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## 100% REAL GCE WAEC GENERAL MATHEMATICS RUNZ ANSWERS

“); }10a)
YX/XZ=XM/MZ
W/10=8/15
15W=10*8 W=5.33cm.

10bi)
q^2=p^2+r^2-2prcos tita
q^2=20^2+15-2*20*15 c0s 90
q^2=400+225-0
q^2=625 q=sqroot625
q=25km.

10bii)
p/sinP=q/sinQ=r/sinR
25/sin90=15/sinR
sinR=15*1/25 sinR=0.6
R=sin^-1(0.6)
R=36.86degrees
The bearing of p from R
=90+90+90+alpha
alpha=45-36.86 =90+90+90+8.14
=278.14
=278degrees
The bearing of p from R=278degrees.

## 100% REAL GCE WAEC GENERAL MATHEMATICS RUNZ ANSWERS

==================================
9a)
CBA=180-(128-x) sum of angle on a straight line
CBA=52+x
=52+x
Also BCD=180-x(angle on a straight line)
DCQ=180-(180-x) DCQ=180-180+x
DCQ=x
x+52+x+76=180
2x=180-52-76
2x/2=52/2
x=26degrees.
=====================================
8a)
diagram
(8+x)^2 = x^2+32
64+16x+x^2= x^2 + 1024
16x=1024-64=960
therefore 960/16= 60 x=960/16
=60
=68cm.
=====================================
8b)
diagram
(i)volume of a pyramid
=1/3 AH
2601= 1/3 * A * 27
A=7803/27
=289cm^3
Area of square =289 t^2= 289
t= sqr rut(289)
l=17cm.

## 100% REAL GCE WAEC GENERAL MATHEMATICS RUNZ ANSWERS

8bii)
AC^2 = 17^2 +17^2
AC^2 = 289 +289 Ac^2 =578
AC =sqr root (578)
AC=24.04cm
for the triangele COP
CO= 1/2 AC
=1/2 * 24.04 VC^2= 27^2 + 12.07
VC^2= 929 +144.49
VC= SQR root (873.48)
=29.55cm
cos x= 8.5/29.55 cos x=0.2877
x=cos^-1 0.2877
=73.66 degree.
==========================
1a)
1/2log 25/4- 2log10 4/5+log10 320/125
Firstly Log(25/4)^1/2-log(4/5)^2+log10 320/125
Log10 sqrt25/4-log16/25+log10 320/125
Log10 5/2-log10 16/25+log10 320/125
Furthermore – Log10 5/2+log10 320/125-log10 16/25
Log10 [5/2*320/125÷16/25]
Log10 [5/2*320/125*25/16]
Lastly – Log10 10=1.

1b)
% income= 20%
Grant per land =GHC€15.00
Total population from
2003-2007
=1.2*1.2*1.2*1.2*3000=6220.8
=6220.8*15
=ghc€93312
Total grant=GHC€93312.

## 100% REAL GCE WAEC GENERAL MATHEMATICS RUNZ ANSWERS

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
2a)
1/x+1/x+3=1/2
L.C.M=x(x+3)
X+3+x/x(x+3)=1/2
2(2x+3)/x(x+3)=1/2
2(2x+3)=x(x+3)
4x+6=x^2+3x
X^2+3x=4x+6
X^2+3x-4x-6=0
X^2-x-6=0
(X^2-3x)+(2x-6)=0
X(x-3)+2(x-3)=0
(X+2)(x-3)=0
X=-2 or x=3.

2b)
Let d bag of rice be X
Let d bag of beans be Y
X+Y=17—>(I)
2250x+2400y=39600—>(2)
From eqtn (I)
X=17-y
Using elimination method to eliminate Y
2250x+2250y=38250—>(3)
2250x+2400y=39600—>(4)
Eqtn 4- eqtn 3
2400x-2250x = 39600-38250
150x=1350
X=1350/150
X=9
D trader bought 9bags of beans.

## 100% REAL GCE WAEC GENERAL MATHEMATICS RUNZ ANSWERS

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
(3)
=Draw The Diagram=
Area of path –> 2[1/2 (x+2)] + 2(x+1) = 17
x + 2 + 2x = 17
3x + 2 = 17
3x = 17 – 2
also 3x = 15
x = 15/3
x = 5.

(a) Perimeter of garden
= 4x
= 4 x 5
= 20m.

