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Grade 11 and 12 Functions Summary Notes (handwritten)
-
IEB MATHS PAPER 1 GRADE 12 NOTES
-
SUMMARY OF GRADE 12 CALCULUS
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, EQUATIONS + INEQUALITIESafore f b' -
ac ulli 's r r ems
>
fr statins
"
Is ne e ree x
=
nun er Is rk in the same units
'
-
bl b ac
let is it ;
x -1 " -2+3×-1×+1=3 " -2
Convert hours and minutes
✗ = -
n e.
g.
2-
✗ 2+3×2-3=3×-6 Understand the Problem
Za
i. x ?
Sim if
-
Discriminant bxtc
.
i 1×2 : . ✗ 2- ✗ +1 2. Setup the e
to work only in minutes
Golden Tue Z= Unknown
-
e er
: . 2×-1 Situation 1 Glasses rice per
Glass
quantities =
xory
i e Ly si es x
: -X =
£ Cost Price x 3 3x Known Formulae =
simplify :
12
Mts m±Z
State
+
Sell Price Distance 1km speed / time
x h
uatins ctins m 2 1 t.mn
-
=
-
a x
i. Mts m 2 t 12 =
C)
-
selling " " stP=
restrictions 3 Equation "
Price per
-
Total
" =
=
i. m2 -2m + sm -10+12 = -15 Price
3¥
or x
;
.
=
-
=
m2 3m 2 z
item
+ = m =
× .
,o
i. +
. -
. .
!
or
umber of Items
real non - real Cross canoe .
:( m + 2) ( m + 1) = m= -1
.
Context
=/ Let K 300
y
Su stitutin 4+1+4+1
=
1=+0 =
y
+ I :-P per glass = so
=
RG rea = lxb
] SO glasses
1
rc r ems Re ice the repeatec : .
KI = K : . k=z at RG each Rate of work = work done
or
time taken
2 roots with :
y +1=2
:
4=1 ne ualities
eqoa expression variable
- -
a
2 X S
rational
-
3 XZ
, .ca/s2x--xx+6-x= a -3 x2 - 4×-21 - - 100 -
99 x x -
3 ±
+6 a =
} 7) ( k
-
= x
to
✗
+3 ✗ 2+99×-1
2 unequal roots sign only nesice x2 K -
. .
✗ +6 = a = 2+3 or x
KZ X G = a = -2+3
2. Suire
-
-
ne utities 17 si es x -
2) ( ✗ + 3) =
.
.
.
a=s or
Critica cues :
-3 ;7 (x - 1) ( ✗ +100
x -
5=0
'
3C = 2 or I +
+
3. Substitute Cs
. . a = -
sols back in ✗ =-3 * • • •
: I ;l Cvs : 5
.
I N ;
I
] a =
> 2
16 4 3
erfect erfect ( b= ud
-
in +
in etin Lies uare
: - ✗ +2 -
a
+
z
= • + -
:*
< = .
•
, , .
b 2 2 : 1×+212 =
zba
C
Sub values g
.
Rational Irrational
+ =
in
,
Xt za a
: x =
-2
2
a =
-3 ± 3- (2) C- 8
2 EE ?g -3 I 5
unequal
✗ =
unequal 2 Ua ratio rmu i zcz ) : .
x :X -100 or x X or x
-3 ± 3
Zootsare :x=-b±za
'
rational i. ✗
Critical Values Simplify Undefined outputs
=
into
-
"
irrational
4
•
2
?
KY = 4 + 2x
Y =
I +
roots roots Simultaneous • ✗ = x -1 .
xcx -
1) = + 2x are zeroes of the Standard form are not included
-
x2 3x = •
y = -
I =3
Simplify C' + bxtc
- -
.
for one variable x= and
y
=3
inequality represented a> in the final
,
2. Substitute
or
✗ = -1 and y= -2 on a number line if ssi e ineualit
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