NCEA Maths is a core subject covered across all NCEA levels, gradually building in complexity as students progress.
Maths is assessed through a combination of internal and external assessments. To achieve a subject endorsement, students must earn a total of 14 credits, including at least 3 from internal assessments and 3 from external exams.
There are a wide range of internals available, but schools typically select 1 to 4 specific internals to teach each year. These internal assessments generally take two forms: a test-based format conducted by schools, or a research-based format where students investigate a mathematical problem and produce a report on their findings.
Some schools also offer “internal-only” math courses, where students complete more internal assessments instead of sitting external exams. These courses allow students to earn math credits without the pressure of end-of-year exams. However, it’s important to note that a mathematics endorsement is not possible in these courses, as at least 3 credits must come from external exams to qualify.
The external math assessments are sat at the end of the year. Schools will typically choose 2 or 3 to focus on throughout the year. Here is a breakdown of which externals are available in each year:
The NCEA exams are held at the end of the year in a traditional exam format. Students will sit all their test papers within a single exam block. For instance, if a student is taking all three Level 2 exam papers, they will have a 3-hour exam block in which to answer all of them.
Each test paper typically consists of three questions, each with subparts (e.g., 1a, 1b, 1c, etc.). For every question, students are awarded a score ranging from 0 to 8, depending on the complexity of the problems they solve. For example, answering an Excellence-level problem correctly will yield a score of 7 or 8 for that question, while solving a Merit-level problems will result in a score between 5 and 6. Solving Achieved level problems will give a score between 3 and 4. If the student solves no problems or only one Achieved level problem, they will likely score between 0 and 2 for that question.
The final grade is determined by adding up the scores from the three questions. However, it’s important to note that grade cut-offs can vary from assessment to assessment, depending on the specific criteria for each exam.
Below is an example of the question breakdown and the cut scores for the 2023 Level 2 Calculus exam. For reference, 'u' represents an Achieved-level problem, 'r' represents a Merit-level problem, and 't' represents an Excellence-level problem. For the first question in this exam, there was 1 achieved level problem (1a), one merit level problem (1b) and two excellence level problems (1c and 1d). It's worth noting that an attempt at an excellence or merit level question might still award you with a 'u' or an 'r' for a partially complete solution.
For this question, getting one of the two excellence questions right gives you 7/8 points for Question 1, regardless of how well you answered the other three questions! This is why a lot of top students choose to focus on the excellence questions in an exam and sometimes even completely skip the achieved or merit level problems. However, this is a risky strategy!
By adding up your scores from all 3 questions, your grade for the external was given by the following cut scores:
In addition to completing NCEA math subjects, students must also meet a separate numeracy and literacy co-requisite to achieve any level of NCEA. The numeracy component is assessed through a single unit standard, US32406: "Use mathematics and statistics to meet the numeracy demands of a range of situations." This standard is graded as either Achieved or Not Achieved, and it is assessed in a format similar to an external exam, where students complete a series of problems in a test book. The assessment evaluates students' mathematical and statistical skills, and it is typically taken during Level 1, with students working toward it alongside their Level 1 maths courses.
For most schools, students will need to choose between sitting for Calculus or Statistics in Level 3.
Calculus focuses more on understanding rates of change, differentiation, and integration. Statistics emphasizes data analysis, probability, and statistical inference. Calculus is especially useful for careers in fields such as engineering, physics, and computer science, while Statistics is valuable for roles in data analysis, economics, and social sciences. Some degrees have specific requirements for which subject students should take; for example, the University of Auckland’s Engineering degree requires Level 3 Calculus credits. Students should consider their future career aspirations when making this decision. Additionally, students should think about which externals they prefer, as Statistics builds on the probability methods external in Level 2,while the Calculus Methods external in Level 2 prepares students for the Calculus external in Level 3.
Maths is a crucial skill used in many fields beyond the classroom, and the knowledge gained from NCEA Maths can play a significant role in shaping future careers and opportunities for tertiary education. Many industries, including engineering, finance, computer science, medicine, and social sciences, rely heavily on mathematical skills. Having a strong foundation in NCEA Maths opens doors to these fields and more.
Additionally, a wide range of tertiary degrees require some level of mathematical knowledge, even if the degree isn’t directly math-based. For example, engineering, economics, and health sciences often have specific math requirements, such as proficiency in calculus or statistics. Even degrees like architecture, psychology, and business management may involve courses that use mathematical concepts to solve real-world problems. Therefore, building a strong understanding of math in NCEA can provide a competitive advantage and ensure readiness for various career paths and further study.