Math Games

Patterns and relationships
• Apply co-ordinate geometry techniques to points and lines.
• Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs.
• Use arithmetic and geometric sequences and series.
• Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions.
• Choose appropriate networks to fi nd optimal solutions.

Equations and expressions
• Manipulate rational, exponential, and logarithmic algebraic expressions.
• Form and use linear, quadratic, and simple trigonometric equations.
• Form and use pairs of simultaneous equations, one of which may be non-linear.

Calculus
• Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs.
• Apply differentiation and anti-differentiation techniques to polynomials.

Statistical investigation
• Carry out investigations of phenomena, using the statistical enquiry cycle:
– conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets;
– evaluating the choice of measures for variables and the sampling and data collection methods used;
– using relevant contextual knowledge, exploratory data analysis, and statistical inference.
• Make inferences from surveys and experiments:
– making informal predictions, interpolations, and extrapolations;
– using sample statistics to make point estimates of population parameters;
– recognising the effect of sample size on the variability of an estimate.

Statistical literacy
• Evaluate statistically based reports:
– interpreting risk and relative risk;
– identifying sampling and possible non-sampling errors in surveys, including polls.

Probability
• Investigate situations that involve elements of chance:
– comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions;
– calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.