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Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] - Education (5) - Nairaland

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2016 NAIRALAND JAMB TUTORIAL {the Physics Thread } / Nairaland 2016 Jamb Tutorial Classroon [use Of English Thread] / Nairaland 2016 Jamb Tutorial Classroom [chemistry Thread] (2) (3) (4)

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Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Geofavor(m): 11:13am On Sep 10, 2015
I've been under the weather - that's why i haven't been contributing much here. To read and study my textbooks sef na wahala. embarassed

3 Likes

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by HomoSapiien: 2:03pm On Sep 10, 2015
Geofavor:
I've been under the weather - that's why i haven't been contributing much here. To read and study my textbooks sef na wahala. embarassed


Gear up bro.. smiley
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Gifted18(m): 3:19pm On Sep 10, 2015
Bring on any maths problem and the Solution will be provided

1 Like 1 Share

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Geofavor(m): 8:32pm On Sep 10, 2015
Gifted18:
Bring on any maths problem and the Solution will be provided
Pls solve this asap

1 Like 1 Share

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Gifted18(m): 11:00am On Sep 11, 2015
[quote author=Geofavor post=37881509] Pls solve this asap. Wia z d question
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Geofavor(m): 11:44am On Sep 11, 2015
[quote author=Gifted18 post=37898878][/quote]lol. Didn't you see the photo?
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Gifted18(m): 11:50am On Sep 11, 2015
Geofavor:
lol. Didn't you see the photo?
I was unable to view it clearly. Write it out
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Geofavor(m): 12:10pm On Sep 11, 2015
Gifted18:
I was unable to view it clearly. Write it out
i can't. The question has a diagram.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Geofavor(m): 2:33pm On Sep 12, 2015
Orezy5 welldone.


I want to suggest that;

the syllabus be followed accordingly from the start.

One or two topics per week.(depending on how large a topic is)

pls do not hesitate to volunteer to teach a topic you are a genius at when it's time for that topic.


Jamb questions on the topic which anybody couldn't solve should be posted.
Then the topic's tutor or other students who have understood the topic properly can now do justice to the questions.


Cc
homosapiiens

affable0709

francis95

cee001

markpeakson

kunlexic

thankyoujesus

others.

1 Like

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Nobody: 3:33pm On Sep 12, 2015
.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orezy5(m): 4:00pm On Sep 12, 2015
Geofavor:
Orezy5 welldone.


I want to suggest that;

the syllabus be followed accordingly from the start.

One or two topics per week.(depending on how large a topic is)

pls do not hesitate to volunteer to teach a topic you are a genius at when it's time for that topic.


Jamb questions on the topic which anybody couldn't solve should be posted.
Then the topic's tutor or other students who have understood the topic properly can now do justice to the questions.


Cc
homosapiiens

affable0709

francis95

cee001

markpeakson

kunlexic

thankyoujesus

others.
ok boss!

bt i'm nt done with the one i'm teaching nw. it remains just a subtopic then i'm going to switch.
thanks

1 Like 1 Share

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Nobody: 4:01pm On Sep 12, 2015
Tobiee:
ProphetUdeme do u know any jamb lesson academy u can recommend?
yeah plenty. Depending on its location and distanc from your area. There are two best lessons i could recommend for you.
1 Uyo High School, oron rd. Uyo
2. Glad tidings college, oron rd. Mbiabong.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Umartins1(m): 4:30pm On Sep 12, 2015
Geofavor:

Pls solve this asap


Consider triangles POQ and TOU,


POQ= TOU (alternate <s and PQ//TU)


QPO= TUO (alt <s and PQ//TU)


<POQ= <TOU (opposite angles)


Therefore, triangle POQ is similar to triangle TOU



Area of POQ / area of TOU = 32 / 52


= 9/25


Area of triangle POQ = 9/25 X 50


= 18cm2



(B)

If you can sketch the diagram and apply the formular for finding the area of trapezium, that is 1/2 (a+b)h, you will arrive at 224cm2...... But alternatively,



Let the height of triangle TOU= a


In TOU, 1/2 X 5a = 50


5a= 100


a= 20cm



Let the height of triangle POQ= b


In POQ, 1/2 X 3b = 18


3b= 36


b= 12cm




Therefore, the height of trapezium PQRS = h


h= a+b


H= 12cm+20cm


H= 32cm


Area of trapezium PQRS = area of parallelogram STQP + area of parallelogram RQPU + area of triangle POQ - area of triangle TOU



