2a2)(a3)
Option C (3a2)(a + 3)
Option D (3a + 2)(a  3)
Question 14 Solve the equation 3a + 10 = a^{2}
Option A 5, 2
Option B 5, 2
Option C 10, 0
Option D 5, 2
SOLUTION Question 13 and 14 of UI Post UTME past question are quintessences of wit of quadratic equation
recall that quadratic equation is any equation whose unknown is of power two i.e ax^{2} + bx + c
When solving problems in quadratic equations we use of the following methods, each still yielding same answer
they include 1) factorizing 2) graphing 3) completing square 4) formula method
For Question 13 we are ask to factorize completely
So 3a^{2}  11a + 6.
method we are going to look for two algebraic numbers whose sum will give us 11a and their product = 3a^{2} × 6 = 18a^{2}
they are 2a and 9a (please do verify incase you are not cleared)
so in place of 11a we write 2a  9a
i.e 3a^{2}  11a + 6 = 3a^{2}  2a  9a + 6, we can now factorize this by regrouping it
(3a^{2}  2a) + ( 9a + 6) factorizing each bracket to obtain a(3a  2)  3(3a  2) = (3a  2)(a  3)
So correct Option is A
For Question 14, we can obtain the roots by solving the equation using any of the listed method, lets still use factorizing method
so, 3a + 10 = a^{2} = a^{2}  3a  10 = 0
so we look for two numbers whose sum is 3a and product is 10a^{2}
that should be +2a and 5a
So a^{2}  3a  10 = a^{2} + 2a  5a  10 = 0
by grouping (a^{2} + 2a) + ( 5a  10) = a(a + 2) 5(a + 2) = (a  5)(a + 2) = 0
so a  5 = 0, then a = 5. and a + 2 = 0, a = 2
D is the correct Option.

eberechi nnaekpe
question 13..answer is option A.. question 14..answer is option D
0 01042016 15:50:00 +0000

Chima Sunday (Tutor)
Thumb up to you @Eberechi Nnaekpe for that wonderful, bold and intelligent attempt keep it up.
0 04042016 12:52:00 +0000

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