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Friday March 29th 2024

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Waec 2018 Further Maths Objective And Theory Answers

F/MATHS OBJECTIVE:
1-10 BCADDDDDBB
11-20 BAABCCDDCC
21-30 BCABBAABAB
31-40 CBADBDDCAB


F/MATHS THEORY ANSWERS

1)
X-3|2 2| 4|5 2 | 3|5 2|= -24
| -4 6-x| |2 6-x| |2 -4| X-3(12-2x 8) 4(30-5x-4) 3(-20-4) = -24
X-3(20-2x) 4(26-5x) 3(-24)= -24
20x - 2x² - 60 6x 104 - 20x - 72 = -24
-2x² 6x - 60 104-72 24 = 0
-2x² 6x - 4 = 0
Divide through by -2
X² - 3X 2 = 0
X² - 2X - X 2= 0
X(X-2)-1(X-2)=0
(X - 1)(X - 2)=0
X=1 OR X=2
=====================
(2)
Log 3x - 3logx³ 2 = 0
Log 3x - 3log3³/log3x 2 = 0
Log3x - 3/log3x 2 = 0
P - 3/p 2 = 0 where P = log3x
P² - 3 2p = 0
P² 2p - 3 = 0
(p 3) ( p - 1) = 0
P = -3 OR p = 1
But log3x = p
when p = -3
Log3x = -3
X = 3-³ = 1/27
And when P = 1
Log3x = 1
X = 3¹ = 3
=====================
(3a)
U= x-2 ; hence X = u 2
Therefore:
X^3 5/(x-2)^4 = (u 2)^3 5/ (u 2-2)^4
=(u 2)^3 5/u^4
(3b)
(u 2)^3 5/u^4 = (u 2)^3/u^4 5/u^4
And X = 1/27 OR 3
=====================
(4)
Sn = n/2[2a (n-1)d]
S12 = 12/6[2a 11d]
S12= 6[2a 11d] = 168
2a 11d = 28-------(1)
Also
T3 = a 2d = 7---------(2)
Multiplying 1 by 2
2a 4d = 14
Eqn 1 minus Eqn 3 gives
7d = 14
d = 2
Putting this in eqn 2
a 2(2) = 7
a (4) = 7
a = 7 - 4
a = 3
Common difference = 2
=====================
5)
Tabulate
X,y,d,d^2
A 8,6,2,4
B 5,3,2,4
C 1,4,-3,9
D 7,8,-1,1
E 2,5,-3,9
F 6,7,-1,1
G 3,1,2,4
H 4,2,2,4
Ed^2 =4+4+9+1+9+1+4+4 =36
r=1-6£d^2/n(n^2-1)
=1-6*36/8(8^2-1)=1-216/504
=1-0.43
=0.57
=====================
(6)
It follow that:
P(n) = 1/3 and p(k)¹ = 1 - 1/3 = 2/3
P(T) = 1/5 and P(T)¹ = 1- 1/5 = 4/5
Hence,
probability that only one if the them will be solve the questions will be:

= (1/3 × 4/5) (1/5 × 2/3) = 4/15 2/15
= 6/15
= 2/5
=====================
(7)
m = 3i - 2j ; n = 2i 3j ; p = i 6j
Therefore:
4(3i - 2j) 2(2i 3j) -3(-i 6j)
12i - 8j 4i 6j 3i - 18j
12i 4i 3i - 8j 6j - 18j
19i = 20j
=====================
(8)
m1 = 20kg
u1 = 8ms-1
m2 = 30kg
u2 = 50ms-1
(a)
In same direction
m1u1 m2u2 = (m1 m2)v
20 × 80 30 × 50 = (20 30)v
1600 1500 = 50v 3100/50 = 50/50
V = 62ms-1
(b)
In opposite direction
m1u1 - m2u2 = (m1 u2)V
20×30 - 30×50 = (20 30)V
1600 - 1500 = 50V
100/50 = 50V/50
V = 2m/s

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