Algebra
(perfsa) equal (0)
Quadratic equations
+ -
real rational
unequal
discriminant (4)
of
irrational ; unequal
= bz
~ roots equation
x -
=
b -
49C
>
2d non-real
-method
·
·
surds -> perform a check !
·
complete the square > d must = 1
>
more c over
> add (b) " to both sides
>
factorise and solve
simultaneous
·
·
inequalities & factorise
+ +
< 1 =
3))CVs
CV CV
>
number line
>
Solve
Exponents Logs
2
3
S
b
xb
a +
x9 =
x
log is
·
base 10 if not said .
.
b
x"
a
x
-
= =
x
exponent form > log form
·
laws (x)b = 9
- b
-BPAL
I
BAP
(xy)"
base power answer
=
x9 .
ya
xo 1 by
>log
=
a a
y
= =
x
- 9
= ca Sec2 = ,
(A xB)
factorise
log log
A
log B
=
·
I term ,
+
A A &
·
I term , prime basea simplify log
( *) =
log A-logB
,
x b log
trinomials (desc order of
log ,
=
x
· .
middle term (first term) log =
I
L solve
log m logm
=
log , a
=
a
surds (rationalise denominator if asked
only
log(a)
·
. = 1
logab
logy1 0
=
log , 0 undefined
=
, sequences & Series
.
1 Arithmetic sequences .
2 Geometric sequences
Tn = a + (n 1)d-
Tn = arn-1
Common
·
Common Ist
·
difference ist ratio
Tz
·
(T2 T1) =
(T3 - Tz) +1 = =
r
.
3 Quadratic sequences
Tn = an + bn + C
a + b + c = Ti Tz T3
? 2
3a + b =
29 - d
.
4
Arithmetic Series .
5 Geometric Series
Sn = (2a + (n -
1)d] Sn = a(r -
1)
r -
1
·
if 1st Sn = (a 1)
given and last terms : +
·
to find a term
given the sums : Th = Sn-Sn-
.
6 Sum to
infinity (converges) 7
Sigma
last value subs in
So d
-
general
Tnt
.
=
Th
1 -
r
general
& first value subs in general .
* NB !
n = last -
first + 1
( if not
starting at 1)
(perfsa) equal (0)
Quadratic equations
+ -
real rational
unequal
discriminant (4)
of
irrational ; unequal
= bz
~ roots equation
x -
=
b -
49C
>
2d non-real
-method
·
·
surds -> perform a check !
·
complete the square > d must = 1
>
more c over
> add (b) " to both sides
>
factorise and solve
simultaneous
·
·
inequalities & factorise
+ +
< 1 =
3))CVs
CV CV
>
number line
>
Solve
Exponents Logs
2
3
S
b
xb
a +
x9 =
x
log is
·
base 10 if not said .
.
b
x"
a
x
-
= =
x
exponent form > log form
·
laws (x)b = 9
- b
-BPAL
I
BAP
(xy)"
base power answer
=
x9 .
ya
xo 1 by
>log
=
a a
y
= =
x
- 9
= ca Sec2 = ,
(A xB)
factorise
log log
A
log B
=
·
I term ,
+
A A &
·
I term , prime basea simplify log
( *) =
log A-logB
,
x b log
trinomials (desc order of
log ,
=
x
· .
middle term (first term) log =
I
L solve
log m logm
=
log , a
=
a
surds (rationalise denominator if asked
only
log(a)
·
. = 1
logab
logy1 0
=
log , 0 undefined
=
, sequences & Series
.
1 Arithmetic sequences .
2 Geometric sequences
Tn = a + (n 1)d-
Tn = arn-1
Common
·
Common Ist
·
difference ist ratio
Tz
·
(T2 T1) =
(T3 - Tz) +1 = =
r
.
3 Quadratic sequences
Tn = an + bn + C
a + b + c = Ti Tz T3
? 2
3a + b =
29 - d
.
4
Arithmetic Series .
5 Geometric Series
Sn = (2a + (n -
1)d] Sn = a(r -
1)
r -
1
·
if 1st Sn = (a 1)
given and last terms : +
·
to find a term
given the sums : Th = Sn-Sn-
.
6 Sum to
infinity (converges) 7
Sigma
last value subs in
So d
-
general
Tnt
.
=
Th
1 -
r
general
& first value subs in general .
* NB !
n = last -
first + 1
( if not
starting at 1)
