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Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations - Education (3) - Nairaland

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Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Nobody: 11:18am On Apr 16, 2013
Adex097: 1)If y=√x^2 + 1 , then dy/dx at X=-1 is
A. √2/2
B.-√2/2
C. √2
D.-√2

2)Differentiate 3/(1-2x)^2 with respect to x.
A. 12/(1-2x)^3
B. -12/(1-2x)^3
C. 12(1-2x)^-4
D. 6/(1-2x)^3

3)Integrate (x - 1/x)^2 with respect to x.
A. 1/3(x-1/x)^3 + c
B. X^3/3 - x - 1/x^3 + c
C. X^3/3 - 2x + 1/x^3 + c
D. X^3 - 2x -1/x + c

Good luck
1.B 2.A 3.D
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 11:22am On Apr 16, 2013
Adex097: 1)If y=√x^2 + 1 , then dy/dx at X=-1 is
A. √2/2
B.-√2/2
C. √2
D.-√2

2)Differentiate 3/(1-2x)^2 with respect to x.
A. 12/(1-2x)^3
B. -12/(1-2x)^3
C. 12(1-2x)^-4
D. 6/(1-2x)^3

3)Integrate (x - 1/x)^2 with respect to x.
A. 1/3(x-1/x)^3 + c
B. X^3/3 - x - 1/x^3 + c
C. X^3/3 - 2x + 1/x^3 + c
D. X^3 - 2x -1/x + c

Good luck

1. B
2. B
3. D
correction needed ASAP
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Adex097: 8:02pm On Apr 16, 2013
Ortarico:

LOL. . .no myn me jare, didn't get the msg of d question. Had thought it was (3/y)^2 which would definitely bcum 9/y^2. . .funi me
lol..shine ur eye well well
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Adex097: 9:57pm On Apr 16, 2013
Ortarico:

1. B
2. B
3. D
correction needed ASAP
score: 2/3
Sir Bussy: 1.B 2.A 3.D
score: 3/3
tshabalala: b/a/d
score: 3/3
Edis4christ:
1) B
2) A
3) A
score; 2/3
papindinho: the way the number one is composed is nt that clear
2* a
3*d am gonna wait for the number one correction.... Ma answer is nt in the option
score; 2/3
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Adex097: 12:12am On Apr 17, 2013
1) The Sine, cosine and tangent of 240' are, respectively
A. √3/2, -1/2 and √3
B. -√3/2 , -1/2 and √3
C. -√3/2 , 1/2 and -√3
D. √3/2 , 1/2 and √3


2)Which of the following have the same values as sin 15' ?
(I) Sin 165' (ii) Sin 285'
(Iii)Sin (-15') (iv)Sin(-195')

A. I and ii only
B. Iii and iv only
C. I and iii only
D. I and iv only

3). Two of the angles of a triangle are 120' ans 45' . If the side facing the angle 45' is 10cm long , then the side facing the angle 120' is

A. 5√3 cm
B. 5√6 cm
C. 10√2 cm
D. 20 cm
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 7:58am On Apr 17, 2013
Adex097: 1) The Sine, cosine and tangent of 240' are, respectively
A. √3/2, -1/2 and √3
B. -√3/2 , -1/2 and √3
C. -√3/2 , 1/2 and -√3
D. √3/2 , 1/2 and √3


2)Which of the following have the same values as sin 15' ?
(I) Sin 165' (ii) Sin 285'
(Iii)Sin (-15') (iv)Sin(-195')

A. I and ii only
B. Iii and iv only
C. I and iii only
D. I and iv only

3). Two of the angles of a triangle are 120' ans 45' . If the side facing the angle 45' is 10cm long , then the side facing the angle 120' is

A. 5√3 cm
B. 5√6 cm
C. 10√2 cm
D. 20 cm

1. B
2. D
3. B
oga Adex post the former correction nah
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Adex097: 9:11am On Apr 17, 2013
^^^^ sorry...I don forget
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by papindinho(m): 11:37am On Apr 17, 2013
Adex097: 1) The Sine, cosine and tangent of 240' are, respectively
A. √3/2, -1/2 and √3
B. -√3/2 , -1/2 and √3
C. -√3/2 , 1/2 and -√3
D. √3/2 , 1/2 and √3


