National 4 Applications of Mathematics

Applications Test practice

Practise breadth, application, integration and reasoning across the three mandatory units. This is independent preparation for the internally assessed Added Value Unit—not an official test.

Course overviewOrdinary mixed revision

Public test structure reflected here

Part 1: 15 marks
No calculator · about 20 minutes

Part 2: 30 marks
Calculator permitted · about 40 minutes

Total: 45 marks

Reasoning: 60% in this practice set

This independently generated set follows the public breadth and conditions. It is not an official Qualifications Scotland assessment and does not award the qualification.

Part 1

Non-calculator number processes

  1. Number Skills2 marks

    1. A store has 381 items, sells 60, then receives 77. How many items are there now?

  2. Fractions2 marks

    2. Simplify .

  3. Percentages2 marks

    3. In a survey, 6 out of 10 pupils chose art. What percentage chose art?

  4. Ratio and Direct Proportion2 marks

    4. Simplify the ratio 20:40.

  5. Time and Planning2 marks

    5. A journey starts at 09:20 and ends at 11:45. How long is the journey?

  6. Finance, Pay and Money2 marks

    6. A weekly budget has £320.00 income, £130.00 rent, £80.00 food, and £20.00 travel. How much is left?

  7. Measurement, Scale and Navigation3 marks

    7. Convert 3.5 kg to grams.

Part 2

Calculator-permitted application and reasoning

  1. Finance, Pay and Money2 marks

    1. For 36 hours, Job A pays £11.00 per hour. Job B pays £12.00 per hour but costs £30.00 for travel. Which gives the better financial outcome, and by how much?

  2. Statistics and Data2 marks

    2. A frequency table has scores 4, 5, 6 and 7 with frequencies 3, 5, 8, 3. Which score is most common?

    Scores

    Score 43
    Score 55
    Score 68
    Score 73
  3. Measurement, Scale and Navigation2 marks

    3. Convert 4.5 litres to millilitres.

  4. Perimeter, Area and Pythagoras2 marks

    4. A rhombus has perpendicular diagonals 12 m and 8 m. Calculate its area.

  5. Volume and Capacity2 marks

    5. Use the cuboid diagram. Find the volume.

    Cuboid

    Use the labels and units shown in the diagram.

  6. Probability and Risk2 marks

    6. In 32 trials, an event happened 17 times. Find the experimental probability of the event.

  7. Speed, Distance and Time3 marks

    7. A minibus leaves at 11:00 and arrives at 12:30 after travelling 60 km. Find the average speed.

  8. Finance, Pay and Money3 marks

    8. Gross pay is £620.00. A simplified deduction rate of 12% is supplied. Calculate the deduction.

  9. Statistics and Data3 marks

    9. A travel survey is shown in the bar chart. Identify the most common method, compare it with walking, and find the range.

  10. Measurement, Scale and Navigation3 marks

    10. A jug contains 1 litre 500 ml. A bottle adds 500 ml more. What is the total in millilitres?

  11. Perimeter, Area and Pythagoras3 marks

    11. Use π and give the area of the circle to 1 decimal place.

  12. Volume and Capacity3 marks

    12. A box is 25 cm long. A shelf is 225 cm long. How many boxes fit in one row?