Year 9 Maths • AC9M9SP03 • Authored homework
Geometric algorithms
Design, test and refine algorithms that use a sequence of geometric steps, transformations, measurements or construction rules to solve spatial problems. Show working, use correct units or notation, and check reasonableness.
Part A
Short-answer questions
What is an algorithm in a geometry context?
Write three ordered steps for constructing a perpendicular bisector.
Why must the order of steps in a geometric algorithm be clear?
Give one example of a geometric construction that can be described as an algorithm.
What does it mean to test an algorithm?
Explain how a flow chart can help describe a geometric process.
Identify one error that could occur in an algorithm for drawing a scaled shape.
Why should an algorithm include exact measurements or rules?
State one way to refine an algorithm after testing it.
Correct this misconception: “An algorithm only belongs in computer coding, not geometry.”
Part B
Long-answer questions
Write a step-by-step algorithm for enlarging a triangle by scale factor 2 from the origin on a coordinate grid.
Design an algorithm to draw a rectangle with a fixed perimeter of 30 cm and maximum possible area. Explain how you would test it.
Create a sequence of steps for locating the midpoint of a line segment on a grid, then test it with two examples.
Write and refine an algorithm for constructing a triangle when two sides and the included angle are known.
A student’s algorithm for a scale drawing misses the unit conversion step. Explain the error and rewrite the algorithm.
Use pseudocode or numbered instructions to describe how to classify a triangle from its side lengths.
Design an algorithm for checking whether two shapes are similar using side ratios and angle information.
Compare a written algorithm and a flow chart for solving a geometry problem. Which is clearer and why?
Create a geometric algorithm that uses Pythagoras or trigonometry as one step, then test it with values.
Write a full response explaining how you designed, tested and improved a geometric algorithm for a practical spatial problem.
Part C
Research and understanding task
Design a geometric algorithm for a real task, such as drawing a floor plan, scaling an image, checking a ramp angle, cutting a shape, or constructing a garden layout. Write the steps, test with numbers, find one weakness and improve it.