2)Which of the following have the same values as sin 15' ?
(I) Sin 165' (ii) Sin 285'
(Iii)Sin (-15') (iv)Sin(-195')

A. I and ii only
B. Iii and iv only
C. I and iii only
D. I and iv only

3). Two of the angles of a triangle are 120' ans 45' . If the side facing the angle 45' is 10cm long , then the side facing the angle 120' is

A. 5√3 cm
B. 5√6 cm
C. 10√2 cm
D. 20 cm
1*b 2*d 3*b
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by nkenta(m): 12:25pm On Apr 17, 2013
JAMB ASSIST 2013

Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by tboy08: 1:43pm On Apr 17, 2013
Wao it has been a while looking forward to seeing a maths thread like this.....hmm infact,i've missed alot
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by tboy08: 1:45pm On Apr 17, 2013
My first question on this thread:
write the two's compliment of the binary 11001?
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by tboy08: 2:14pm On Apr 17, 2013
Integrate 2x + 4/ x^2 + 4x + dx
a)log x + 4 + c
b)in x^2 + 4x + c
c) 2x/4 + c
d) 2x + 4 /2 + c
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 5:11pm On Apr 17, 2013
t.boy007:
My first question on this thread:
write the two's compliment of the binary 11001?

two's complement of 11001= 00110

t.boy007:
Integrate 2x + 4/ x^2 + 4x + dx
a)log x + 4 + c
b)in x^2 + 4x + c
c) 2x/4 + c
d) 2x + 4 /2 + c

b
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Edis4christ(m): 11:22am On Apr 18, 2013
Adex097: 1) The Sine, cosine and tangent of 240' are, respectively
A. √3/2, -1/2 and √3
B. -√3/2 , -1/2 and √3
C. -√3/2 , 1/2 and -√3
D. √3/2 , 1/2 and √3


2)Which of the following have the same values as sin 15' ?
(I) Sin 165' (ii) Sin 285'
(Iii)Sin (-15') (iv)Sin(-195')

A. I and ii only
B. Iii and iv only
C. I and iii only
D. I and iv only

3). Two of the angles of a triangle are 120' ans 45' . If the side facing the angle 45' is 10cm long , then the side facing the angle 120' is

A. 5√3 cm
B. 5√6 cm
C. 10√2 cm
D. 20 cm
1) B
2) D
3) B
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Adex097: 2:17pm On Apr 19, 2013
Ortarico:

1. B
2. D
3. B
oga Adex post the former correction nah
score:::::3/3
papindinho: 1*b 2*d 3*b
score:::::3/3
Edis4christ:
1) B
2) D
3) B
score:::::3/3......
Kudos to you all
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Adex097: 2:19pm On Apr 19, 2013
I'm so so sorry guys...I've been busy. Lately
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Adex097: 2:34pm On Apr 19, 2013
Which of the following angles cannot be constructed with a ruler and a pair of compasses only?
A. 105'
B. 112 1/2' (one hundred nd twelve and half degree)
C. 115'
D. 120'
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by mathefaro(m): 6:56am On Apr 20, 2013
Adex097: Which of the following angles cannot be constructed with a ruler and a pair of compasses only?
A. 105'
B. 112 1/2' (one hundred nd twelve and half degree)
C. 115'
D. 120'
of coz, dat should be C-115° although you know what u've used there is not degrees but minutes, talking about (')
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by mathefaro(m): 7:03am On Apr 20, 2013
1. A Gp of a positive terms and a Ap have same first term.the sum of their first terms is 3 the sum of their second term is 3/2, and the sum of their third term is 6.find the sum of their fifth terms

2. A trader bought 30articles.he sold 20 of
them at a gain of 16% and sold the
remainder at a loss of 4%.find the
percentage profit/loss on the articles.

