Level 2 Mathematics Combined
12MTH Course DescriptionTeacher in Charge: Ms A. Kuan.
Recommended Prior LearningAchievement in Level 1 Mathematics with an Achieved+ grade in AS 1.4 Mathematical Reasoning is required or at the discretion of the Teacher in Charge or Learning Area Director.
Students must have been in 11MTA/11MTH [ if at EGGS the previous year]
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.
12 Mathematics combined
This course is a combination of the Level 2 Calculus and Statistics courses. It cannot be taken in conjunction with any other Level 2 Mathematics course.
Students will be placed in either 12MTH or 12MTA so that they are in a class learning at the right pace for them.
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
This is a general outline only. The order and specific concepts taught may vary depending on the class and teacher, as topics are adapted to meet the learning needs of each group.
Algebra
Indices & Logarithms
•Use power rules to simplify expressions
•Work with surds
•Solve powers by changing the base
•Use logarithms to: Solve exponential equations
•Solve real-life exponential problems
Factorising
•Take out common factors
•Group terms to factorise
•Factorise quadratics:- Simple trinomials
- More complex trinomials
- Special types: Difference of squares, Perfect squares, Disguised quadratics
Solving Quadratics
•Solve using: Factorising, Quadratic formula, Completing the square
•Use the discriminant to: Determine how many solutions, Identify when the graph touches the x-axis
•Form equations from known roots
•Solve word problems involving quadratic graphs
Algebra Skills
•Solve linear equations and inequalities
•Solve simultaneous equations
•Rearrange formulas to make a different variable the subject
Algebraic Fractions
•Simplify fractions with like and unlike denominators
•Multiply and divide algebraic fractions
•Use factorising when simplifying fractions
Graphical Methods
* Graphing linear, quadratic, cubic, exponential, and trigonometric functions
* Key features: intercepts, turning points, asymptotes, maxima/minima
* Sketching and interpreting graphs
* Solving equations and inequalities graphically
* Graph transformations (shifts, stretches, reflections)
* Using technology (e.g. graphics calculator) to solve problems
* Real-world contexts modelled with graphs
Term 2
Trigonometry
*Sine, cosine, and tangent ratios in right-angled triangles
*The sine rule and cosine rule (including ambiguous case)
*Solving triangles (angles and sides)
*Applications in 2D and 3D contexts
*Area of triangle using trigonometry (½ab sin C)
*Using radians and degrees
Probability
*Probability with tables, tree diagrams, and Venn diagrams
*Conditional probability
*Independent vs dependent events
*Probability distributions: discrete, binomial
*Calculating expected value
*Relative frequency vs theoretical probability
* Interpreting contextual probability situations
* Risk and relative risk
Term 3
Calculus
*Differentiation of polynomial,
*Finding gradients of curves and equations of tangents
*Applications: Maxima and minima problems
*Rates of change (e.g. velocity, growth)
* Optimisation problems (geometry, real-world contexts)
*Sketching gradient and original function graphs (basic qualitative understanding)
*Interpreting turning points
Term 4
Intensive review of all NCEA standards
Assessment Policy & Procedures Pathway
Level 3 Calculus, Level 3 Mathematics, Level 3 Statistics A, Level 3 Statistics B
Mathematics and Statistics is a foundation for further study in a range of learning areas including engineering, commerce, science, social science, health sciences and information management. Satisfactory completion of this course allows students to proceed to any of the Level 3 courses in Mathematics, Calculus or Statistics.
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.
Write-on workbook : Walker Mathematics 2.6 Algebra, 2.7 Calculus $10 each [ both are required].
Write-on workbook : Internals $6
In addition, students are expected to bring standard stationery items, including: A ruler, Glue stick, 3 x 1J8 exercise books
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.
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.