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Mathematics

Chima Sunday (Tutor)
22-06-2016 15:34:00 +0000

Try your best to solve these questions. Show working on paper when necessary and include a picture of your hand written Solution in your response. Wish you the best!

1. If m is the gradient of the line pq - px - qy = 0; and q ≠ 0. Find 1/m
A. q/p
B. p/q
C. -q/p
D. -p/q
(oau)

Updated Solution
equation of a straight line, y = mx + c; were m = slope or gradient
so for pq - px - qy = 0
making y subject formular
y = (-p/q)x + p
so by comparison with equation of straight line, m = (-p/q)
so 1/m = (-q/p)

2. If α and β are the roots of the quadratic equation, x2 - 10x + 2 = 0. Find the value of 1/α2 + 1/β2.
A. 26
B. 24
C. 3/2
D. 3
(uniben)

Updated Solution
If α and β are the roots of the quadratic equation, then we can construct the equation as x2 - (α + β)x + αβ = 0
then comparing this with x2 - 10x + 2 = 0
it seen that (α + β) = 10; and αβ = 2
so 1/α2 + 1/β2 = (α2 + β2)/α2β2 = [(α + β)2 - 2αβ]/(αβ)2 (please try and convince yourself that this is true by working it out)
now substituting we that
1/α2 + 1/β2 = [(10)2 - 2(2)]/(2)2
= (100 - 4)/4 = 96/4 = 24

3. If sec2x + tan2x = 3, find the value of x
A. 30o
B. 45o
C. 60o
D. 90o
(abu)

Updated Solution
recall that sin2x + cos2x = 1
divide through by cos2x to have
tan2x + 1 = sec2x
were sec2x = 1/cos2x
substituting sec2x into the question, we have
tan2x + 1 + tan2x = 3
so 2tan2x = 3 -1 = 2
tan2x = 1
square rooting both side to have
tanx = 1
thus x = tan-1(1) = 45

• Olabode Olayiwola

Aii... Back in a jiff

2 22-06-2016 15:42:00 +0000

• Olabode Olayiwola

Been trying.... Don't understand

2 22-06-2016 16:25:00 +0000

2 22-06-2016 17:05:00 +0000

• Jonathanowo Akinlabi

1 c 2 a 3 b

2 22-06-2016 17:20:00 +0000

• Chima Sunday (Tutor)

Thanks to you @Jonathan for such a fearless attempt keep it up and also to you Olabode you are most respectfully welcome. Please @ all do know that this post has been updated with its detailed solution, so try and check it up. Equally, you are free to ask any question. Once again you are welcome and thank you.

2 23-06-2016 14:05:00 +0000