Higher Applications Modelling Revision

Question 1

Which statement best describes a mathematical model?

choosing a model

A simplified representation of a real situationA calculation that never needs unitsA guarantee of the exact futureA graph with no assumptions

Question 2

A cost starts at 6 pounds and increases by 2 pounds per item. Which model is suitable?

gradient and intercept

C = 6 × 2ⁿC = 6 + 2nC = 6 ÷ nC = n² − 6

Question 3

What is the growth factor for a repeated 7% increase?

exponential models

Your answer

Question 4

A length is 50 cm ± 0.5 cm. Give the lower acceptable value.

tolerance and error

Your answer

Question 5

Which is the best interpretation of a model prediction?

model limitations

An estimate based on assumptionsA reason to ignore contextA value that must happenA unit-free answer

Question 6

A workshop models daily cost in pounds by C = 3n² + 5n + 30, where n is the number of batches (1 ≤ n ≤ 10). For 8 batches and a budget of £257, which decision follows if the model remains valid?

model limitations

The model guarantees the exact real costPredicted cost £262; over budget by £5Predicted cost £262; within budget by £5Predicted cost £94; use a linear calculation

Question 7

Which model is most likely for repeated percentage depreciation?

exponential models

Exponential decayBox plotLinear increaseVenn diagram

Question 8

What does the intercept usually mean in a cost model?

gradient and intercept

Cost per unitStarting or fixed costPercentage decreaseMaximum error

Question 9

Which model may be suitable when an area depends on a changing length?

quadratic models

Tree diagramLinear onlyQuadratic modelTwo-proportion test

Question 10

Use C = 15 + 4h when h = 3.

substitution

Your answer

Question 11

Why should units be checked before using a model output?

unit checking

Units never matterWrong units can make a sensible-looking answer wrongUnits prove the modelUnits replace calculations

Question 12

What is a good reason to use a spreadsheet for modelling?

technology modelling

To make predictions exactTo remove all limitationsTo test different assumptions quicklyTo avoid checking formulae

Mathematical Modelling mixed revision quiz

Check your understanding

Which statement best describes a mathematical model?

A cost starts at 6 pounds and increases by 2 pounds per item. Which model is suitable?

What is the growth factor for a repeated 7% increase?

A length is 50 cm ± 0.5 cm. Give the lower acceptable value.

Which is the best interpretation of a model prediction?

A workshop models daily cost in pounds by C = 3n² + 5n + 30, where n is the number of batches (1 ≤ n ≤ 10). For 8 batches and a budget of £257, which decision follows if the model remains valid?

Which model is most likely for repeated percentage depreciation?

What does the intercept usually mean in a cost model?

Which model may be suitable when an area depends on a changing length?

Use C = 15 + 4h when h = 3.

Why should units be checked before using a model output?

What is a good reason to use a spreadsheet for modelling?

Mathematical Modelling mixed revision quiz

Check your understanding

Which statement best describes a mathematical model?

A cost starts at 6 pounds and increases by 2 pounds per item. Which model is suitable?

What is the growth factor for a repeated 7% increase?

A length is 50 cm ± 0.5 cm. Give the lower acceptable value.

Which is the best interpretation of a model prediction?

A workshop models daily cost in pounds by C = 3n2 + 5n + 30, where n is the number of batches (1 ≤ n ≤ 10). For 8 batches and a budget of £257, which decision follows if the model remains valid?

Which model is most likely for repeated percentage depreciation?

What does the intercept usually mean in a cost model?

Which model may be suitable when an area depends on a changing length?

Use C = 15 + 4h when h = 3.

Why should units be checked before using a model output?

What is a good reason to use a spreadsheet for modelling?

A workshop models daily cost in pounds by C = 3n² + 5n + 30, where n is the number of batches (1 ≤ n ≤ 10). For 8 batches and a budget of £257, which decision follows if the model remains valid?