Year 12 Mathematics
with statistics

Mathematics is the science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics).

This course is designed for you if you are interested in pursuing Mathematics to a higher level and really enjoy problem solving, algebra and investigating data and chance. The course covers a broad range of mathematical concepts but has a specific leaning towards Probability and Statistical Analysis with the aim of preparing students for the Level 3 Statistics course. (Note: all three L3 Mathematics courses are available to students who take Mathematics with Statistics in Year 12).

If you enjoyed the challenge of solving a wide range of problems in the Year 11 Mathematics course and particularly liked doing the Statistics investigation, and you look forward to continuing to improve your problem solving and reasoning skills, you should consider taking this course.

We live in a world in which we are flooded with information. It is crucial to be able to analyse and consider the validity of claims before we accept them as truth. Statistics is the study of the collection, organisation, analysis and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments. Virtually every job requires people with statistical knowledge.

Potential Pathways from this Subject
Mathematics at Year 13 divides into three courses:

Calculus
Statistics
Mathematics (General)

You may do both Calculus and Statistics or Calculus and Mathematics in Year 13, but not Statistics and Mathematics due to the overlap between these two courses.

This course will cover the following topics: 

• Algebra

• Trigonometry

• Probability

• Statistical inference and analytical report writing

• Simulations and chance

The NCEA Level 2 Mathematics with Statistics course follows on Year 11 Mathematics. The course has a strong focus on developing your algebraic reasoning skills (both abstractly as well as through trigonometry applications) but there is an equal focus on investigating elements of chance, organising and interpreting data and developing critical thinking and analytical skills.

Carry out investigations of phenomena, using the statistical inquiry cycle :

• using existing data sets and seeking explanations  

• using informed contextual knowledge, exploratory data analysis, and statistical inference

• communicating findings in the form of a statistical report  

Make inferences from surveys and experiments:  

• determining estimates of the difference in values for two groups 

• use methods such as simulations to assess the strength of evidence for a claim

Investigate situations that involve elements of chance  

• calculating probabilities of independent, combined, and conditional events 

• calculating and interpreting expected values and standard deviations of discrete random variables  

• applying probability models such as the normal distribution to calculate theoretical probabilities

We recommend this course if you gain proficient or advancing on assessments in Year 11 and a strong score on the end of year exam.

Entry into the course is subject to HOD approval.

aSSESSMENT

This course offers five NCEA Level 2 achievement standards. Three standards are assessed internally and two standards are assessed externally by end-of-year examination.

The following standards may be offered and assessed:

• AS 91261 - Apply algebraic methods in solving problems [2.6] (4 credits - External)

• AS 91259 - Apply trigonometric methods in solving problems [2.4] (3 credits)

• AS 91267 - Apply probability methods in solving problems [2.12] (4 credits - External) [L]

• AS 91264 - Apply statistical methods to make an inference [2.9] (4 credits) [L]

• AS 91268 - Investigate a situation involving elements of chance using a simulation [2.13] (2 credits) [L]

[L] These standards contribute to the literacy requirement for NCEA Level 1.

Note: A casio fx–9750GII graphics calculator is compulsory for this course.

Qualifications:  Credits towards NCEA Level 2.

NZQA Mathematics Subject Resources

http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/mathematics/levels

School Policy for NCEA Assessment

You should be aware of the school procedures for NCEA assessment.  They can be found on the school website at this link. There you will find answers to frequently asked questions about how NCEA works as well as guidance about how to apply for extensions, reconsiderations or the process for withdrawing from a standard.