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Maths (Essay & Objective) Waec 2017 Free Expo Answers
============================
Thursday, 20th April, 2017
General Mathematics 2 (Essay) 09.30am - 12.00pm
General Mathematics 1 (Objective) 2.00pm - 3.30pm
============================

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MATHS OBJ:
1-10: CBBCCACBBC
11-20: CACBAAAADB
21-30: BBADBCCACB
31-40: BBCACBDADA
41-50: DDACCCDDCB



================================
*SECTION A ANS ALL QUESTIONS*
================================

1 a)
(y -1 ) log 4 ^ 10 = ylog 16 ^ 10
log 4 ^ 10 ( y -1 )= log 16 ^ y 10
4 ^ ( y -1 )= 16 y
4 ^ y -1 = 4 ^ 2 y
y- 1 = 2 y
-1 = 2 y= y
-1 = y
y= -y

1 b )
let the actual time for 5 km / hr be t
for 4 km /hr = 30 mint + t
4 km /hr =0 . 5 + t
distance = 4 (0 . 5 + t )
= 2 * 4 t
for 5 km /hr , time = t
distance =5 t
1 + 4 t = 5 t
t= 2 hrs
actual distance = 5 * 2 = 10 km

================================

2a)
2/3 (3x - 5) - 3/5 (2x - 3) = 3
(15) x 2/3 (3x - 5) - 3/5 (15) (2x - 3) = 3(15)
10(3x -5) - 9(2x - 3) = 45
30x - 50 - 18x + 27 = 45.
12x - 23 = 45
12x = 45+23
12x = 68
X = 68/12
X = 5.67

2b)
80 = n+r ( ext. < equal sum of opp int. < s )
80 = n+r ------------ (i)
M = 80 + 92 - n
M = 172 - n ----------- (ii)
80 + 92 - n + 180 - m = 180°‎
80 + 92 + 180 - n - m = 180°‎
352 - n - m = 180
-n - m = 180 - 352‎
- n - m = - 172°‎
m + n = 172°‎

===============================

3a) ‎
Tan 23.6° = h/50
Cross multiply
Tan 23.6° x h/50
h = 50 tan 23.6°
= 21.844m‎
‎aprox. 22m

3b)
Area of A = 1/2bh
45 = 1/2 x 10 x h
45 = 5h
h = 9cm
Area of < QTUS = 1/2 ( QT + US)h
= 1/2 ( 6 + 16)9
= 99cm^2

================================

4 a)
T 6 =37
T 6 =a + ( 6 - 1 )d
T 6 =a + 5 d
a + 5 d = 37 - --- -( eq1 )
s 6 = 147
sn = n / 2 (2 a + (n -1 ) d )
147 = 3 (2 a + 5 d )
49 = 2 a + 5 d
2 a+ 5 d = 49 -- -- (eq 2 )
a + 5 d = 37 - --( eq1 )
2 a+ 5 d = 49 -- -( eq2 )
a =12

4 b )
S 15 = 15 /2 ( 2 (12 )+ 14 d )
S 15 = 15 /2 ( 24 + 14 d )
from(1 )
a + 5 d = 37
12 + 5 d = 37
5 d =37 -12
5 d =25
d =5
S 15 = 15 /2 ( 24 + 14 (15 )
S 15 = 15 / 2 (24 + 70 )
S 15 = 15 /2 * 94
S 15 = 15 * 42
S 15 = 630

================================

5a)
Let bag=B
Shoe= S
U=120
n(BnS)=45, n(s)=x+11, n(b)=x
n(SnB')=x+11-45
=x-34
n(BnS') = 45

5b)
Y - 45 + 45 + Y - 34 = 120
2Y - 34 = 120
2Y = 120 - 34
2Y = 154
Y = 154/2
Y = 77
11+x=77+11
= 88
Therefor 88 bought shoes costumer

5c)
n(bag)= 77 customers
Pr. =77/120


================================
*SECTION B ANS 5 QUESTIONS ONLY*
================================

8) 
In Table Form / Tabular form

X = 1,2,3,4,5
F = m+2, m-1, 2m-3, m+5, 3m-4 = 8m - 1‎
Fx = m+2, 2m-2, 6m-9, 4m+20, 15m-20 = 28m - 9‎

But x̄ ( this symbol (x̄) means X bar) 
= 75/23‎
ΣFx / Σf = 75/23 = 28m - 9/8m-1
  75/23 = 28m - 9/8m - 1
Cross multiply 
75(8m-1) = 23(28m-9)
600m - 75 = 644m - 207
 -75 + 207 = 644m - 600m
132 = 44m
M = 3

8b)
In tabular form
X = 1,2,3,4,5
F = 5,2,3,8,5
Cum Freq= 5,7,10,18,23

Q1 = (N+1/4) = (23+1/4)
 = 6

Q3 = (3N + 1/4) = (3*23+1/4)
 = 18

Inter quarter range = Q3 - Q1
 =. 18-6
 = 12

8bii)
Pr. (at least 4 mark)
= 8+3+2+5/23
 = 18/23‎



10)
Sin x = 5/13
Using pythagoras rule
M^2 = 13^2 - 5^2 (^ means Raise to power)
M^2 = 169 - 25
M ^2 = 144
M = √144
M = 12
Hence:
Cos x - 2sin x / 2tan x
12/13 - 2(5/13) / 2(5/12)
‎= 12/13 - 10/23 / 5/6
FIND LCM
= 12 - 10/13 / 5/6
= 12/65

