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Higher Applications homework set

Higher Applications of Mathematics support | 25-40 minutes | Mixed practice

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Pupil instructions

Answer each question in your jotter or on the printed sheet. Show enough working for your teacher to see your method.

  1. A regression line predicts sales from advert spend. Why might a prediction outside the data range be unreliable?

    Support hint: Mark the data range first.

  2. A model predicts y = 10x + 3. What does 10 represent?

    Support hint: Identify intercept separately.

  3. Revision: In a spreadsheet, which formula finds the mean of C2:C11?

    Support hint: Highlight the range.

  4. An investment grows by 7% per year. What multiplier models one year?

    Support hint: Use 5% increase = 1.05.

  5. A sample has mean 20 and standard deviation 4. What does larger standard deviation mean?

    Support hint: Compare two small datasets.

  6. Supported practice: Loan A costs £320 per month for 24 months plus a £150 fee. Loan B costs £336 per month with no fee. Which has the lower total cost?

    Support hint: Set up a two-column finance table.

  7. A route option is cheaper but takes 30 minutes longer. What should the final decision refer to?

    Support hint: Underline the priority in the question.

  8. Consolidation: Two suppliers have the same mean delivery time. Supplier A has standard deviation 7 days and Supplier B has standard deviation 11 days. Which is more consistent?

    Support hint: Write consistency means less variation.

  9. Challenge: A scatterplot has a weak negative trend. Write one cautious conclusion.

    Support hint: Use direction words first.

  10. A model predicts y = 4x + 3. What does 4 represent?

    Support hint: Identify intercept separately.

Answer key

  1. It is extrapolation beyond the observed data

    Predictions outside the data range rely on the model continuing to behave the same way.

  2. Rate of change / gradient

    In a linear model, x coefficient is the rate of change.

  3. =AVERAGE(C2:C11)

    Use AVERAGE over the range.

  4. 1.07

    Add the percentage increase to 1.

  5. More spread from the mean

    Standard deviation measures spread.

  6. Loan A

    Compare total repayment, including the fee.

  7. The stated priority or constraint

    A good decision uses the priority, such as cost, time or reliability, before choosing.

  8. Supplier A

    The smaller standard deviation shows less spread and more consistency.

  9. As one variable increases, the other tends to decrease, but the relationship is weak.

    Describe trend strength and direction.

  10. Rate of change / gradient

    In a linear model, x coefficient is the rate of change.