Compound Measures – GCSE Maths

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Introduction

  • When we calculate a quantity using other quantities then it is called a Compound Measure which represents the relationship between these quantities and the units used.
  • The Compound Measures are denoted as Ratio or Rate such as “per” unit (km/h, m/s etc.)
  • These Measures are widely used in Business, Engineering and Science and solving real-life problems.

Examples:

    1. Speed
    2. Density
    3. Pressure

Diagram showing the speed formula s = d ÷ t with a car travelling along a road, used to explain compound measures of speed, distance and time for GCSE maths.

Easy Way to Solve Problems

  • We can make it easy to solve the problems related to Compound Measures by learning the Triangle method.
  • Consider following three Compound Measures –

Diagram showing the speed triangle with distance at the top and speed and time at the base, used to explain speed, distance, and time in GCSE maths for the formula speed = distance divided by time 

Diagram showing the pressure formula triangle with force at the top and pressure and area at the base, used to explain pressure calculations in GCSE maths for the formula : pressure = force divided by area

Diagram showing the density triangle with mass at the top and density and volume at the base, used to explain density calculations in GCSE maths using the formula : density = mass divided by volume

How to use the Triangle Method

  • Let us see the use of the Triangle to find one quantity if the other two are known.

Speed–distance–time triangle used in GCSE maths to show the relationship between speed, distance, and time as a compound measure

To find Speed:

  • Hide Speed in the Triangle, then using Distance and Time as the quantities remaining, formula for calculating Speed will be- Formula of speed derived by using the speed, distance and time triangle representing speed as a compound measure

To find Distance:

  • Hide Distance in the Triangle, then using Speed and Time as the quantities remaining, formula for calculating Distance is Distance shown within the speed–distance–time relationship, representing distance in GCSE compound measures, showing distance = speed x time
To find Time:
  • Hide Time in the Triangle, then using Speed and Distance as the quantities remaining formula for calculating Time is –
Formula of time derived by using the speed, distance and time triangle representing time as a compound measure where time = distance divided by speed

certified Physics and Maths tutorSolved Example

Problem: If a distance of 50m is travelled in 10 seconds then what is the speed of the vehicle?

Solution:

         Step #1: Write the FormulaFormula of speed derived by using the speed, distance and time triangle representing speed as a compound measure where speed = distance divided by time

Step #2: Substitute the known values in the formula

Solution of step by step solved example of compound measures

Step #3: SolveSolution of step by step solved example of compound measures

certified Physics and Maths tutorSolved Example

Problem: If mass of a liquid is 1kg and the volume is 200cm3, then find out its Density.

Step #1: Write the FormulaSolution of step by step solved example of compound measures

Step #2: Substitute the known values in the formulaSolution of step by step solved example of compound measures

Step #3: SolveSolution of step by step solved example of compound measures

certified Physics and Maths tutorSolved Example

Problem: Suppose a block of 100cm2 area is lying on the table and Peter starts lifting it with force of 10N. Then find out the Pressure applied in the process?

Solution:

Step #1: Write the Formula

Solution of step by step solved example of compound measures

Step #2: Substitute the known values in the formula

Solution of step by step solved example of compound measures

Step #3: Solve 

Solution of step by step solved example of compound measures

 

certified Physics and Maths tutorSolved Example

Problem: If Olivia runs at a speed of 20km/h, then how far will she run in 5 hours?

an illustration depicting people running that is part of a question solved step by step for the maths topic compound measures

Solution:

Step #1: Write the Formula

Distance shown within the speed–distance–time relationship, representing distance in GCSE compound measures, showing distance = speed x time

Step #2: Substitute the known values in the formula

Solution of step by step solved example of compound measures

Step #3: Solve 

Solution of step by step solved example of compound measures

 

certified Physics and Maths tutorSolved Example : Reasoning Problems

1. A rock weighs 18g and its volume is found to be 24cm3,then find out the density of the rock?

image of rock for a problem on compound measures for maths gcse

Solution:

The mass and and volume of the rock are given as – Mass = 18g, Volume = 24cm3

 Step #1: Write the Formula

Solution of step by step solved example of compound measuresStep #2: Substitute the known values in the formula and solve 

Solution of step by step solved example of compound measures

certified Physics and Maths tutorSolved Example : Reasoning Problem

2. Suppose a train travels with the speed of 100km/h and the distance between two stations (A to B) is 400 meters and third station(from B to C) is 500 meters then find out the total time taken by the train to travel the distance from first to third station(A to C)?

An image showing the illustrated depiction of a reasoning problem for compound measures of gcse math syllabus. it shows the railwasy station and the distance between 3 different train stations

Solution:

First we need to convert the units of speed which are in km/h into m/sec by multiplying it with 5/18.

Solution of step by step solved example of compound measures

 Total distance from A to C is –

distance from A to B + distance from B to C

800 + 1400 = 2200 meters

Step #1: Write the FormulaFormula of time derived by using the speed, distance and time triangle representing time as a compound measure where time = distance divided by speed

Step #2: Substitute the known values in the formula and solveSolution of step by step solved example of compound measures

certified Physics and Maths tutorSolved Example : Reasoning Problem

Problem: Calculate the pressure exerted by the block shown in diagram ?

image showing a block for a compound measures reasoning problem for maths gcse

Solution:

The force applied by block is 475N and area –

            Step #1: Write the Formula for Area, substitute known values and solveSolution of step by step solved example of compound measures

Step #1: Write the Formula For Pressure, substitute known values and solve 

Solution of step by step solved example of compound measures

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