Time and temperature

Two special types of unit conversions likely to appear in Quantitative Reasoning are time and temperature.

You are no doubt very familiar with these concepts from previous maths coursework and everyday life. But they can make for error-prone calculations under the time pressure of Test Day.

You can learn to improve accuracy and limit mistakes by taking some time to revise the common challenges with these familiar topics and practise carefully but quickly as you get ready for Test Day.

Some QR questions may involve different units of time, so you must be ready to convert:

• between units that are less than a day, such as hours, minutes and seconds.
• between days and longer periods, such as weeks, months and years.
• among an unusual mix of times, like converting hours to weeks or converting days to seconds.

Take a moment to sense check while you work. Ask yourself: ‘Should I have more or less of the new units, compared to the old units?’

Some QR questions may include clock times, which come with specific challenges when you are trying to work quickly.

You can work with times in three different time formats:

• am/pm clock times written with a colon or full stop (6:30pm; 7.45am, 11.59pm)
• 24-hour clock times written with or without a colon or full stop (18:30, 07.45, 2359)
• the actual number of hours, with any minutes included in decimal form as a partial hour

Choose the simplest format for the maths required, though in most cases, you will likely need the actual number of hours with minutes expressed as decimals.

Most commonly, you will need to convert clock times into actual hours.

• Set aside any whole hours.
• Divide the minutes by 60 to find the decimal equivalent.
• Combine the minutes in decimal form with the whole number of hours.

You may also need to convert actual hours into clock times:

• Set aside the complete hours – the whole number to the left of the decimal point.
• Multiply the decimal by 60 to convert into minutes.
• This will be the clock equivalent in hours and minutes.

Sometimes, you must add or subtract the clock equivalent in hours or minutes to find a change in clock times.

• First, add or subtract the hours only.
• Add or subtract the minutes. If the new minutes are less than 60, you have the new time.
• If the new minutes are greater than 60, you must divide by 60 to find the additional hour(s) which you must add or subtract from the number of hours. Then, multiply the remainder by 60 to find the final minutes in the new time.

A question may involve different time zones which puts the focus on relative times.

You must choose a time zone to use to compare or convert times as you solve.

Two common approaches:

• Use a simple reference time zone such as Greenwich Mean Time (GMT), then compare or convert other times into the reference time zone.
• Use a time zone in the question as the basis for all other times you must compare or convert. Most likely, this will be the latest or earliest time zone involved.

Temperature is an occasional but infrequent topic in the official UCAT practice materials. So you may or may not see questions involving temperature conversions on Test Day.

You do not need to know the conversion formula for different temperature scales. The UCAT will include a formula or equation, though you may need to reverse the formula.

Most commonly, the UCAT will ask about temperatures in Celsius (centigrade) or Fahrenheit. You will then need to convert to the other temperature scale.

Less commonly, the UCAT could ask about temperatures in Kelvin, but this is much simpler as you may well remember from science coursework that 0°C = 273.15 K.

Even so, you should use the conversion equation provided as it could impact the accuracy of calculations. This applies for any conversions between Celsius and Fahrenheit, as the formula could be expressed a number of different ways.

When working with temperature, always check the units of the answer choices. You may need to convert temperature scales as part of your calculations.

Watch out for wrong answer traps that give the accurate number in the incorrect temperature scale, which is possible if you omit the final conversion.

You may see negative temperatures in some QR sets, and you may have to use negative values when calculating or converting temperatures.

Don’t worry – any temperature conversion formulae work just as well with negative values.

It also does not matter when you average temperatures whether you:

• Convert each individual temperature, then average the converted values, or
• Average the temperatures on the original scale, then convert to the new scale.
• This is because the temperature conversion formula is a linear transformation, so it maintains the relative difference regardless of your approach.

You do not need to memorise any values in temperature scales for the UCAT. But you may find it useful to familiarise yourself with some common comparison points on the Celsius and Fahrenheit scales.

Some questions will include temperature with other maths concepts. As always, find the goal from the question and set up mentally before you go to the calculator.

Take a moment to confirm before you convert, as a temperature conversion may be entirely unnecessary. It may or may not lead to a wrong answer trap, but in any case – an extra calculation will waste valuable time.