Level 3 Mathematics
13MTH Course DescriptionTeacher in Charge: Mr M. Po'e-Tofaeono.
Recommended Prior LearningAt least 12 credits in Level 2 Mathematics Combined [12MTH, 12MTA, 11MTX] or Level 2 Mathematics Calculus.
Not suitable for students with limited English
Choosing the Right Mathematics Course for You
At Level 2 and 3, Mathematics splits into more specialised courses. Your choice should reflect your learning strengths and future plans. Below is a guide to help you decide which pathway is best for you.
Statistics is the study of data, how it is collected, analysed, and interpreted to support decision-making. It enables us to identify patterns, assess reliability, and make informed predictions based on evidence. Students develop skills in evaluating real-world information and drawing conclusions using statistical techniques.
Statistics is widely applied in fields such as health sciences, psychology, law, business, education, and environmental studies.
Calculus is the branch of mathematics concerned with change and motion. It focuses on rates of change and the accumulation of quantities, using algebraic and graphical methods to model real-world situations. Students learn to solve complex problems involving speed, growth, area under curves, and optimisation.
Calculus is essential for careers in engineering, physics, architecture, computer science, and any discipline requiring advanced mathematical modelling.
LEVEL 3 MATHEMATICS [ Combined Statistics and Calculus]
This course is a combination of Level 3 Calculus and Statistics. It cannot be taken in conjunction with any other Level 3 Mathematics or Statistics course. The course is for people who require a background in both Calculus and Statistics, but who wish to take only one Mathematics subject.
If you are unsure which course of Mathematics to study, speak to your current Maths teacher. They know your strengths and can help you decide which course best suits your goals.
Course Overview
Term 1
The following topics will be covered, however, due to unforeseen circumstances, topic order and concepts might change throughout the year.
DIFFERENTIATION
-Understand and apply the concept of a derivative as the rate of change (or gradient of a curve)
-Differentiate basic functions using rules:
-Use derivatives to find gradients of curves and equations of tangent and normal lines
-Identify stationary points and determine whether they are maximum, minimum or points of inflection
-Use second derivative to analyse concavity and nature of turning points
-Apply differentiation to solve real-world problems, such as: Maximising or minimising quantities (e.g. profit, area, distance)
-Finding rates of change in motion or growth contexts
-Sketch or interpret the shape of functions based on gradient and turning point information
-Communicate solutions clearly and in context
TIME SERIES data
-Analyse data that is collected over time (e.g. monthly temperatures, sales figures, interest rates)
-Identify and describe components of a time series:
-Trend (overall direction – increasing, decreasing, or steady)
-Seasonal pattern (repeating cycles across regular intervals, e.g. monthly or quarterly)
-Irregular/Random variation (unpredictable fluctuations)
-Fit a moving average to smooth short-term fluctuations and highlight the trend
-Calculate and interpret seasonal indices to remove seasonal variation
-Adjust data to remove seasonal effects so the underlying trend is easier to see & to make predictions
-Interpret findings in context and communicate uncertainty or limitations of forecasts
Term 2
SIMULTANEOUS EQUATIONS
-Set up and solve systems of equations involving two or three variables
-Use a combination of:*Substitution (replacing one variable in terms of another)
*Elimination (adding or subtracting equations to eliminate a variable)
-Apply systems of equations to real-world problems, such as: *Intersection points of two lines or curves
*Mixture problems (e.g. concentrations or investments)
*Geometry or measurement situations (e.g. finding dimensions of a shape)
-Solve linear–nonlinear systems (e.g. line and parabola, or exponential and linear)
-Interpret the meaning of solutions in context:
-One solution (unique point of intersection)
-No solution (inconsistent system)
-Infinite solutions (dependent system)
-Clearly state assumptions, reasoning, and conclusions in context
LINEAR PROGRAMMING
-Formulate and solve optimisation problems involving constraints and objectives
-Define decision variables clearly
-Construct inequalities from word problems to represent constraints
-Graph inequalities to create a feasible region on a set of axes
-Identify the objective function (e.g. maximise profit or minimise cost)
-Apply linear programming techniques to find the maximum or minimum value
-Understand how the optimal solution is found at a vertex (corner point) of the feasible region
-Use graphing to interpret real-world implications of the solution
-Clearly justify conclusions and discuss any limitations or assumptions
Differentiation cont.
Term 3
EVALUATE STATISTICALLY BASED REPORTS
-Critically read and evaluate a real-world statistical report (e.g. from a news article, research summary, government document)
-Identify the purpose of the report what question(s) is it trying to answer?
-Assess the population of interest and how the data was collected (e.g. survey, observational study, experiment)
-Evaluate whether the sample is representative of the population
-Consider the method of data collection were there possible sources of bias?
-Interpret the statistical measures used (e.g. percentages, medians, margins of error)
-Check whether language used in the report is appropriate does it overstate or mislead?
e.g. Does it wrongly claim causation from correlation?
-Identify and evaluate any assumptions or limitations in the report
-Determine whether the conclusions are justified based on the data and methods
-Clearly communicate your critique using evidence and statistical reasoning
DIFFERENTIATION cont.
Term 4
Review all prior concepts in preparation for NCEA external examinations.
Assessment Policy & Procedures Course Costs and Equipment/ Stationery requirements
Students will need a Casio graphic calculator (fx-9860GIII, approximately $180). Older models such as the Casio fx-9750G are also suitable. If in doubt, please check with your Mathematics teacher before purchasing whether from the school or other retailers.
Nulake EAS 3.12 Statistical Reports Workbook, $10
Nulake EAS 3.6 Differentiation Workbook, $10
Note: All prices are approximate and may change slightly due to updates from suppliers or production costs. We will do our best to keep any changes as minimal as possible.
In addition, students will need standard stationary items: A ruler, glue stick, three 1J8 exercise books
If the cost of any item presents a challenge, we warmly encourage you to contact the Dean early in Term 1 next year to discuss possible support.