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++MATHS SYMBOL CLASS for 2014
* 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.
X:1,2,3,4,
FX: 4,6,8,10
FX-Xbar: 10,8,6,4,
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....
IN A CLEARER WAY-
→ comma means NEXT LINE(e.g)
x : 1,2,3
fx : 4,5,6
fx-xbar : 10,8,6,4
x|fx |fx-x¯¯|
1| 4 | 10 |
2| 6 | 8 |
3| 8 | 6 |
4| 10| 4 |
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.
(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 |
2)*=multiplication sign.
3)^ = Riase to pwer
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(x¯¯)
7)Pie = pie symbol eg Area of a circle is (Pie r2).
(8. )Tita = θ eg Sinθ.
10)Root or Rut or Sqrt or sqr root = √ ; eg Root2 means √2
11)/ means ÷
12)----(1) means equation 1






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(1a) Simplify
-->(6/10*32*4/100)/ (12/10*8/1000*16/100)
-->(6*32*4/10*1000)*(10*1000*100/12*8*16)
-->(6*32*4*100/12*8*16)
-->(6*2*4*100/12*= 6*100/12
-->=50
(1b)
<AEF=<EBH (corresponding angle)
<EBH=3x(degree)
<GHC=<HBE=7x(degree)(same reason)
120(degree)+7x(degree)+3x(degree)=360
(degree) angle at a point
120+10x=360
10x=360-120
10x=240
x=240/10=24(degree)
(2a)
3sqrt(25*3)-sqrt(4*3)+sqrt(27*4)
15sqrt(3)-2sqrt(3)+2sqrt(27)
15sqrt(3)-2sqrt(3)+2sqrt(9*3)
15sqrt(3)-2sqrt(3)+6sqrt(3)=19sqrt(3)
(2b)
124n=232five
(1*n^2)+(2*n^1)+(4*n^o):(2*5^2)+(3*5^1)
+(2*5^o)
n^2+2n+4=50+15+2
n^2+2n+4-67=0
n^2+2n-63=0
n(n-7)+9n-63=0
n(n-7)+9(n-7)=0
(n+9)(n-7)=0
n=-9 or n=7:. n=7

(3a) Let p=1/x ,q=1/y p+q=5 ---->equ
(1) q-p=1 ---->equ(2) p+q=5 ---->equ(1) p+q=1
---->equ(2) Add equ(1) and equ(2) 2q=6 ,
q=6/2=3 Substitute q=3 into equation(1) p+q=5
p+3=5 P=5-3 p=2 Recall p=1/x , 2=1/x, x=1/2
q=1/y, 3=1/y , y=1/3 Therefore: x=1/2 , y=1/3
(3b) Where the road is good 72:x/0.75
x=72*0.75 x=54km Where the road is bad
48:x/0.75 x=48*0.75 x=36km Number of
kilometers of good surface is 54km