Area of parallelogram STQP= bXh


= 3X32


= 96cm2



Area of parallelogram RQPU is also 96cm2



Area of triangle POQ= 50cm2



Area of triangle TOU= 18cm2



Therefore, area of trapezium PQRS =



(96 + 96 + 50 - 18)cm2


= 224cm2

3 Likes 2 Shares

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Nobody: 4:44pm On Sep 12, 2015
.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by maxdozie(m): 5:20pm On Sep 12, 2015
Hey Guy .. Am so Glad I found such a thread on nairaland ... Am not that good in maths and seriously an online class would do me well... But can we make it more organized?? Not just trowing questions and answering .. Let's make it look like a class..
Maybe Someone opening a whatsapp Group would be a nice idea??
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by ayokunlei(m): 5:23pm On Sep 12, 2015
prof -Umartins1 ,welldone for all the good work. Are you an undergraduate / or a graduate Sir?
Just interested in knowing you
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Umartins1(m): 7:04pm On Sep 12, 2015
ayokunlei:
prof -Umartins1 ,welldone for all the good work. Are you an undergraduate / or a graduate Sir?
Just interested in knowing you


Hmmm... Let me say an undergraduate. But....



It's a long story.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by thankyouJesus(m): 7:04pm On Sep 12, 2015
Geofavor:
Orezy5 welldone.


I want to suggest that;

the syllabus be followed accordingly from the start.

One or two topics per week.(depending on how large a topic is)

pls do not hesitate to volunteer to teach a topic you are a genius at when it's time for that topic.


Jamb questions on the topic which anybody couldn't solve should be posted.
Then the topic's tutor or other students who have understood the topic properly can now do justice to the questions.


Cc
homosapiiens

affable0709

francis95

cee001

markpeakson

kunlexic

thankyoujesus

others.
Still on mute mode, if for any urgency, alert me.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Aspiregreat: 8:46pm On Sep 12, 2015
Great work here....more power to your elbows.

1 Like

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by ayokunlei(m): 9:25pm On Sep 12, 2015
Umartins1:


Hmmm... Let me say an undergraduate. But....


It's a long story.
okay sir
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orezy5(m): 8:21am On Sep 13, 2015
PARALLEL AND PERPENDICULAR LINES

parallel lines
parallel lines/equations are those equations that have the same gradient/slope, i.e according to the general form of equation of straight lines, y=mx + c where m is the gradient(have u forgotten?), the gradient of parallel lines remain the same.

example one:
one line passes through the points (-1, -2) and (1, 2); another line passes through the points (-2, 0) and (0, 4). Are these lines parallel?

solution
to answer this question, we're going to find the slopes of the lines:
since m(gradient)=y2 - y1/x2 - x1,
let's find the slope of the first line:
m1=2 -(-2)/1 -(-1)

=2 + 2/1 + 1

=4/2
m1= 2

now let's find the slope of the other line:

m2=4 - 0/0 -(-2)

=4/0 + 2
=4/2
m2= 2

since these two lines have the same slopes, then these lines are parallel.

example two:

given the line 2x - 3y=9 and the point (4, -1), find the line through the point that is parallel to the given line.

solution
since we've known earlier that parallel lines have the same slope/gradient, we're going to solve as follows:

let's find the slope of the equation: 2x - 3y=9

according to the general form: y=mx + c, let us re-arrange the equation to suit the general form:

2x - 3y=9
-3y= -2x + 9
divide both sides by -3

-3y/-3 = -2x/-3 + 9/-3

y=2/3x - 3.

now,when we compare the two equations(i.e this equation and the general form), we can see that the slope, m= 2/3

now that we've gotten the slope of the equation, since parallel lines have the same slope, the the parallel line through (4, -1) will also have slope m=2/3. so, we're going to use the point-slope formula to find the line(hope you've not forgotten the formula sha. lol)

y - y1=m(x - x1)
m=2/3,
x1=4,
y1= -1

y -(-1) = 2/3(x - 4)

open the brackets:
y + 1 = 2x - 8/3

cross multiply:
3(y + 1)= 2x - 8

3y + 3=2x - 8
collect like terms:
3y= 2x -8 -3
3y=2x - 11.

