Mathematics by PNBHS

Mathematics and Statistics

Mathematics; Alternative Mathematics; Calculus; Statistics

Year 10 Mathematics - 10MAT

A compulsory core subject designed to develop numeracy skills to enable students to continue their study of Mathematics into the senior school.

Level One Mathematics - 11MTX

Mathematics is a compulsory subject at Year 11.

The course will teach students at levels 5 & 6 of the New Zealand Curriculum giving them the knowledge at skills required for success at Year 12. Students will be placed in classes based on their demonstrated mathematical ability. They will sit one external and two internal NZQA Level 1 Achievement Standards. Selected students will be given additional opportunities to meet the necessary Level 1 Numeracy requirements.
Course cost: $15

Level Two Mathematics - 12MTX

An internally assessed course following the National Curriculum including: Mathematics, Probability & Statistics. This course is designed for students who need Mathematics credits at Level 2 but may not intend to do Mathematics courses at Level 3.

Cost: $20

Internal Assessments
US28094 Produce a balanced household budget and adjust the budget to reflect changing financial circumstances.

AS91256 Apply co-ordinate geometry methods in solving problems (2.1)

AS91258 Apply sequences and series in solving problems (2.3)
AS91259 Apply trigonometric relationships in solving problems (2.4)
AS91260 Apply network methods in solving problems (2.5)
AS91268 Investigate a situation involving elements of chance using a simulation (2.13)
External Assessments
AS91267 Apply probability methods in solving problems (2.12)

Level Two Calculus - 12CLC

A comprehensive course following the National Curriculum including: Algebra, Graphs and Calculus. This course should be thought of a part of a two year programme leading toward level 3 Calculus and Scholarship.
Access to a graphics calculator is essential.
The Level 2 Mathematics, 12MTX, course is recommended for students who do not meet these entry requirements
Cost:$20

Internal Assessments
AS91256 Apply co-ordinate geometry methods in solving problems (2.1)
AS91257 Apply graphical methods in solving problems (2.2)
AS91258 Apply sequences and series in solving problems (2.3)
AS91259 Apply trigonometric relationships in solving problems (2.4)
AS91269 Apply systems of equations in solving problems (2.14)
External Assessments
AS91261 Apply algebraic methods in solving problems (2.6)
AS91262 Apply calculus methods in solving problems (2.7)


Level Two Statistics - 12STS

Statistics involves identifying problems that can be explored by the use of appropriate data, designing investigations, collecting data, exploring and using patterns and relationships in data, solving problems, and communicating findings. Statistics also involves interpreting statistical information, evaluating data-based arguments, and dealing with uncertainty and variation.

The course is mainly internally assessed via a series of projects which will require access to a laptop.

"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write." - H.G. Wells

Cost:$20

The level 2 Mathematics, 12MTX, course is recommended for students who do not intend to enter 13STS

Internal Assessments
AS91263 Design a questionnaire (2.8)
AS91264 Use statistical methods to make an inference (2.9)
AS91265 Conduct an experiment to investigate a situation using statistical methods (2.10)
AS91266 Evaluate a statistically based report (2.11)
AS91268 Investigate a situation involving elements of chance using a simulation (2.13)
AS91260 Apply network methods in solving problems (2.5) 


External Assessments
AS91267 Apply probability methods in solving problems (2.12)

Level Three Calculus - 13CLC

Calculus is a tool used to model the way our world changes. Engineers and scientists apply it to analyse large physical structures or model evolutionary trajectories of cell structures. Weather forecasts are generated using, among other techniques, calculus as is tracking the flux of our geomagnetic field. Economists rely on calculus to analyse the stock market, track currency shifts or develop new air travel routes. Good graphic designers and computer animation artists rely heavily on calculus for their creative outcomes. Health students need physics to get into their dental, medical or veterinary courses? Tertiary Level Physics becomes much more accessible with a knowledge of calculus. In short, calculus opens many doors.

Level 3 Calculus has a strong dependency on algebraic skills and problem solving. In addition, good reading comprehension is required for problem analysis.

Level Three Prerequisites: 18 Credits from Level 2 including 2.6 & 2.7.
Cost: $20

Internal Assessments
AS 91574 Apply linear programming methods in solving problems (3.2) and/or AS 91587 Apply systems of equations in solving problems (3.15) and/or AS 91573 Apply the algebra of conic sections in solving problems (3.1)
External Assessments
AS 91577 Apply the algebra of complex numbers in solving problems (3.5)
AS 91578 Apply differentiation methods in solving problems (3.6)
AS 91579 Apply integration methods in solving problems (3.7)

Level Three Mathematics - 13MTX

This course has been designed for students who have not met the entry requirements for Calculus but would like to continue with Mathematics rather than a pure Statistics course at Level Three. This course covers the basics of Operational Research

Level Three Prerequisites: 14 Credits from Level 2 Mathematics or an NCEA Level 2 certificate, students who have fewer than 14 Mathematics credits will be subject to review during term 1.
Cost: $20

Internal Assessments
AS 91574 Apply linear programming methods in solving problems (3.2)
AS 91576 Use critical path analysis in solving problems (3.4)
AS 91580 Investigate time series data (3.8)
AS 91583 Conduct an experiment to investigate a situation using experimental design principles (3.11)
AS 91587 Apply systems of simultaneous equations in solving problems (3.15)
External Assessments
AS 91585 Apply probability concepts in solving problems (3.13)

Level Three Statistics - 13STS 

The key to making sense of all the data now at our disposal is statistics. At leading companies, decisions are increasingly made by conducting experiments that draw on the core skills of statisticians. Rather than relying on gut instinct, businesses now find ways to test hypotheses and use statistical methods to analyse the results, applying the classic scientific method to decision-making.

Consider the teams of medical researchers running clinical trials or analysing the outcomes of patients after a therapy has been made widely available: they have to select the parameters to study, assess the results, and draw the right conclusions about a drug's effectiveness and safety. Online advertisers trying to micro-target consumers must be able to detect patterns in the massive amount of clickstream data they gather from the Web. Risk managers on Wall Street, retail buyers choosing this season's merchandise, environmental scientists, sports analysts, and military strategists all rely on the ability to synthesize data and predict outcomes.

This course builds on the quite substantial statistics concepts already covered by this stage. This course has a high literacy demand. All of the internal Achievement Standards are assessed by a written report which will require access to a laptop. Students will complete 2 of 3.8, 3.9 & 3.10.

Prerequisites: 16 Credits from Level 2 including 2.9 & 2.12.

Cost: $20

Internal Assessments
AS 91580 Investigate time series data (3.8)
AS 91581 Investigate bi-variate measurement data (3.9)
AS 91582 Use statistical methods to make a formal inference (3.10)
AS 91583 Conduct an experiment to investigate a situation using experimental design principles (3.11)

External Assessments
AS 91584 Evaluate statistically based reports (3.12)
AS 91585 Apply probability concepts in solving problems (3.13)
AS 91586 Apply probability distributions in solving problems (3.14)