(4a) Area(A)= (tita/360*pieR^2) -(1/2R^2Sin
(tita)) 504:((90/360)*22/7*r^2)-(1/2*r^2*sin90)
504:(0.25*3.142*r^2)-(0.5r2) 504= 0.7855r^2 -
0.5r^2 504= 0.2855r^2 r^2= 504/0.2855
r^2=1765.32 r:sqrt(1765.32) r=42cm
============ NOTE: Tita means tita sign(it
looks like crossd-zero)
(4b) Draw the diagram <RQS=66(degree) {base
angles of isoceles) ===================
PLS NOTE: Tita means tita sign. It look like
crossed zero. And also note: r:sqrt(1765.32)
means r= _/1765.32
=====================
(5) Pr(x)=0.5, Pr(X^1)=0.5 Pr(Y^1)=0.3 , Pr(y)
=0.7 (a) Pr(both contracts):-pr(x)*Pr(y)
=0.5*0.7=0.35 (5b) Pr(exactly one of the
contracts)= Pr(X)*Pr(Y^1) +Pr(X^1)*Pr(y) :
(0.5*0.3)+(0.5*0.7) =0.15+0.35 =0.5 (5c) Pr
(Neither of the contrasts) = pr(X^1)*Pr(Y^1)
=0.5*0.3 =0.15
(6a) 3/(2p-1/2):(1/3)/(p/4+1/2). 6/(4p-1)=4/(3p
+6). 6(3p+6)=4(4p-1). 18p+36=16p-4. 2p=-40,
p=-20.
(12a) Given, 5cos(x+8.5)-1=0 C0s(x+8.5)^o=1/5
cos(x+8.5)^o=0.2 x+8.5^o=Cos^-1(0.2) x
+8.5^o=78.46 x=78.46-8.5 x=69.96^o x=
70(degree)
(12bii) QR^2:(PR^2)+(PQ^2)
-2PR*PCOS(RPQ) P^2=32^2+24^2-2(32)(24)
COS45(DEGREE) P^2=1600-1536*0.7071
P^2=1600-1086.1 P^2=513.88 P:sqrt(513.88)
p=22.67km Distance QR=22.67km (12biii) 32/sin
(tita)=22.67/sin45(deg), sin(tita)=0.9981
tita:sin^-1(0.9981) tita=86(degree)

(3a)Let p=1/x ,q=1/yp q=5 ---->equ(1)q-p=1 ---->equ(2)p q=5 ---->equ(1)p q=1 ---->equ(2)Add equ(1) and equ(2)2q=6 , q=6/2=3Substitle q=3 into equation(1)p q=5p 3=5P=5-3p=2Recall p=1/x , 2=1/x, x=1/2q=1/y, 3=1/y , y=1/3Therefore: x=1/2 , y=1/3(3b)Wherethe road is good72=x/0.75x=72*0.75x=54kmWhere the road is bad48=x/0.75x=48*0.75x=36kmNumber of kilometers of good surface is 54km(4a)Area(A)= (tita/360*pieR^2) -(1/2R^2Sin(tita))504=((90/360)*22/7*r^2)-(1/2*r^2*sin90)504=(0.25*3.142*r^2)-(0.5r2)504= 0.7855r^2 - 0.5r^2504= 0.2855r^2r^2= 504/0.2855r^2=1765.32r=Sqrt(1765.32)r=42cm(4b)Drawthe diagram:::KEEP REFRESHING THIS

(12a)Given, 5cos(x+8.5)-1=0C0s(x+8.5)^o=1/5cos(x+8.5)^o=0.2x+8.5^o=Cos^-1(0.2)x+8.5^o=78.46x=78.46-8.5x=69.96^ox=70(degree)(12bii)QR^2=(PR^2)+(PQ^2)-2PR*PCOS(RPQ)P^2=32^2+24^2-2(32)(24)COS45(DEGREE)P^2=1600-1536*0.7071P^2=1600-1086.1P^2=513.88P=sqrt(513.88)p=22.67kmDistance QR=22.67km(12biii)32/sin(tita)=22.67/sin45(deg),sin(tita)=0.9981tita=sin^-1(0.9981)tita=86(degree)(5)Pr(x)=0.5, Pr(X^1)=0.5Pr(Y^1)=0.3 , Pr(Y)=0.7(a)Pr(both contracts)=Pr(x)*Pr(Y)=0.5*0.7=0.35(b)Pr(exactly one of the contracts)=Pr(X)*Pr(Y^1)+Pr(X^1)*Pr(Y)=(0.5*0.3)+(0.5*0.7)=0.15+0.35=0.5(c)Pr(Neither of the contrasts)= pr(X^1)*Pr(Y^1)=0.5*0.3=0.15(4a)Area(A)= (tita/360*pieR^2) -(1/2R^2Sin(tita))504=((90/360)*22/7*r^2)-(1/2*r^2*sin90)504=(0.25*3.142*r^2)-(0.5r2)504= 0.7855r^2 - 0.5r^2504= 0.2855r^2r^2= 504/0.2855r^2=1765.32r=Sqrt(1765.32)r=42cm(4b)Drawthe diagram