so, the final answer is 3y= 2x - 11
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orezy5(m): 8:51am On Sep 13, 2015
example three:

find the value of p, if the line which passes through (-1, -p) and (-2p, 2) is parallel to the line 2y + 8x - 17=0

solution
since both lines are parallel, they have the same slope/gradient.
let's find the gradient of 2y + 8x -17=0
as you all know that the general form of straight line equations is y=mx + c, let's re-arrange the equation to suit this arrangement:

2y + 8x - 17=0
2y= -8x + 17
make y the subject of the formula by dividing both sides by 2:

2y/2= -8x/2 + 17/2
y= -4x + 17/2
therefore, the gradient is -4.

now that we've gotten the value of the slope, let's find the value of p by using the gradient formula:
m=y2 - y1/x2 - x1

m=-4,
x1= -1,
x2= -2p,
y1= -p,
y2= 2.

-4= 2-(-p)/-2p -(-1)

-4= 2 + p/-2p + 1
cross multiply:
-4(-2p + 1)= 2 + p
open the bracket:

8p - 4= 2 + p
collect like terms:

8p - p= 2 + 4
7p= 6

divide both sides by 7:
7p/7 = 6/7
therefore, the value of p is= 6/7.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orestino(m): 9:54am On Sep 13, 2015
Orezy5:
example three:

find the value of p, if the line which passes through (-1, -p) and (-2p, 2) is parallel to the line 2y + 8x - 17=0

solution
since both lines are parallel, they have the same slope/gradient.
let's find the gradient of 2y + 8x -17=0
as you all know that the general form of straight line equations is y=mx + c, let's re-arrange the equation to suit this arrangement:

2y + 8x - 17=0
2y= -8x + 17
make y the subject of the formula by dividing both sides by 2:

2y/2= -8x/2 + 17/2
y= -4x + 17/2
therefore, the gradient is -4.

now that we've gotten the value of the slope, let's find the value of p by using the gradient formula:
m=y2 - y1/x2 - x1

m=-4,
x1= -1,
x2= -2p,
y1= -p,
y2= 2.

-4= 2-(-p)/-2p -(-1)

-4= 2 + p/-2p + 1
cross multiply:
-4(-2p + 1)= 2 + p
open the bracket:

8p - 4= 2 + p
collect like terms:

8p - p= 2 + 4
7p= 6

divide both sides by 7:
7p/7 = 6/7
therefore, the value of p is= 6/7.
nice one orezy... I would love to teach statistics though
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orestino(m): 9:55am On Sep 13, 2015
Orezy5:
example three:

find the value of p, if the line which passes through (-1, -p) and (-2p, 2) is parallel to the line 2y + 8x - 17=0

solution
since both lines are parallel, they have the same slope/gradient.
let's find the gradient of 2y + 8x -17=0
as you all know that the general form of straight line equations is y=mx + c, let's re-arrange the equation to suit this arrangement:

2y + 8x - 17=0
2y= -8x + 17
make y the subject of the formula by dividing both sides by 2:

2y/2= -8x/2 + 17/2
y= -4x + 17/2
therefore, the gradient is -4.

now that we've gotten the value of the slope, let's find the value of p by using the gradient formula:
m=y2 - y1/x2 - x1

m=-4,
x1= -1,
x2= -2p,
y1= -p,
y2= 2.

-4= 2-(-p)/-2p -(-1)

-4= 2 + p/-2p + 1
cross multiply:
-4(-2p + 1)= 2 + p
open the bracket:

8p - 4= 2 + p
collect like terms:

8p - p= 2 + 4
7p= 6

divide both sides by 7:
7p/7 = 6/7
therefore, the value of p is= 6/7.
nice one orezy... I would love to teach statistics though
Orezy5:
[color=#000099]example three:

find the value of p, if the line which passes through (-1, -p) and (-2p, 2) is parallel to the line 2y + 8x - 17=0

solution
since both lines are parallel, they have the same slope/gradient.
let's find the gradient of 2y + 8x -17=0
as you all know that the general form of straight line equations is y=mx + c, let's re-arrange the equation to suit this arrangement:

2y + 8x - 17=0
2y= -8x + 17
make y the subject of the formula by dividing both sides by 2:

2y/2= -8x/2 + 17/2
y= -4x + 17/2
therefore, the gradient is -4.

now that we've gotten the value of the slope, let's find the value of p by using the gradient formula:
m=y2 - y1/x2 - x1

m=-4,
x1= -1,
x2= -2p,
y1= -p,
y2= 2.

