Year 10 Maths • AC9M10M05 • Authored homework
Proportion and scaling models
Use mathematical modelling to solve practical problems involving direct proportion, rates, ratio, scaling, similar figures and conversion between real and model quantities. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Define direct proportion.
If y is directly proportional to x and x doubles, what happens to y?
A recipe for 4 people uses 300 g of rice. How much rice is needed for 10 people?
A map scale is 1 cm represents 5 km. What real distance is represented by 6 cm?
Convert a scale of 1:50 into a sentence.
Explain why units must be consistent in scale problems.
A model is built at 1:20 scale. Is the model larger or smaller than the real object?
Give one example where direct proportion is reasonable.
Give one example where direct proportion may not be reasonable.
Correct this misconception: “Doubling the side length of a shape doubles its area.”
Part B
Long-answer questions
A floor plan uses a scale of 1:100. A wall is 7.2 cm on the plan. Find the real wall length in metres.
A photograph is enlarged by scale factor 1.5. Original dimensions are 12 cm by 8 cm. Find the new dimensions and compare the areas.
A car travels 180 km using 12 L of fuel. Assuming direct proportion, estimate fuel used for 450 km and state a limitation.
A recipe uses flour, sugar and butter in the ratio 5:2:3. Scale the recipe to use 800 g of flour.
A model bridge is 42 cm long and represents a real bridge 21 m long. Find the scale and use it to find the real width if the model width is 8 cm.
Compare linear scale factor, area scale factor and volume scale factor using a cube enlarged by factor 3.
A student scales a 2D shape by 4 and says the area also scales by 4. Explain and correct the error.
Create a practical scaling problem involving a map, model, recipe or plan and solve it fully.
Explain how proportional modelling can be useful but also risky when the relationship is not truly proportional.
Write a full modelling response using assumptions, variables, proportional calculation, answer and limitation.
Part C
Research and understanding task
Choose a real scale model, map, plan, recipe or design. Identify the scale or proportional relationship, calculate at least two unknown values, and discuss whether proportional modelling is appropriate.