Hebron Christian College
Mathematics
Course Outline 2014
NCEA Level 3 – Year 13
NZ Curriculum Level 8
Introduction
New Zealand Curriculum Achievement Objectives
 Choose and apply a variety of integration and anti-differentiation techniques to functions and
relations, using both analytical and numerical methods
 Form differential equations and interpret the solutions
Learning outcomes
By the end of the course, students will be able to:
 Differentiate functions and use derivatives to solve problems.




Manipulate complex numbers and present them graphically. Form and use polynomial and
other non-linear equations
Find optimal solutions to practical problems, using linear programming methods
Form and use systems of simultaneous equations to solve 3-dimensional problems
Manipulate trigonometric expressions; form and use trigonometric equations
Topics to be studied
Please refer to Year Plan, shown below
Standards and credits
This Year 13 Subject course contributes 21 credits towards your Level 3 National Certificate of Educational
Achievement. The credits are spread over 5 achievement standards, 2 of which are assessed externally in
the examination, and 3 which are internally assessed. NOTE: Students who aim to study Engineering at
Auckland University are required to undertake Achievement Standard 91579 (Apply Integration methods in
solving problems) through the Correspondence School
Standard Title
Internal
or
external
External
Credits
Literacy
or
numeracy
91578
Apply differentiation methods in solving
6
(3.6)
problems
91577
Apply the algebra of complex numbers in External
5
(3.5)
solving problems
91574
Apply linear programming methods in
Internal
3
(3.2)
solving problems
91587
Apply systems of simultaneous equations Internal
3
(3.15)
in solving problems
91575
Apply trigonometric methods in solving
Internal
4
(3.3)
problems
For literacy and numeracy see: Staff share:\NCEA - Literacy and numeracy at Level 1 (for Level 1 NCEA) or
Literacy at Level 2 and 3 (for UE)
Resubmissions and further assessment opportunities in mathematics with calculus
Students studying this subject will have one opportunity to be assessed against each of the internal
assessments. Students will have resubmission opportunities according to NZQA rules. For further information
about resubmissions, further assessment opportunities and the Hebron Christian College assessment policy,
refer to the New Zealand Qualifications Framework pages in your handbook.
Course work, homework, textbooks and stationery
Homework:
Homework will be set regularly and will be a minimum requirement for personal success in this subject.
Students are required to submit homework for checking at the end of each week.
“It is the glory of God to conceal a matter, but the glory of kings is to search out a matter.” Proverbs 25v2
Textbook and Workbook:


ESA Study Guide, Level 3, Calculus
Level 3 Calculus, AME Workbook
The development of independent learning skills is vital. Students should:


Organize ideas and concepts into their own words/pictures/symbols/annotations to support their
personal learning styles.
Explore resources such as textbooks, workbooks, websites, teacher supplied resources, practice
assessments, the knowledge and discoveries of their peers, and everyday experiences to extend their
learning. The NZQA website is a very important resource and should be used regularly for
assessment preparation:
http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/mathematics/levels/
Stationery Requirements:



1 x Clearfile
2 x 1E8 Exercise & Notes books
Calculator – a graphics calculator is required for lessons and the external assessments.
Approximate Year Plan
Class work and assessments will generally fit into the plan below, although there will be some flexibility.
Week
1
Term 2
Rates of change
4
Term 1
Equations with
unique solutions
Geometric
interpretation of
solutions
Equations with no
solutions
Word problems
5
CAMP
EXAMS
6
Limits of
derivatives
Derivatives of
functions
Derivatives of
functions
Applications of
derivatives
Feasible Regions
Applications of
derivatives
Rates of change
(Term Break)
(Term Break)
2
3
7
8
9
10
11
Optimization
Linear
Inequalities
Linear Inequalities
Optimization
Optimization
Trigonometric
Graphs
Record of grades
Practice external assessments
Standard
Class test
Differentiation (3.6)
Term 1/week 10
Complex Numbers
Term 3/week 6
(3.5)
Internal assessments
Standard
Systems of
Equations(3.15)
Linear
programming(3.2)
Trigonometric
Methods(3.3)
Due date
Term 1/week 4
Term 2/week 8
Term 3/week 3
Term 3
Trigonometric
Identities
Trigonometric
Identities
Term 4
Revision
Trigonometric
Equations
Polynomials with
real numbers
Complex numbers
set and properties
Polynomials with
complex roots
Argand Diagram.
Polar form
EXAMS
Revision
De Moivre’s
Theorem. Solving
equations
Locus and the
Argand Diagram
(Term Break)
NCEA EXAMS
Mid-year exam
Yes
No
Grade
Revision
Study leave
NCEA EXAMS
NCEA EXAMS
NCEA EXAMS
NCEA EXAMS
End of year exam
Yes