Jump to
Journey Browse New Idea Samples Rubric Data Sets Y11 Practice
Menu
Sign up Sign in

Year 11 Practice Task

Practice prompts for exploring the mathematics behind real-world scenarios — stats, parabolas, sinusoidal functions, dice probability and box optimisation. This is non-graded practice, the goal is to develop your writing and mathematical thinking before Y12.

Back to Library

Each scenario has essential questions (entry points) and advanced questions (for deeper investigation).

Activity 1: Skills Development Task (make a copy) Configure
Scenario 1 — Statistics & Large Data Set

Use statistics to explore the large data set below. A fake report on an unrelated topic is provided for reference.

Open Data Set Configure Example Report

Essential:

  1. Is there a correlation between height and weight?
  2. 25% of the population are less than what height?
  3. What is the probability of selecting a right-handed person who plays tennis?

Advanced:

  1. Break the population into subcategories — are tennis players taller on average? Do IQ results follow a normal distribution?
  2. Given a tennis player is selected, what is the probability they are left-handed?
Scenario 2 — Sound Mirrors & Parabolas

Research the purpose of 'Sound Mirrors' and fit a parabolic curve to a real example.

See an Example Configure

Essential:

  1. Can you import an image to Desmos or GeoGebra, then fit a parabolic curve to the shape?

Advanced:

  1. Parabola or circle — which fits better?
  2. What is a focus point on a quadratic?
  3. Can you scale up the quadratic function? Do you need to change the location of the focus?
Scenario 3 — Sunrise & Sunset

Fit a sinusoidal function to sunrise and sunset time data.

Sample Processed Data Configure Raw Data (other cities) Configure

Essential:

  1. Can you fit a sinusoidal function to the data?
  2. Can you use piecewise functions to mathematically articulate daylight saving time?
  3. Can you develop a function for the length of a day at any given time of year?

Advanced:

  1. How does this compare for cities at different latitudes?
  2. How does this function need to be adapted for faster-spinning planets?
  3. What assumptions can you make about the orbit to make this manageable?
Scenario 4 — 100 Dice Problem

Roll 100 dice; each time remove the sixes. Record how many dice remain after each roll.

PolyPad Simulation Configure

Essential:

  1. How long does it take for all the dice to disappear?
  2. Can you connect this to geometric sequences and exponential functions?
  3. How does this relate to radioactive decay?

Advanced:

  1. How can this be adapted for different numbers of faces?
  2. How can you mathematically compare expectation with experimentation?
Scenario 5 — Box Optimisation

Take a rectangular piece of card 20 × 30 cm and cut a square from each corner. Fold up the sides to form an open-top box.

GeoGebra Visualisation Configure

Essential:

  1. What is the maximum volume of a box you can make?
  2. Can you generalise this for a box from a card with dimensions a × b?

Advanced:

  1. What if you tried to draw the net of a cylinder on the card? What is the maximum volume?