Summary Aqa A Level Further Mathematics Year 1 Notes
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Course
AQA Further Maths A Level First Year Topics
Institution
AQA
First Year notes of a past AQA A Level Further Maths student, were incredibly useful to facilitate getting an A* in AQA Further Maths in 2024. Includes all first year topics of AQA further maths, including mechanics and statistics, cohesive and includes both notes and example questions. Studying ma...
Perpendicular HALF LINES arg(2-2) =
distance between
2= x +
yi 2, =
X+ yi 12-2 ) ,
e
fixed point
>
fixed point variable point
& variable point bisector arg(x yi 2) = + -
circles 12-al-ra= centre r= radius
z = x+ yi 12-4) =
12- 2i) distancefram 24 arg(2-ao arg((x 2) + yi) = -
(2 (2 +3i)) (x + (y2)i)
same dis from ze Zi tano tan =
((x 4) yi)
↓
-
= 5 -
+ =
tan
22
3i)
2
5
(x + yi (x 4) + y2
,
Zi =
-
2 -
= 5 -
= x + (y 2)2
-
X
O
-----
y
=
53x 25
((x 2) (y 3)i) 5 4
-
-
+ - =
-
8x + 16 =
4y +4 3/2
Circle centre 1T/
2x 3 3 X2
(X 2) + (y 3)" y
-
25 (2, 3) radius 5
= -
- -
=
,
(2 0,
&
, 3x2 2x + 4 4x" 1(x 26x
g
+ 15x = 0
=2
-
- -
axi + bx + C
p q + if f(z) = 0
has roots pag
roots p q 1 + 2i factor f(z )
*
,
X = is a . then =
G
p +q = find pi + g2
pq
= find cubic a
: X = 1-2i is a factor
polynomial with roof
·
.
=
.
pq
·
(p + q) p + q2-2pq =
3 & 4+ i (X -(1 2i))(x + -
(1 -
zi)
ax + bx d
roots =
3 , 4+ , 4-i
i
+ (x +
X X(l + zi) X(l 2i) + 5
(3)2 2(5) E B 2
:
i)
- -
-
(x 3)(x (4 + i))(x (4
= -
=
roots p g r
-
-
- -
X2 - 2x + 5 -> complex quadratic factor
-
, ,
p + q+ r= (x 3)(x2 8x + 17)
find
+
-
4x2 3x quadratic factor
-
real
·
- -
pq gr + +
pr = x2 2x+ 5 4x" 1(x + 26x2- 15x
X (lx 4(x 51
&
=
+ -
-
-
-
par = ·
+= 4x" 8x3 + 20x3
-
6x
3
0 3x + 15x
G
- -
ax" + bx (x + dx 6x2 15X
=
3x*
ROOTS OF
+ + e -
+ -
4/5
i
·
roots p g , r, S
,
& g O
p + q + r+s = POLYNOMIALS
.
2
x(x2 - 2x + 5)(4x 3) 3
=
=
↓
-
pa + pr + ps + gr + qs +s
-
X(4x 3)(X (1 2i))(x (1 + (i)
=
TRANSFORMING
- -
=
- -
par +
pqs +
prs + srq EQUATIONS
parse 3x3 x-
+ 2x + 5 =
0
: roots =
1 + 2i , 1-2i ,
0 ,
34
has roots p g ,r
(a + bi)(a bi)
,
a + b2 =
-
find cubic equation with roots (p-2) (G-2) , ,
(r-2)
METHOD 2
p + q+ r = 5x2 + bx + c = 0
p 2 +
q 2 +r z p + g+ r 6 METHOD
-
=
1
- -
-
has root 4 + 7 :
=
- -
6 =
7= X p q r =
, ,
find b & C
2 r 2
u p z g
-
-
-
= , ,
=
par-2(pa + ar +
rp) -
8
a 3 b =1 34d =
2 16
--
=
: -
2(z) -
8 = =
:
3x + 17x + 34x + 29 65 =
5 c 325 =
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