12B Maths – Semester 1
Periodic Functions and Applications 3
OPTIMISATION USING DERIVATIVES
Introduction to integration
1
UNIT LEARNING GOALS:
x  cos x  1

Pythagorean identity sin

Solve trigonometric equations within a specified domain
 algebraically in simple situations (multiple angles are not essential)
 using technology to any complexity
Find derivatives of functions involving sin x and cos x

2
2

Applications of the derivatives of sin x and cos x in life-related
situations.
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Know positive and negative values of the derivative as an indication of the points
at which the function is increasing or decreasing

Know zero values of the derivative as an indication of stationary points

Understand concept of relative maxima and minima and greatest and least value
of functions

Apply methods of determining the nature of stationary points

greatest and least values of a function in a given interval
--------------------------------------------------------------------------------------------------
definition of the definite integral and its relation to the area under a
curve

the value of the limit of a sum as a definite integral

definition of the indefinite integral

rules for integration including
 a f ( x) dx
[ f ( x)  g ( x)]dx
 f ( ax  b) dx
Resources
Quest 12B:
Glossary: Integral, Optimise
Assessment
 Exam
Success Criteria:
 Accurate and successful
completion of problems
from the textbook.
 Reached set Target.
Key Verbs
 Integrate
 Understand
 Apply
 Solve
 Graph
 Sketch
 Define
12B Maths – SEMESTER 1 cont.
EXPONENTIAL AND LOGARITHMIC FUNCTIONS II
OPTIMISATION USING DERIVATIVES II
2
UNIT LEARNING GOALS:
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definitions of ax and loga x, for a > 1 (SLE 1)

logarithmic laws and definitions

definition of the exponential function ex

Assessment

Exam
Success Criteria:

Accurate and successful
completion of problems from the
textbook.

Reached set Target
graphs of, and the relationships between, y = ax, y = loga x for a = e and
other values of a (SLEs 3, 6, 12, 14, 16, 17, 18)
Key Verbs

graphs of y = ekx for k  0
use of logarithms to solve equations involving indices
------------------------------------------------------------------------------------
recognition of the problem to be optimised (maximised or minimised)

identification of variables and construction of the function to be optimised
:
Resources
Quest 12B:
Glossary: Exponential, Logarithmic, Optimise





Understand
Apply
Solve
Graph
Sketch
 Define
 Optimise
12B Maths – SEMESTER 2
EXPONENTIAL AND LOGARITHMIC FUNCTIONS AND APPLICATIONS III
INTEGRATION II
APPLIED STATISITICAL ANALYSIS II
1
UNIT LEARNING GOALS:
 development of algebraic models from appropriate datasets
using logarithms and/or exponents
 derivatives of exponential and logarithmic functions for base e
 applications of exponential and logarithmic functions, and the
derivative of exponential functions
-------------------------------------------------------------------------- indefinite integrals of simple polynomial functions, simple
1
exponential functions, sin (ax + b), cos (ax + b) and
a xb
 use of integration to find area
 practical applications of the integral
 use trapezoidal rule for the approximation of a value of a definite
integral numerically
-------------------------------------------------------------------------- identification of the binomial situation and use of tables or
technology for binomial probabilities
 understand the concept of a probability distribution for a
continuous random variable; notion of expected value and
median for a continuous variable
 understand and use the normal model and use of standard
normal tables or technology
Resources
Quest 12B:
Glossary: Binomial probability
Assessment
 Exam
Success Criteria:
 Accurate and successful
completion of problems
from the textbook.
 Reached set Target
Key Verbs
 Derive
 Integrate
 Identify
12B Maths – SEMESTER II cont.
OPTIMISATION USING DERIVATIVES III
EXPONENTIAL AND LOGARITHMIC FUNCTIONS AND APPLICATIONS IV
1
UNIT LEARNING GOALS:
 applications of the derivative to optimisation in life-related
situations using a variety of function types
 interpretation of mathematical solutions and their
communication in a form appropriate to the given
problem
----------------------------------------------------------------- applications of geometric progressions to compound
interest including past, present and future values
 applications of geometric progressions to annuities and
amortising a loan
Resources
Quest 12B
Glossary: Annuities, Amortisation
Assessment
 Exam
Success Criteria:
 Accurate and successful
completion of problems
from the textbook.
 Reached set Target
Key Verbs
 Apply
 Differentiate
 Calculate