Scholarship

Scholarship Maths

Overview

Scholarship maths is a difficult course designed to challenge the very best maths students. Students attempting scholarship maths will be expected to use knowledge of mathematics by combining techniques and concepts from patterns and relationships, equations and expressions, and calculus, to solve complex problems in unfamiliar or generalised situations. The questions could be taken from any level 8 Mathematics AOs of the New Zealand Curriculum (M8–1 to M8–12), including content that isn't covered in the level 3 maths course at Wā Ora. Individual questions may cover the content of more than one area. Questions may be set in both mathematical and real-life contexts. Questions involving unfamiliar situations may be set, but necessary information will be supplied in the question....read more

Formulae and tables booklet

Formulae and tables booklet

Student resources

Maths Olympiad problems
CalcEX problems

Past exams

2023	exam+answers
2022	exam	answers
2021	exam	answers
2020	exam	answers
2019	exam	answers
2018	exam	answers
2017	exam	answers
2016	exam	answers
2015	exam	answers
2014	exam	answers
2013	exam	answers
2012	exam	answers
2011	exam	answers
2010	exam	answers
2009	exam	answers
2008	exam	answers
2007	exam	answers
2006	exam	answers
2005	exam	answers
2004	exam	answers

Standard

Standard (December 2012)

Curriculum links

The questions in this course can come from any of the level 8 New Zealand Curriculum calculus achievement objectives:

Patterns and relationships

• M8-1 Apply the geometry of conic sections
• M8-2 Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions
• M8-3 Use permutations and combinations
• M8-4 Use curve fitting, log modelling, and linear programming techniques
• M8-5 Develop network diagrams to find optimal solutions, including critical paths

Equations and expressions

• M8-6 Manipulate trigonometric expressions
• M8-7 Form and use trigonometric, polynomial, and other non-linear equations
• M8-8 Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context
• M8-9 Manipulate complex numbers and present them graphically

Calculus

• M8-10 Identify discontinuities and limits of functions
• M8-11 Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods
• M8-12 Form differential equations and interpret the solutions

Scholarship Statistics

Overview

Scholarship statistics is a difficult course designed to challenge the very best statistics students. Students attempting scholarship statistics will be expected to use knowledge of statistics to apply statistical and probability concepts and methods to complex problems in contexts which may be unfamiliar, interpret and, where appropriate, make inferences and clearly communicate concepts and findings. Questions will be set in the areas of Statistical investigation, Statistical literacy, and Probability (which may include use of permutations, combinations, and expectation), all having real-life contexts. Individual questions may cover the content of more than one area. There will be an emphasis on data analysis and interpretation.

Formulae and tables booklet

Formulae and tables booklet

Past exams

2023	exam+answers
2022	exam	answers
2021	exam	answers
2020	exam	answers
2019	exam	answers
2018	exam	answers
2017	exam	answers
2016	exam	answers
2015	exam	answers
2014	exam	answers
2013	exam	answers
2012	exam	answers
2011	exam	answers
2010	exam	answers
2009	exam	answers
2008	exam	answers
2007	exam	answers
2006	exam	answers
2005	exam	answers
2004	exam	answers

Standard

Standard (December 2012)

Curriculum links

The questions in this course can come from any of the level 8 statistics achievement objectives:

Statistical investigation

• S8-1 Carry out investigations of phenomena, using the statistical enquiry cycle:
  • conducting experiments using experimental design principles, conducting surveys, and using existing data sets
  • finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations and making predictions
  • using informed contextual knowledge, exploratory data analysis, and statistical inference
  • communicating findings and evaluating all stages of the cycle.
• S8-2 Make inferences from surveys and experiments:
  • determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
  • using methods such as resampling or randomisation to assess the strength of evidence.

Statistical literacy

• S8-3 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
  • critiquing causal-relationship claims
  • interpreting margins of error.

Probability

• S8-4 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 distributions such as the Poisson, binomial, and normal.

Questions can also come from the following level 8 calculus achievement objective:

• M8-3 Use permutations and combinations