Faculty of Mathematics The aims of the Mathematics Department are to:   Help to develop a belief in the value of mathematics and its usefulness   Nurture confidence in mathematical ability   Encourage a continuing and creative interest in mathematics   Help to foster and develop mathematical talent Mathematics is a compulsory subject in Years 7 to 11. In Year 11 and 12, students may choose Mathematics or Alternative Mathematics as one of their subject options. In Year 13, two Mathematics options are offered: Calculus or Statistics and Modelling.

Department Staff HOD Mathematics: Neil Harris nharris@stmaryak.school.nz Assistant HOD: Rachel Blanchard rblanchard@stmaryak.school.nz Teachers: Kate Hamilton     Laura Leman     Brian Nolan     Lorraine O'Carroll

Years 7 and 8 Mathematics Our aim is to provide goals and challenges for all; those who find acquisition of mathematical knowledge and skills difficult as well as gifted and talented students. Classes are streamed to ensure students work at their appropriate level. Teachers adapt learning contexts to stimulate and enrich all students.  All students cover the following Process Skills:  applying and reflecting on mathematics’ ideas, participating in teams and groups, making conjectures, thinking logically, using technology in mathematical contexts, interpreting written mathematics and using mathematical language. These skills – problem solving, reasoning, and communicating mathematical ideas – are learned and assessed within the context of the more specific knowledge and skills of the ‘strands’: Number, Measurement, Geometry, Algebra and Statistics. Back to top

Year 9 Mathematics The course covers all strands of the mathematics curriculum, including Number, Measurement, Geometry, Algebra and Statistics.  It aims to help students develop a belief in the value of mathematics and its usefulness to them, as well as fostering the development of mathematical skills, understanding, logical thinking, and problem solving, that will provide students with confidence to deal with mathematics, both in the work place and everyday life.  Assessment: Time Series Task Topic tests on Number, Measurement, Algebra and Geometry Simulation Task Mid Year and End of Year Common Tests Back to top

Year 10 Mathematics The course builds on the work covered in Year 9, again covering the main strands of the mathematics curriculum, including Number, Measurement, Geometry, Algebra and Statistics.  It also aims to help students develop a belief in the value of mathematics and its usefulness to them; as well as fostering the development of mathematical skills, understanding, logical thinking, and problem solving.  This course is designed to give a good background to students moving on to sit the Level 1 NCEA course in Mathematics, and as such, students will sit the Internal NCEA Level 1 Achievement Standard in Geometry, worth two credits. Assessment: Statistical investigation Topic tests on Number, Measurement, Algebra, Graphs and Trigonometry Mid Year and End of Year Common Tests AS 90150 - Use geometric techniques to produce a pattern or object - 2 credits. Internal (1.4) Back to top

Year 11 Mathematics This is the Year 11 course to prepare students for the NCEA Level 1 qualification in Mathematics. The course is designed to meet the requirements of the Level 1 Achievement Standards while also fulfilling the relevant sections of “Mathematics in the New Zealand Curriculum”.  Students will undertake two internal Achievements Standards in Measurement and Statistics, as well as external Achievement Standards covering Number, Algebra, Graphs, Trigonometry, Geometry and Probability.   Assessment: No  Title Credits   Internal Achievement Standards   1.3 Solve  problems involving measurement of everyday objects 3 1.5  Use statistical methods and information 3   External Achievement Standards   1.7  Solve straightforward number problems in context 3 1.2 Sketch and interpret linear or quadratic graphs 3 1.8 Solve right angled triangle problems 2 1.1 Use straightforward algebraic methods and solve equations 4 1.6 Determine probabilities 2 1.9 Use geometric reasoning to solve problems 2 Further credits may be gained from Internal Unit Standard assessments.   Back to top

Level 1 Alternative Mathematics This course is designed for students who are not able to meet the requirements of an Achievement Standards based course.  The goal is for students to achieve the 8 mathematics credits required for NCEA Level 1, as well as the 14 credits required for entrance to University and degree courses.  The course addresses the five main strands of learning: Number, Measurement, Geometry, Algebra and Statistics with most of the course aimed at Level 4 and 5 of the Mathematics Curriculum. Assessment: No  Title Credits   Internal Unit Standards   8489 Number- Solve problems which require calculation with whole numbers 2 8490 Number- Solve problems using calculators with numbers expressed in different forms  2  8491 Number – Read and interpret information presented in tables and graphs 2 8492 Measurement –Use standard units of measurement 3 5236 Trigonometry – Use Pythagoras or Trigonometry to solve problems involving right angled triangles 2 5224 Number – Use decimals and percentages to solve problems 2 5225 Number – Use fractions, ratio, and proportion to solve problems 2 5231 Geometry - Use constructions and make drawings for geometrical situations 2 Back to top

