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Functional Skills Maths Level 2 Linear Rules and Rates of Change — practice questions

Explore 10 free Linear Rules and Rates of Change questions in Functional Skills Maths Level 2 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Rules and Rates of Change questions and exercises with answers

Showing questions 1–10 of 10.

A tank fills at a steady rate. After 3 minutes it holds 46 litres, and after 8 minutes it holds 96 litres. At what rate is the tank filling?Read the answer and worked solution →A delivery firm works out a rate of change using cost in pounds as the output and the number of parcels as the input. What units does that rate carry?Read the answer and worked solution →A gym records the total paid against the length of membership. Two months costs £74 and six months costs £158. How much does each extra month add?Read the answer and worked solution →A phone credit balance follows B = 45 - 3.75d, where B is the balance in pounds and d is the number of days. On which day does the balance reach zero?Read the answer and worked solution →One line has a rate of change of 4. A second line crosses it at a right angle. What is the rate of change of the second line?Read the answer and worked solution →Knock out the false billing claimsRead the answer and worked solution →Sort lines by the axis they crossRead the answer and worked solution →Line up three rules that run parallelRead the answer and worked solution →Drag each rate to the way its line slantsRead the answer and worked solution →Tap the steeper of the two linesRead the answer and worked solution →

Worked practice questions

A tank fills at a steady rate. After 3 minutes it holds 46 litres, and after 8 minutes it holds 96 litres. At what rate is the tank filling?

  1. 12 litres per minute
  2. 10 litres per minute
  3. 18 litres per minute
  4. 15 litres per minute
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Correct answer: B. 10 litres per minute

1. The output is the volume in litres and the input is the time in minutes. 2. The volume changes by 96 litres minus 46 litres, which is 50 litres. 3. The time changes by 8 minutes minus 3 minutes, which is 5 minutes. 4. Dividing the change in output by the change in input gives 50 litres divided by 5 minutes, which is 10 litres per minute. 5. Option A comes from dividing 96 by 8 and ignoring the 46 litres already in the tank, which is the usual trap here. _Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_

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A delivery firm works out a rate of change using cost in pounds as the output and the number of parcels as the input. What units does that rate carry?

  1. Parcels per hour
  2. Pounds per pound
  3. Pounds per parcel
  4. Parcels per pound
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Correct answer: C. Pounds per parcel

1. A rate of change is the change in output divided by the change in input. 2. Dividing pounds by parcels leaves units of pounds for each one parcel. 3. Option D turns the division upside down, which would answer a different question. 4. So the rate carries units of pounds per parcel, option C. _Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_

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A gym records the total paid against the length of membership. Two months costs £74 and six months costs £158. How much does each extra month add?

  1. £26 per month
  2. £24 per month
  3. £19 per month
  4. £21 per month
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Correct answer: D. £21 per month

1. Pair each length with its total: 2 months with £74, and 6 months with £158. 2. The total changes by £158 minus £74, which is £84. 3. The length changes by 6 months minus 2 months, which is 4 months. 4. Dividing £84 by 4 months gives £21 for each extra month. 5. Option A comes from dividing £158 by 6 months, which wrongly treats the joining fee as part of the monthly charge. _Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_

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