Download Year 11B Unit Plan

11B Maths – Semester 1
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
INTRODUCTION TO FUNCTIONS I
PERIODIC FUNCTIONS AND APPLICATIONS
1
UNIT LEARNING GOALS:


Understand and apply the index laws and definitions
Solution (solve) of equations involving indices
--------------------------------------------------------------
Understand concepts of function, domain and range

Ordered pairs, tables, graphs and equations as
representations of functions and relations

Graphs as a representation of the points whose
coordinates satisfy an equation


Distinction between functions and relations
Understand distinctions between continuous
functions, discontinuous functions and discrete
functions
---------------------------------------------------------------
definition of a radian and its relationship with degrees

trigonometry, including the definition and practical
applications of the sine, cosine and tangent ratios

simple practical applications of the sine and cosine
rules (the ambiguous case is not essential)

definition of a periodic function, the period and
amplitude

definition of the trigonometric functions sine, cosine
and tangent of any angle in degrees and in radians
Resources
Quest 11B:
Glossary: Domain, Range, Continuous, Discrete.
Assessment
 Exam
Success Criteria:
 Accurate and successful
completion of problems
from the textbook.
 Reached set Target.
Key Verbs
 Understand
 Apply
 Solve
11B Maths – SEMESTER 1 cont
APPLIED STATISTICAL ANALYSIS
INTRODUCTION TO FUNCTIONS II
2
UNIT LEARNING GOALS:
----------------------------------------------------------------------------------
identification of variables and types of variables and data
(continuous and discrete); practical aspects of collection and entry
of data

select and use in context appropriate graphical and tabular
displays for different types of data including pie charts, bar charts,
tables, histograms, stem-and-leaf and box plots

use of summary statistics including mean, median, standard
deviation and interquartile distance as appropriate descriptors of
features of data in context

use of graphical displays and summary statistics in describing key
features of data, particularly in comparing datasets and exploring
possible relationships

use of relative frequencies to estimate probabilities; the notion of
probabilities of individual values for discrete variables and
intervals for continuous variables

probability distribution and expected value for a discrete variable
------------------------------------------------------------------------------

general shapes of functions, including:
polynomials up to degree 4
reciprocal functions
absolute value functions
practical applications:
polynomials up to degree 2
reciprocal functions
absolute value functions
Resources
Quest 11B:
Glossary: continuous, discrete, standard deviation, stem and leaf
plot, reciprocal function, absolute value function
Assessment

Exam
Success Criteria:

Accurate and successful
completion of problems from the
textbook.

Reached set Target
Key Verbs
 Define
 Identify
 Apply
 Graph
 Estimate
 Present
 Compare
11B Maths – SEMESTER 2
RATES OF CHANGE
INTRODUCTION TO FUNCTIONS III
PERIODIC FUNCTIONS AND APPLICATIONS II
1
UNIT LEARNING GOALS:

concept of rate of change

calculation of average rates of change in both practical and purely
mathematical situations

interpretation of the average rate of change as the gradient of the
secant

understanding of a limit in simple situations

definition of the derivative of a function at a point
 derivative of simple algebraic functions from first principles
-------------------------------------------------------------------------
relationships between the graph of
f ( x  a) , af
the constant a


(x), f (ax)
f (x) and the graphs of f ( x)  a ,
for both positive and negative values of
solutions to simultaneous equations in two variables:
 graphically, using technology
 algebraically (linear and quadratic equations only)
composition of two functions
 Concept of the inverse of a function
--------------------------------------------------------------------------
y  sin x , y  cos x and y  tan x for any angle in degrees
(  360   x  360  ) and in radians (  2  x  2 )

graphs of

significance of the constants A, B, C and D on the graphs of
y  Asin B( x  C )  D , y  A cos B( x  C )  D

applications of periodic functions
Resources
Quest 11B:
Glossary: Inverse function, Simultaneous equations, Limit
11B Maths – SEMESTER II
Assessment
 Exam
Success Criteria:
 Accurate and successful
completion of problems
from the textbook.
 Reached set Target
Key Verbs
 Understand
 Interpret
 Apply
 Sketch
 Solve
RATES OF CHANGE
1
UNIT LEARNING GOALS:
 evaluation of the derivative of a function at a point
 interpretation of instantaneous rate of change at a point as
the gradient of a tangent and as the derivative at that
point
 rules for differentiation including:
d n
p for rational values of n
dp
d
[ k f (r )]
dr
d
[ f ( s)  g ( s) ]
ds
d
[ f (t ) g (t ) ]
(Product rule)
dt
d
f [ g ( x)]
(Chain rule)
dx
 interpretation of the derivative as the gradient function
 practical applications of instantaneous rates of change
Resources
Quest 11B
Glossary: Product rule, Chain Rule
Assessment
 Exam
Success Criteria:
 Accurate and successful
completion of problems
from the textbook.
 Reached set Target
Key Verbs
 Evaluate
 Differentiate
Significant amounts of
procedural knowledge in this
unit