-4= 2-(-p)/-2p -(-1)

-4= 2 + p/-2p + 1
cross multiply:
-4(-2p + 1)= 2 + p
open the bracket:

8p - 4= 2 + p
collect like terms:

8p - p= 2 + 4
7p= 6

divide both sides by 7:
7p/7 = 6/7
therefore, the value of p is= 6/7.
nice one orezy... I would love to teach statistics though[/color]
Orezy5:
example three:

find the value of p, if the line which passes through (-1, -p) and (-2p, 2) is parallel to the line 2y + 8x - 17=0

solution
since both lines are parallel, they have the same slope/gradient.
let's find the gradient of 2y + 8x -17=0
as you all know that the general form of straight line equations is y=mx + c, let's re-arrange the equation to suit this arrangement:

2y + 8x - 17=0
2y= -8x + 17
make y the subject of the formula by dividing both sides by 2:

2y/2= -8x/2 + 17/2
y= -4x + 17/2
therefore, the gradient is -4.

now that we've gotten the value of the slope, let's find the value of p by using the gradient formula:
m=y2 - y1/x2 - x1

m=-4,
x1= -1,
x2= -2p,
y1= -p,
y2= 2.

-4= 2-(-p)/-2p -(-1)

-4= 2 + p/-2p + 1
cross multiply:
-4(-2p + 1)= 2 + p
open the bracket:

8p - 4= 2 + p
collect like terms:

8p - p= 2 + 4
7p= 6

divide both sides by 7:
7p/7 = 6/7
therefore, the value of p is= 6/7.
nice one orezy... I would love to teach statistics though
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orezy5(m): 12:25pm On Sep 13, 2015
Orestino:
nice one orezy... I would love to teach statistics though nice one orezy... I would love to teach statistics though nice one orezy... I would love to teach statistics though
yeah.
u are free to teach any topic u feel that u can handle.
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orezy5(m): 8:40am On Sep 14, 2015
PERPENDICULAR LINES

Perpendicular lines are a bit more complicated. If we visualise a line with positive slope, then the perdendicular line must have a negative slope, because it is a decreasing line. so, perpendicular slopes have opposite signs(i.e, if the slope of a parallel line is positive, that of a perpendicular line will be a negative reciprocal of the slope of the parallel line and vice versa.)

the other opposite thing with perpendicular slopes is that their values are reciprocals; i.e if you take the one slope value and flip it upside down. put this together with the sign change, and you get that the slope of the perpendicular line is the negative reciprocal of the slope of the original line- and two lines with slopes that are negative reciprocals of each other are perpendicular to each other. in numbers, if the one line's slope is m=4/5, then the perpendicular line's slope will be m= -5/4. if the one line's slope is m= -2, then the perpendicular lines slope will be m=1/2.

example one:
one line passes through the points (0, -4) and (-1, -7); another line passes through the points (3,0) and (-3, 2). are these lines perpendicular?

solution

to determine whether the lines are perpendicular or not, we're going to find the values of the slopes of the two lines:
for the 1st line:
x1= 0,
y1= -4,
x2= -1,
y2= -7
since m=y2 - y1/x2 - x1,
m1= -7 -(-4)/-1 -0

m1= -7 + 4/-1
m1= -3/-1
m1= 3

now, let's find the slope of the second line:
x1= 3,
y1=0,
x2= -3,
y2= 2

m2= 2 - 0/-3 -3
m2=2/-6
m2= -1/3

now that we've gotten the values of the slopes of the two lines, since we've known earlier that the slopes of perpendicular lines are the negative reciprocals of each other. if i were to flip the '3' and then change its sign, i would get -1/3, in other words, the slopes are negative reciprocals.
therefore, the lines are perpendicular.

example two:
find the equation of the perpendicular at point (4, 3) to the line y + 2x=5.

solution
let's find the slope of the line y + 2x=5.
let's re-arrange the equation to suit the general formula:
y + 2x=5
y= -2x + 5.
if we compare this to the general formula, we can see that the slope is -2.

now that we've gotten the slope of the equation, and we said earlier that perpendicular lines have slopes that are of negative reciprocals to each other, let's find the slope of the point (4, 3).
to find the slope, flip the '-2' upside down, we get 1/-2, then change the sign, it becomes 1/2.
now that we've gotten the slope, let's use the point-slope formula to find the equation of the line:
y - y1=m(x - x1)
m=1/2,
x1= 4,
y1= 3.
y - 3= 1/2(x - 4)
open the bracket:
y - 3= x - 4/2
cross multiply:
2(y - 3)= x - 4
2y - 6= x - 4
collect like terms and bring all the variables to one side:
2y - x= -4 + 6
2y - x= 2
therefore, the equation of the perpendicular at point (4, 3) to the line y + 2x=5 is 2y - x=2.