10b)
Draw a triangle LACB
in triangle LCB
Hyp^2 = Opp^2 + Adj^2
12^2 = 9.6^2 + |CB|^2
144 = 92.16 = |CB|^2
144 – 92.16 = |CB|^2
51.84 = |CB|^2
therefore, |CB| = √51.84
|CB| = 7.2m
|AC| + |CB| =|AB|
|AC| + 7.2m = 10m
|AC| = 10m – 7.2m

|AC| = 2.8m
In triangle LCA
Hyp^2 = Opp^2 + Adj^2
|LA|^2 = |AC|^2 + |LC|^2

|LA|^2 = 2.8^2 + 9.6^2

|LA|^2 = 7.84 + 92.16

|LA|^2 =100

|LA| = √100

|LA| = 10m

10bii)
in triangle LCA
sinθ = Opp/Hyp
sinθ = |LC|/|LA|
sinθ = 9.6/10
sinθ = 0.96
θ = sin^-1 (0.96)
θ = 73.74

===============================

13ai)
given
x(*)y=x+y/2
i)3(*)2/5=3+2/5/2
=(15+2/5)*1/2
=17/5*1/2
=17/10= 1,7/10

13aii)
8(*)y=8^1/4
=8+y/2 =33/4
32+4y=66
4y=66-32
4y=34
y=34/4
y=17/2
y=8^1/2

13b)
given DABC
AB=(^-4/6) and AC =(3/^-8)
so AP =1/2(^-4/6)
AP=(^-2/3)
hence
CP = CA + AP
CP= -(3/^8)+(^-2/3)
CP = (^-5/11)




























MATHS OBJ:
1-10: CBBCCACBBC
11-20: CACBAAAADB
21-30: BBADBCCACB
31-40: BBCACBDADA
41-50: DDACCCDDCB



*WAEC 2017: SYMBOLS/SIGNS FOR MATHS, PHYSICS, CHEMISTRY, ECONOMICS AND ALL OTHER CALCULATION SUBJECTS.*


* means multiplication
tita u should know dat.
rais means raise to power

^ means raise to power
sqr rut/ squar rut means square
root

----(1) means equation 1
yr means year

f(x-xbar) means x MINUS x BAR as in statistics which means that
MINUS WILL BE ON TOP OF x.

, (Comma) means NEXT LINE, THIS MEANS THAT THE FOLLOWING NUMBER IS UNDER THE NUMBER IT
IS FOLLOWING i.e UNDER. It is
usually used during STATISTICS
when drawing a table.

EXAMPLE 1.
X:1,2,3,4,5,6
FX: 4,6,8,10,12
FX-Xbar: 10,8,6,4,2,1
DRAW A TABLE WITH X|FX|(FX-
Xbar)

The above statement means
that:
~ For X, it has 1 2 3 4 5 6 under it.
which means 1 is under 2, 2 is
under 1, 3 is under 2, 4 is under 3
and so on...

~Under FX you have 4, then 6
under 4, then 8 under 6, then 10
under 8, then 12 under 10.....
~Under FX-Xbar you have 10,
then 8 under 10, then 6 under 8,
then 4 under 6, then 2 under 4,
then 1 under 2....

ANOTHER EXAMPLE:
Class interval:
60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99.
X: 62,67,72,77,82,87,92,97.
F: 2,3,6,11,8,7,2,1.
FX:124,201,432,847,656,609,184,97.
F(x-x bar)2:
561.12,414.18,273.36,33.66,84.48,476.42,351.12,333.06

MEANING OF THE ABOVE
EXPRESSION:
Bar means Minus on top of d
number or Variable and comma
means next line which means
each of them are unda. Eg 60-64
is unda Class interval, then 65-69
is unda 60-64,etc .So comma
means unda.
NOTE THAT WHEN U SEE
SOMETHING LIKE THE ABOVE TWO EXAMPLES, U WILL NEED TO DRAW A TABLE..

YOU NEED TO KNOW THESE ALSO:

MATHS CODES:

1) , (comma) means next line.

2) * =multiplication sign.

3) figures after any alphabet or
closed bracket means superscript or raised to power eg (i)4x3 means 4x raised to power

3.(ii)(2x+y)2 means (2x+y)raised
to power two.

4) P also means raised to power
eg 10P6 means 10 raised to
power six.

5) log3(base 4) ..Note:the base
must be SUBSCRIPT .

6) x bar = mean symbol

7) Pie = pie symbol eg Area of a
circle is (Pie r2).

8) Tita = angle symbol eg Sin(tita).

FORUM IS NOW OPEN... LETS HEAR UR QUESTION... IN A CLEARER WAY

/ means ÷

→ * means X

→ tita means θ

→ rais means x4

→ ^ means √

→ cube rut e.g 3√27

→ squar root means √

→ ----(1) means equation 1

→ bar means

¯¯e.g xbar = x¯¯

→ comma means NEXT LINE(e.g)

x : 1,2,3
fx : 4,5,6
fx-xbar : 7,8,9

x|fx |x¯¯|
1| 4 | 7 |
2| 5 | 8 |
3| 6 | 9 |

*Please ask Questions on anywhere u are confuse*



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