# What do we test?

Physics and Mathematics are extremely broad scientific disciplines, even at the high school level. Below is a guideline for what one would expect to find in the Physics and Mathematics Competition.

You may find that you may not be completely familiar with all of the content, as some of this may be a slight extension from what you learn in class, or new material completely.

Contents that are not covered in NCEA will be explained and expanded upon within the question, so as to not advantage any students.

Refer to Sample Questions or email contact@nzpmc.com to further clarify the difficulty of the tested concepts.

The following sections list the materials covered for physics. A handful of concepts listed here may be unfamiliar to most curriculums. For these concepts, only basic understanding is expected and required. Refer to Sample Questions or email contact@nzpmc.com to further clarify the difficulty of the tested concepts.

# Syllabus

For a comprehensive list of specific concepts you should know for each division, please refer to the following document:

# Junior Physics

As junior science does not have a nationally standardised curriculum like the senior division, we will be testing Physics and Maths content that is typically covered in common textbooks such as the year 9 and year 10 ESA. Mastery of the junior division questions would imply a mastery of these common junior physics curriculums. Reasonable extension of concepts to year 11 is made.

For Junior division physics, we highly recommend that you study with a NCEA level 1 Physics AME workbook or study guide, because they tend to cover Year 9 and 10 much more comprehensively and at a greater depth.

# Junior Mathematics

Algebra

Sequence and general formula

Linear equation

Quadratic equation

Algebraic simplification

Intersection between two graphs

Simultaneous equations

Geometry

Angles

Shapes

Measurement

Trigonometry

Use the sine and cosine rules to find the length of sides in a triangle

Coordinate geometry

Find the gradient of parallel and perpendicular lines.

Recall that the perpendicular distance is the shortest distance from a point to a line

Probability

Single and combined events

Determining if events are mutually independent

Simple discrete probability distributions

# Senior Physics

We assume your familiarity of physics contents up to NCEA level 3. However, you should be able to get through more than ~70% of the competition with NCEA level 2 knowledge.

# Mechanics

Translational Dynamics

Kinematics

Gravitation/Circular Motion

Energy

Simple Harmonic Motion (SHM)

Mechanics content outside of NCEA:

Kinetic Friction

Basic Calculus methods in Kinematics

Vector Mechanics

# Waves

Interference

Refraction

Optics

Doppler Effect

Diffraction

Stationary Waves

We will not be testing any Waves content outside of NCEA.

# Electricity and Magnetism

Basic Circuitry (AC and DC)

Electric Fields

Magnetic Fields / Force on a Moving Charge

Electromagnetic induction (Generators/Motors)

Capacitors

Inductors

We will not be testing any Electricity and Magnetism content outside of NCEA.

# Quantum/Modern Physics

Nuclear Reactions

Atomic Energy Levels

Photoelectric Effect

Radioactive Decay

Wave particle duality

We will not be testing any Quantum/Modern Physics content outside of NCEA.

Following sections list the materials covered for mathematics. A handful of concepts listed here may be unfamiliar to most curriculums. For these concepts, only basic understanding is expected and required. Refer to Sample Questions and the full Syllabus to further clarify the difficulty of the tested concepts.

# Senior Mathematics

Calculus

Differentiation of regular polynomials

Differentiation of trigonometric and logarithmic functions

Integration of regular polynomials

Integration by substitution method

Integration by parts method

Algebra

Evaluation of common logarithms, exponentials, and trigonometric functions

Complex number and locus

Parametric equations for common graphs

Common modelling problems with exponential graphs

Permutations and combinatorics