IA 첨삭 패키지
ToK 첨삭 패키지
커리큘럼
자주묻는질문
인재채용
Mentoring Program Curriculum (1)
/
Subjects
/
Maths AA
/
Topics
/
1. Number and Algebra
수학
영어
화학
생물
경제
전시회 Exhibition
에세이 Essay
일회성 첨삭
방학특강
정규반
Mentoring Program Curriculum (1)
/
Subjects
/
Maths AA
/
Topics
/
1. Number and Algebra
IA 첨삭 패키지
수학
영어
화학
생물
경제
ToK 첨삭 패키지
전시회 Exhibition
에세이 Essay
일회성 첨삭
커리큘럼
방학특강
정규반
자주묻는질문
인재채용
1. Number and Algebra
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Sub-topics
•
Arithmetic sequences and series (1.2)
•
Use of the formulae for the
n
t
h
n^{th}
n
t
h
term and the sum of the first
n
n
n
terms of the sequence.
•
Use of sigma notations of sums of arithmetic sequences.
•
Applications
•
Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life.
•
Geometric sequences and series. (1.3)
•
Use of the formulae for the
n
t
h
n^{th}
n
t
h
term and the sum of the first
n
n
n
terms of the sequence.
1.2 Sequences and Series
•
Simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side (LHS to RHS) proof. (1.6)
•
The symbols and notation for equality and identity.
•
Proof by mathematical induction (AHL 1.15)
•
Proof by contradiction
•
Use of a counterexample to show that a statement is not always true.
1.3 Proof and Reasoning
•
The binomial theorem: expansion of
(
a
+
b
)
n
(a + b)^n
(
a
+
b
)
n
,
n
∈
N
n ∈ N
n
∈
N
.
(1.9)
•
Use of Pascal’s triangle and
n
C
r
^nC_r
n
C
r
.
•
Counting principles, including permutations and combinations. (AHL 1.10)
•
Extension of the binomial theorem to fractional and negative indices, ie
(
a
+
b
)
n
(a + b)^n
(
a
+
b
)
n
,
n
∈
Q
n ∈ Q
n
∈
Q
.
Use of Pascal’s triangle
Figure 1.4.1
Pascal’s triangle
1.4 Binomial Theorems and Combinatorics
•
The number
i
i
i
, where
i
2
=
−
1
i^2=-1
i
2
=
−
1
.
(1.12)
•
Cartesian form
z
=
a
+
b
i
z = a + bi
z
=
a
+
bi
; the terms real part, imaginary part, conjugate, modulus and argument.
•
The complex plane.
•
Modulus–argument (polar) form:
z
=
r
(
cos
θ
+
i
sin
θ
)
=
r
c
i
s
θ
z = r(\cosθ + i\sinθ) = rcisθ
z
=
r
(
cos
θ
+
i
sin
θ
)
=
rc
i
s
θ
(1.13)
•
Euler form:
z
=
r
e
i
θ
z = re^{iθ}
z
=
r
e
i
θ
•
Sums, products and quotients in Cartesian, polar or Euler forms and their geometric interpretation.
•
Complex conjugate roots of quadratic and polynomial equations with real coefficients.
(1.14)
1.5 Complex Numbers (HL)
1.6 Linear Equations (HL)