MATHS
Grade 12
IEB
,
,
,
, Sequences and Series
Functions and Inverses
Cubic Polynomials
Differential Calculus
General Trigonometry
Trigonometry in
Triangles
Analytical Geometry
Euclidean Geometry
Financial Mathematics
Statistics
The Counting
Probability
Principle
, Sequences and Series
Chapter 1
General Rules Sigma
a = T1
n = Position (n∈ Ν
d = Constant Difference
Tn = Value of Term Number of terms = p – q + 1
T3 = S3 – S2
T5 = S5 – S4
Quadratic Cubic
Arithmetic Sequence Arithmetic Series
$
#$ = 2' + $ − 1 +
Tn = a + (n-1)d 2
$
#$ = (' + -)
2
Geometric Geometric
Sequence Sequence
'(/ $ − 1) !≠1
#$ =
Tn = ar !"# /−1
Conditions for
' Convergence:
#∞ =
1−/ −1 < ! < 1
, Functions and Inverses
Chapter 2
Function and Type Line of Symmetry
• Vertical Line Test:
y=x
• whether it is a function
• Horizontal Line Test:
• One-to-one function
• Many-to-one function
Inverse of one-to-one
*The opposite procedure of the
original function
Inverse of Exponential
Function Determining Inverse of one-to-one
functions
1. Swop x and y
*No restrictions necessary 2. Make y the subject
*Use table method to find a point 3. Rewrite in form 1 "% = …
*Need to make y subject of formula:
done using logarithms (logs)
1. Make y the subject using logs
2. Draw original and inverse
Inverse of Many-to-one
Determining Inverse of many-to-one
functions (Quadratic Function)
1. Use table method or intercepts
Expression: loga x defines only if: to draw original
• 0 < ' < 1 =/ ' > 1 2. For inverse: Make y the subject
(a cannot be negative, zero or 1) 3. ± 5 will not be a function ∴
• 5>0 78#9/:;9 <=>':$ (of original)
(x cannot be negative or zero) a) Situation 1: where 5 ≥ 0
b) Situation 2: where 5 ≤ 0
4. Remember to include inverse
over line of symmetry and write
restrictions
Grade 12
IEB
,
,
,
, Sequences and Series
Functions and Inverses
Cubic Polynomials
Differential Calculus
General Trigonometry
Trigonometry in
Triangles
Analytical Geometry
Euclidean Geometry
Financial Mathematics
Statistics
The Counting
Probability
Principle
, Sequences and Series
Chapter 1
General Rules Sigma
a = T1
n = Position (n∈ Ν
d = Constant Difference
Tn = Value of Term Number of terms = p – q + 1
T3 = S3 – S2
T5 = S5 – S4
Quadratic Cubic
Arithmetic Sequence Arithmetic Series
$
#$ = 2' + $ − 1 +
Tn = a + (n-1)d 2
$
#$ = (' + -)
2
Geometric Geometric
Sequence Sequence
'(/ $ − 1) !≠1
#$ =
Tn = ar !"# /−1
Conditions for
' Convergence:
#∞ =
1−/ −1 < ! < 1
, Functions and Inverses
Chapter 2
Function and Type Line of Symmetry
• Vertical Line Test:
y=x
• whether it is a function
• Horizontal Line Test:
• One-to-one function
• Many-to-one function
Inverse of one-to-one
*The opposite procedure of the
original function
Inverse of Exponential
Function Determining Inverse of one-to-one
functions
1. Swop x and y
*No restrictions necessary 2. Make y the subject
*Use table method to find a point 3. Rewrite in form 1 "% = …
*Need to make y subject of formula:
done using logarithms (logs)
1. Make y the subject using logs
2. Draw original and inverse
Inverse of Many-to-one
Determining Inverse of many-to-one
functions (Quadratic Function)
1. Use table method or intercepts
Expression: loga x defines only if: to draw original
• 0 < ' < 1 =/ ' > 1 2. For inverse: Make y the subject
(a cannot be negative, zero or 1) 3. ± 5 will not be a function ∴
• 5>0 78#9/:;9 <=>':$ (of original)
(x cannot be negative or zero) a) Situation 1: where 5 ≥ 0
b) Situation 2: where 5 ≤ 0
4. Remember to include inverse
over line of symmetry and write
restrictions
