Hebron Christian CollegeMathematicsCourse Outline 2014NCEA Level 3 – Year 13NZ 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 outcomesBy 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 creditsThis 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

Credits Literacy or numeracy

91578 (3.6)

Apply differentiation methods in solving problems

External 6

91577 (3.5)

Apply the algebra of complex numbers in solving problems

External 5

91574 (3.2)

Apply linear programming methods in solving problems

Internal 3

91587 (3.15)

Apply systems of simultaneous equations in solving problems

Internal 3

91575 (3.3)

Apply trigonometric methods in solving problems

Internal 4

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 calculusStudents 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 PlanClass work and assessments will generally fit into the plan below, although there will be some flexibility.

Week Term 1 Term 2 Term 3 Term 41 Equations with

unique solutionsRates of change Trigonometric

IdentitiesRevision

2 Geometric interpretation of solutions

Optimization Trigonometric Identities

Revision

3 Equations with no solutions

Linear Inequalities

Trigonometric Equations

Revision

4 Word problems Linear Inequalities Polynomials with real numbers

Study leave

5 CAMP EXAMS Complex numbers set and properties

NCEA EXAMS

6 Limits of derivatives

Feasible Regions Polynomials with complex roots

NCEA EXAMS

7 Derivatives of functions

Optimization Argand Diagram. Polar form

NCEA EXAMS

8 Derivatives of functions

Optimization EXAMS NCEA EXAMS

9 Applications of derivatives

Trigonometric Graphs

De Moivre’s Theorem. Solving equations

NCEA EXAMS

10 Applications of derivatives

(Term Break) Locus and the Argand Diagram

11 Rates of change (Term Break)(Term Break)

Record of gradesPractice external assessmentsStandard Class test Mid-year exam End of year examDifferentiation (3.6) Term 1/week 10 YesComplex Numbers (3.5)

Term 3/week 6 No Yes

Internal assessmentsStandard Due date GradeSystems of Equations(3.15)

Term 1/week 4

Linear programming(3.2)

Term 2/week 8

Trigonometric Methods(3.3)

Term 3/week 3