3. Find the value of x.if
(x+3) ^3 + (x+4) ^3 = (2x+7) ^3

I'm sorry for my questions haven't got options. just show ur workinz
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by sazy(m): 6:53pm On Apr 20, 2013
1.B 2.D 3.B
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by emekakelvin(m): 1:35pm On May 05, 2013
Guy i just try my luck
mathefaro: 1. A Gp of a positive terms and a Ap have same first term.the sum of their first terms is 3 the sum of their second term is 3/2, and the sum of their third term is 6.find the sum of their fifth terms

2. A trader bought 30articles.he sold 20 of
them at a gain of 16% and sold the
remainder at a loss of 4%.find the
percentage profit/loss on the articles.

3. Find the value of x.if
(x+3) ^3 + (x+4) ^3 = (2x+7) ^3

I'm sorry for my questions haven't got options. just show ur workinz
(1)17 (2) no idea (3)7+square root of 241/4 and 7-squareroot of 241/4
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 11:36am On May 16, 2013
mathefaro: 1. A Gp of a positive terms and a Ap have same first term.the sum of their first terms is 3 the sum of their second term is 3/2, and the sum of their third term is 6.find the sum of their fifth terms

2. A trader bought 30articles.he sold 20 of
them at a gain of 16% and sold the
remainder at a loss of 4%.find the
percentage profit/loss on the articles.

3. Find the value of x.if
(x+3) ^3 + (x+4) ^3 = (2x+7) ^3

I'm sorry for my questions haven't got options. just show ur workinz

choi, Let's Go There (LGT)...

1
first term:
a+a=3
a= 3/2

second term:
ar+a+d= 3/2
ar+a= 3/2 - d
multiplyn thru by 2:
2a (r+1)= 3-2d
but a= 3/2;
simplifyn gives:
3+3r= 3 - 2d
3r= -2d
d= -3r/2.....

3rd term gives:
a+2d+ar2= 6
simplifyn givs. . .
a(1+r2)= 6-2d
giving 3/2(1+r2)= 6-2d
reduce by multiplyn thru by 2. . .
3r2= 9 - 4d
but d= -3r/2
substitutn givs 3r2-6r-9=0
r2 - 2r - 3=0
r=3 or -1....but r=3 since term r is positive, hence a=3/2, r=3 and d=-9/2

hence d sum of their 5th term;
==> a+4d+ar4= 122

courtesy My Oga At The Top; Sir Onioshine

2 Likes

Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 12:43pm On May 16, 2013
2.

Sale of 20 articles at a gain of 16%= 116%
: 20*116/100= 23.2% actual gain

Sale of 10 articles at a loss of 6%= 96%
:10*96/100= 9.6%
actual gain

p/l= 100-(23.2+9.6)
p/l= 100-32.8
loss= 67.2%....in my own sha
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by mathefaro(m): 12:58pm On May 16, 2013
Ortarico:

choi, Let's Go There (LGT)...

1
first term:
a+a=3
a= 3/2

second term:
ar+a+d= 3/2
ar+a= 3/2 - d
multiplyn thru by 2:
2a (r+1)= 3-2d
but a= 3/2;
simplifyn gives:
3+3r= 3 - 2d
3r= -2d
d= -3r/2.....

3rd term gives:
a+2d+ar2= 6
simplifyn givs. . .
a(1+r2)= 6-2d
giving 3/2(1+r2)= 6-2d
reduce by multiplyn thru by 2. . .
3r2= 9 - 4d
but d= -3r/2
substitutn givs 3r2-6r-9=0
r2 - 2r - 3=0
r=3 or -1....but r=3 since term r is positive, hence a=3/2, r=3 and d=-9/2

hence d sum of their 5th term;
==> a+4d+ar4= 122

courtesy My Oga At The Top; Sir Onioshine
Good work. Welldone, but you made a slight mistake in your final answer. please check and make necessary corrections
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by mathefaro(m): 1:20pm On May 16, 2013
Ortarico: 2.

