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National 5 Applications homework set

Exam-style Applications practice | 25-35 minutes | Mixed practice

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Date:

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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 plan uses scale 1:50. A wall is 12 cm on the plan. What is the real length in metres?

    Support hint: Work in cm first.

  2. Catch-up: Mixed check: A class has mean 66. Set A has standard deviation 4 and Set B has standard deviation 9. Which set is more consistent?

    Support hint: Write 'more consistent = less spread'

  3. A cylinder-style container has volume 750 ml. How many litres is this?

    Support hint: Use 1000 ml = 1 litre.

  4. A rectangle is 17 m by 11 m. What is its area?

    Support hint: Draw the rectangle and label both sides.

  5. Find the mean of 7, 11, 15, 17 and 20.

    Support hint: Count the values first.

  6. A jacket costs £96 and is reduced by 25%. What is the sale price?

    Support hint: Calculate 25%, then subtract.

  7. Challenge: A whole-population data set has Σ(x − μ)² = 40 and N = 5. Calculate the population standard deviation.

    Support hint: Underline whole-population.

  8. For a standard deviation table, x = 11 and the mean is 7. Complete x − mean and (x − mean)².

    Support hint: Write the subtraction before squaring.

  9. A route is 42 km in 50 minutes. Name the unit conversion needed before finding average speed in km/h.

    Support hint: Divide minutes by 60.

  10. A journey is 180 miles and takes 2 hours 15 minutes. What time in hours should be used for average speed?

    Support hint: Convert minutes to a fraction of an hour.

  11. Consolidation: A worker earns £12.40 per hour for 41 hours and pays 20% tax. Estimate take-home pay.

    Support hint: Use 20% tax means 80% remains.

  12. The probability of rain is 710. Write this as a percentage.

    Support hint: Use tenths.

Answer key

  1. 6.0 m

    Multiply by 50 cm, then convert to metres.

  2. Set A

    Smaller standard deviation means values are closer to the mean.

  3. 0.75 litres

    Divide ml by 1000.

  4. 187 m²

    Area is length × width and uses square units

  5. 14.0

    Add all values and divide by 5.

  6. £72.00

    Find 75% of the original price.

  7. σ ≈ 2.83

    Use σ = √(40 ÷ 5) = √8.

  8. 4 and 16

    Subtract the mean first, then square the difference.

  9. Convert 50 minutes to hours

    Speed in km/h needs time in hours

  10. 2.25 hours

    15 minutes is 15 ÷ 60 = 0.25 hours

  11. £406.72

    Find gross pay, then calculate 80% after tax.

  12. 70%

    Convert fraction to decimal or percent.