AS Level/ A-Level Core Pure 1 – A* Further Mathematics Pearson Edexcel Summary Notes (8FM0) (9FM0)
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Course
Core Pure 1
Institution
PEARSON (PEARSON)
AS Level/ A-Level Core Pure 1 Further Mathematics Pearson Edexcel Summary Notes (8FM0) (9FM0)
All key points and example questions (including step-by-step workings) are included! Notes were designed based on the Edexcel syllabus in preparation for the 2023 Summer Exam.
Chapter 1: Complex Num...
*
- =
a + bi (a DE(R)
, ,
(zEK) · if z = a + bi ,
z = a-bi (complex conjugate
iP = 1 i = -
1
Re(z) =
'Real part of z' = a · if roots of a quadratic equation are a and B ,
then 1z-x)(z B) - =
0
is = -
i
1m(z) =
'Imaginary part of z = b z2 -
(x B)z + +
xB =
0
Chapter 2 :
Argand diagram
Im
A
- =
x +
iy (cartesian form / Z z, = r, (C030 , + iSiNO , ) ,
Ec =
Uc(10902 + iSinOc)
x
| z| 6x
· U2(109(0 (0 , (
+ z , Ec
=
y modulus, r = U, 82) i sin +
O2)
·
+ +
,
N O
arg(z)
=
tan"(π argument , O
> Re ④
= (10610 ,
-
01) + i sin(8 ,
+ O
range : ↑ < arg(z) => ↑
principal argument
-
always sketch !
z , z2) =
/z //Zal
,
arg(z , zc) =
arg(z ,
) +
arg(ze)
z r (c0S0 isinO) (modulus-argument form / 1z , 1
arg/E)
=
Ei
+
= =
arg1z , ) -
arg (zz)
↓ Zal
r (cos0- i sino) =
(cos1 0) -
+
isin) -
Oll
3 3
z ,
= = ,
arg(z , 3) =
3 arg(z , )
loci =
a set of points
e. g
. (i) Iz -
z, ) =
P circle (ii) Iz-z , 1 =
1z-Ec1 perpendicular bisector (iii) arg(z-z , ) =
0 half-line
if det (M) # 0
, non-singular Matrix ,
has inverse A =· a 3 x 3 Matrix 4 steps !
1) calculate det(A) =
((0 -1-1) -
3/0 -2) +
1(0-8) = -1
P of
9
M 3 x 3 Matrix 2) matrix of minors
,
(a
=
13 I
i
0 4
9 h i e. g. minor of 2 in
- O
M -
-
det (M)
a Ye if
=
= A
ef
n i
-
b
df
+ C
aC
9 i gh
h i
9 - - -
minor of a
minor of b of
minor C 3) changing of signs cofactor , c = I
Simultaneous equations :
4) transpose ,
CT =
i switch rows and columns
&
x 6y 22 21
e g
-
+ -
=
. .
60 i
-
I
6x -
2y
-
z = -
16
Y
=
24
5) A" =
det(A) CT
-
2x +
3y + 52 =
24
if A 4 = V
,
then ( = Av
Consistency :
line
i
. e. same plane
Step 1 :
Find det/M).
if det(M) O
,
then one single solution
.
> if det (M) =
0, then follow Step 2 .
Step 2 :
compare the equations of the planes.
*
If 2 of parallel
i
> (i) or more them are , they
. e. not same line plane
look like these .
g )
5)
le . .
3x-24 +
2 =
parallel
6x -
44
+
22 =
9
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