(3b)
=Draw The Diagram=
Area Covered By Both Garden And path
= (x+1) (x+2)
= (5+1) (5+2)
= 6×7
= 42m^2.

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
(4a)
Given: Sinx = 3/5
i.e
=Draw The Diagram=
Using pythogoras triple 3,4,5
CosX + TanX/SinX
=4/5 + 3/4 ÷ 3/5
= 16+15/20 ÷ 3/5
= 31/20 ÷ 3/5
= 31/20 x 5/3
lastly = 31/12.

(4b)
=Draw The Diagram=
Reflex P’Q’T + R’Q’T + P’Q’R = 360 (sum at a point)
200 + 32 + P’Q’R = 360
232 + P’Q’R = 360
P’Q’R = 360 – 232
P’Q’R = 128°
From the Diagram
Q’R’U = P’Q’R = 128° (alternate angles)
Firstly X = Q’R’U + S’R’U
X = 128° + 180
X = 308°.

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
5a)
=Draw The Diagram=
1. | 2. | 3. | 4. | 5. | 6. |
——————————————
1|1,1|1,2 |1,3 |1,4 |1,5 |1,6 |
——————————————-
2|2,1|2,2 |2,3 |2,4 |2,5|2,6 |
——————————————–
3|3,1|3,2 |3,3 |3,4 |3,5|3,6 |
———————————————
4|4,1|4,2 |4,3 |4,4 |4,5|4,6 |
———————————————
5|5,1|5,2 |5,3 |5,4 |5,5|5,6 |
———————————————–
6|6,1|6,2 |6,3 |6,4 |6,5|6,6 |
————————————————

### B) pr(sum of outcome is 8) = 4/36 = 1/9 Bii) pr(product of outcom <10) = 30/36 = 5/6 Biii) pr(outcom contain atleast a 3) = 24/36 = 4/6 = 2/3. °°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°° (6a) 2 X (37)x = 75x 2 X (3x + 7)10 = (7x + 5)10 Finally 2 (3x + 7) = 7x + 5 6x + 14 = 7x + 5 14 – 5 = 7x – 6x 9 = x :- x = 9.

(6b)
Let The Number Of boys be X
Number Of girls in class = x + 5
GIVEN: x+5/+2 = 5/4
5(x+2) = 4(x+5)
5x + 10 = 4x + 20
5x – 4x = 20 – 10
x = 10
(i)Numbers of girsl in class
= x + 5
= 10 + 5
= 15
(ii)Total number of students
= x + x + 5
= 10 + 10 + 5
= 25
(iii)Probability of selecting a boy as class prefect
= 10/24
= 2/5.

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
7a)
|PQ|^2 = |PB|^2 + |BQ|^2
|PQ|^2 = (5 – x )^2 + X^2
Furthermore |PQ|^2 = 25 – 10x + x^2 + x^2 [note ^ means Raise to power]
|PQ|^2 = 2x^2 – 10x + 25
NB: PQ = QR (side of a square)
Area of PQRS = PQ x QR
= PQ x PQ = PQ^2
Area of PQRS = (2x^2 – 10x + 25)m square
GIVEN: 2x^2 – 10 + 25 = 3/5 of 25
= 2x^2 – 10x + 10 = 0
= x^2 – 5 + 5 = 0.

Using General Formular mthod
X = -(-5) ± Square Root (-5)^2 – 4(1)(5)/ (2 x 1)
X = 5 ± Square Root 25 – 20/ 2
Furthermore X = 5 ± Square Root 5 / 2
X = 5 + Square Root 5 / 2 OR 5 – Square Root 5 / 2
X = 3.62 or 1.68.

7b )
L + a / n – 1 = d ———— (I)
2s = n (a + 1) —————- (2)
From eq (1)
L + a = d (n – 1) ————– (3)
Put eq (3 into 2)
2s = nd (n-1)
2s = d (n^2 – n)
S = d ( n^2 – n ) / 2 or
S = dn(n-1)/2.
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°.

#### 100% REAL GCE WAEC GENERAL MATHEMATICS RUNZ ANSWERS

8a)
By using pythagoras
r^2 = (r – 8)^2 + 32^2
r^2 = r^2 – 16r + 64 + 1024
16r = 64 + 1024
r = 1088/16
r = 68
r=68cm
8bi)
{st/pt/
q2=27^2 +12^2
q=sqrt27^2 + 12^2
q=sqrt729+144
q=sqrt873
q=29.5cm.
================================
Good Luck

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