2 Likes

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Francis95(m): 9:41pm On Sep 14, 2015
Geofavor:
Orezy5 welldone.


I want to suggest that;

the syllabus be followed accordingly from the start.

One or two topics per week.(depending on how large a topic is)

pls do not hesitate to volunteer to teach a topic you are a genius at when it's time for that topic.


Jamb questions on the topic which anybody couldn't solve should be posted.
Then the topic's tutor or other students who have understood the topic properly can now do justice to the questions.


Cc
homosapiiens

affable0709

francis95

cee001

markpeakson

kunlexic

thankyoujesus

others.


Mehn.. I love this thread... No probs bro..
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Geofavor(m): 10:43pm On Sep 14, 2015
Umartins1:



Consider triangles POQ and TOU,


POQ= TOU (alternate <s and PQ//TU)


QPO= TUO (alt <s and PQ//TU)


<POQ= <TOU (opposite angles)


Therefore, triangle POQ is similar to triangle TOU



Area of POQ / area of TOU = 32 / 52


= 9/25


Area of triangle POQ = 9/25 X 50


= 18cm2
i think you meant; <PQO = <UTO (alternate <s and PQ//TU)



(B)

If you can sketch the diagram and apply the formular for finding the area of trapezium, that is 1/2 (a+b)h, you will arrive at 224cm2
i've tried sketching and applying the formular, it's not working. Can you pls explain?



...... But alternatively,



Let the height of triangle TOU= a


In TOU, 1/2 X 5a = 50


5a= 100


a= 20cm



Let the height of triangle POQ= b


In POQ, 1/2 X 3b = 18


3b= 36


b= 12cm




Therefore, the height of trapezium PQRS = h


h= a+b


H= 12cm+20cm


H= 32cm
nice thinking.


Area of trapezium PQRS = area of parallelogram STQP + area of parallelogram RQPU + area of triangle POQ - area of triangle TOU



Area of parallelogram STQP= bXh


= 3X32


= 96cm2



Area of parallelogram RQPU is also 96cm2



Area of triangle POQ= 50cm2



Area of triangle TOU= 18cm2




Therefore, area of trapezium PQRS =



(96 + 96 + 50 - 18)cm2


= 224cm2
the texts emboldened got my head spinning 360degrees - you kept on interchanging the parameters.
I had to calm down and solve the question myself (using ur methods. smiley )

but you ended up back on track when you did the final arithmetic.

Now, to the emboldened, i think you meant;

area of trapezium PQRS = area of parallelogram STQP + area of parallelogram RPQU - area of triangle POQ + area of triangle TOU


and secondly, maybe this was because you were rushing,

These ought to be;
area of triangle POQ = 18cm2

area of triangle TOU = 50cm2....

Thanx bro.

1 Like

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Nobody: 11:38pm On Sep 14, 2015
BUMPER 2 BUMPER
Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Geofavor(m): 1:20pm On Sep 15, 2015
Orezy5 well done bro.

Let's start using the syllabus by tomorrow. We don't have to waste too much time on a topic.

So, I'll begin with NUMBER BASE tomorrow.

Everyone should brush through the topic.(it's not hard). So whatever question you have will be attended to after/during llecture.

From the least difficult to the most, we can cover the syllabus if we start now.

3 Likes 1 Share

Re: Nairaland 2016 Jamb Tutorial Classroon [mathematics Thread] by Orezy5(m): 2:23pm On Sep 15, 2015
Geofavor:
Orezy5 well done bro.

Let's start using the syllabus by tomorrow. We don't have to waste too much time on a topic.

So, I'll begin with NUMBER BASE tomorrow.

Everyone should brush through the topic.(it's not hard). So whatever question you have will be attended to after/during llecture.

From the least difficult to the most, we can cover the syllabus if we start now.
ok boss.

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