Sale of 20 articles at a gain of 16%= 116%
: 20*116/100= 23.2% actual gain

Sale of 10 articles at a loss of 6%= 96%
:10*96/100= 9.6%
actual gain

p/l= 100-(23.2+9.6)
p/l= 100-32.8
loss= 67.2%....in my own sha
Not convincing enough, you can do better. It's wrong,i'm sorry
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 1:29pm On May 16, 2013
3.

a3+b3= (a+b)^3 - 3ab(a+b)
sum of powers of 3
:let a= x+3 and b= x+4
substitutn gives:
(x+3)^3 + (x+4)^3= (2x+7)^3 - 3(x+3)(x+4)(2x+7)
==> (2x+7)^3 - 3(x+3)(x+4)(2x+7)
==> (2x+7)^3
==> 3(x+3)(x+4)(2x+7)=0
dividng both sides by 3 and solving the above gives:
x= -3, -4 or -7/2

Courtesy; Oga At The Top, Sir Onioshine
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Nairalanda(m): 1:44pm On May 16, 2013
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Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by mathefaro(m): 1:57pm On May 16, 2013
Ortarico: 3.

a3+b3= (a+b)^3 - 3ab(a+b)
sum of powers of 3
:let a= x+3 and b= x+4
substitutn gives:
(x+3)^3 + (x+4)^3= (2x+7)^3 - 3(x+3)(x+4)(2x+7)
==> (2x+7)^3 - 3(x+3)(x+4)(2x+7)
==> (2x+7)^3
==> 3(x+3)(x+4)(2x+7)=0
dividng both sides by 3 and solving the above gives:
x= -3, -4 or -7/2

Courtesy; Oga At The Top, Sir Onioshine
Bravo, absolutely correct
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 2:36pm On May 16, 2013
mathefaro:
Good work. Welldone, but you made a slight mistake in your final answer. please check and make necessary corrections
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Nobody: 5:14pm On May 16, 2013
^

@Onioshine, solved it correctly! It's just that the answer is 105 and NOT 122==>>

The common ratio of the GP, r = 3 since the GP is positive

Since 2d = -3r, Then the corresponding common difference of the AP, d = -9/2.

Sum of their 5th terms is =>
GP 5th term=> ar^4
AP 5th term=> a + 4d

Sum of 5th terms of both series = ar^4 + a + 4d.
Substituting r, d and a for =>>
r = 3, d = -9/2 and a = 3/2,
The sum of their 5th terms yields =>

= ar^4 + a + 4d
= (3/2)(3)^4 + 3/2 + 4(-9/2)
= 243/2 + 3/2 - 18
= 246/2 - 18
= 105

Hence the sum of the series 5th terms is 105.

1 Like

Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by Ortarico(m): 6:47pm On May 16, 2013
doubleDx: ^

@Onioshine, solved it correctly! It's just that the answer is 129 and NOT 122==>>

The common ratio of the GP, r = 3 since the GP is positive

Since 2d = -3r, Then the corresponding common difference of the AP, d = -9/2.

Sum of their 5th terms is =>
GP 5th term=> ar^4
AP 5th term=> a + 4d

Sum of 5th terms of both series = ar^4 + a + 4d.
Substituting r, d and a for =>>
r = 3, d = -9/2 and a = 3/2,
The sum of their 5th terms yields =>

= ar^4 + a + 4d
= (3/2)(3)^4 + 3/2 + 4(3/2)
= 243/2 + 3/2 + 6
= 258/2
= 129

Hence the sum of the series 5th terms is 129.

ok, thanks for making the correction
Re: Mathematics Tutorial. For Utme, Post-utme & Other Related Examinations by mathefaro(m): 7:13pm On May 16, 2013
doubleDx: ^

@Onioshine, solved it correctly! It's just that the answer is 129 and NOT 122==>>

The common ratio of the GP, r = 3 since the GP is positive

Since 2d = -3r, Then the corresponding common difference of the AP, d = -9/2.

Sum of their 5th terms is =>
GP 5th term=> ar^4
AP 5th term=> a + 4d

Sum of 5th terms of both series = ar^4 + a + 4d.
Substituting r, d and a for =>>
r = 3, d = -9/2 and a = 3/2,
The sum of their 5th terms yields =>

= ar^4 + a + 4d
= (3/2)(3)^4 + 3/2 + 4(3/2)
= 243/2 + 3/2 + 6
= 258/2
= 129

Hence the sum of the series 5th terms is 129.
Wrong, check ur substitution, u made a slight error. d ans is 105

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