Year 12 Mathematics This is the Year 12 course in preparation for the NCEA level 2 qualifications in Mathematics. The course is designed to meet the requirements of the Level 2 Achievement Standards while also fulfilling the relevant sections of “Mathematics in the New Zealand Curriculum".  The course requires good Algebra skills across all of the topics covered.  Students will undertake internal Achievement Standards in practical Trigonometry, Statistics and Probability.  External Achievement Standards covered include Algebra, Graphs, Co-ordinate Geometry, Calculus and Trigonometric Equations. PREREQUISITE SUBJECTS:  14 credits in Year 11 Mathematics, including merit grades in the Algebra (1.1) and Graphs (1.2) Achievement Standards. Assessment: No  Title Credits   Internal Achievement Standards   2.8 Solve practical trigonometry problems 2 2.6 Simulate probability situations, and apply the normal distribution. 2   External Achievement Standards   2.1  Manipulate algebraic expressions and solve equations 4 2.2 Sketch and interpret non-linear graphs 3 2.3 Find and use straightforward derivatives and integrals 4 2.9 Solve straightforward trigonometric equations 2 2.7 Solve straightforward problems involving sequences (OPTIONAL) 2 Equipment: Graphing calculator $78.00 (current price) THIS SUBJECT IS A PREREQUISITE FOR: Year 13 Calculus; Year 13 Statistics and Modelling Back to top

Year 12 Alternative Mathematics This course is designed for students who have not yet reached the 14 mathematics credits required for entrance to University and degree courses, or who have completed Year 11 Alternative Mathematics in the previous year and wish to continue studying mathematics. The course addresses the five main strands of learning: Number, Measurement, Geometry, Algebra and Statistics with most of the course aimed at Level 4 and 5 of the Mathematics Curriculum.  Assessment: No  Title Credits   Internal Unit Standards   5214 Measurement – Use strategies to solve measurement problems 3 12323 Math Studies – Apply mathematics in the design of an object or process for a given purpose 3  5234 Number – Use calculations in money situations 3 12331 Number – Investigate and report on the mathematics of a given project 3 5242 Probability – Determine probabilities 2 12333 Statistics – Demonstrate understanding of, and use, questionnaire design 3 5238 Graphs – Draw and describe graphs involving two variables 4 Back to top

Year 13 Mathematics with Calculus This is the Year 13 course in preparation for the NCEA level 3 qualification in Calculus. The course covers both differentiation and integration concepts, as well as introducing students to the mathematics of complex numbers and conic sections.  The internal assessment component of the course involves modelling real life situations using trigonometric functions. A strong background in algebra is necessary for success in this course. PREREQUISITE SUBJECTS:  14 credits in Year 12 Mathematics, including two out of three of the Algebra (2.1); Graphs (2.2); and Calculus (2.3) Achievement Standards. Assessment No  Title Credits   Internal Achievement Standards   3.3 Solve problems and equations involving trigonometric functions 4   External Achievement Standards   3.1  Differentiate and use derivatives to solve problems 6 3.2 Integrate functions and solve problems by integration, differential equations or numerical methods. 6 3.4 Manipulate real and complex numbers, and solve equations 5 3.5 Sketch graphs and find equations of conic 3 Internal Unit Standard assessments may also occur in this course. Equipment: Graphing calculator $78.00 (current price) Back to top

Year 13 Statistics and Modelling This is the Year 13 course in preparation for the NCEA Level 3 qualification in Statistics and Modelling.  The course covers probability concepts as well as the Normal, Poisson and Binomial distributions.  The algebra of solving equations is also a key element of the course.  Internal assessments involve modelling a variety of data, including time series, and bi-variate, as well as that which can be modelled with power and exponential functions.    PREREQUISITE SUBJECTS:  12 credits in Year 12 Mathematics, including two out of three of the Algebra (2.1); Statistics (2.5); or Probability (2.6) Achievement Standards.  A level of English equivalent to the Level 2 Literacy requirements is also required. Assessment: No  Title Credits   Internal Achievement Standards   3.1 Determine the trend for time series data 3 3.5 Complete a statistical investigation involving bi-variate data 3 3.7 Use a mathematical model involving curve fitting to solve a problem. 3   External Achievement Standards   3.2  Calculate confidence intervals for population parameters 3 3.3 Solve straightforward problems involving probability 4 3.4 Solve equations 4 3.6 Use probability distribution models to solve straightforward problems 4  Internal Unit Standard assessments may also occur in this course.