Maths steps and challenges

At the heart of QR are the four basic operations:

• addition
• subtraction
• multiplication
• division

You will likely perform 100 or more calculations using these operations during the QR section on Test Day.

The challenge is to train your brain through UCAT revision so you can see the shortest path to the goal. Then, you can follow that path using the relevant numbers from the data in the onscreen calculator.

Most Quantitative Reasoning questions involve one, two or three steps. Thus, you can solve for most answers in three or fewer calculations.

Some QR questions will require a single step, often through the use of a common formula such as the mean or percentage change formulae.

Many QR questions will need two or three steps, so you will want to use an efficient sequence to do the calculations. Ideally, you will plan your calculations so the result in the calculator from the first step is the first number you need for the second step. This will be an adjustment – it is not normal in maths exams – but you can learn it.

While most QR questions include visual data such as tables or graphs, you need just a small amount of the data to answer each question.

You must read each question stem to ensure you find the goal before you select the relevant data. You can then set up in your head to allow for quick, accurate calculations with the onscreen calculator.

Initially, you must slow down to let yourself adjust to the mental maths that are the foundation for efficient calculator use. Otherwise, you run the risk of becoming ‘calculator dependent’ – going to the calculator before you have a plan of the maths required to find the answer. You must see the path to the goal before you can follow it.

You will answer many QR questions with a common formula. But much of the time, you must figure out what operations are required and in which order.

Even the most complex data and the wordiest question will boil down to the basic operations: addition, subtraction, multiplication and division.

You must learn to see the path to the goal and calculate quickly and accurately in the best sequence of steps to find the correct answer. No more, no less.

The more comfortable you are with doing basic operations, the quicker you will maximise your marks in QR.

Many QR questions will start off with subtraction or division. You may find it trickier to work quickly when subtraction or division is the first step.

Take a moment to set up in your head before you go to the calculator. You may find that you must slow down to get faster. With practice, you will likely be able to increase speed without compromising accuracy, even when the first step is to subtract or divide.

You can use some mental or calculator shortcuts to ensure all your calculations are associative and commutative:

• You can add a series of positive and negative numbers in any grouping and the result will be the same. Just take care to put minus signs with the right numbers.
• You can multiply by a reciprocal instead of dividing so that a series of multiplications and divisions becomes pure multiplication with the same result.
• You can do any calculations in any order you like, so long as you are aware of the logic of each step as you work towards the correct answer.

Don’t hesitate to write down any intermediate numbers in the notebook if you cannot easily store or keep using them in the calculator.

This may be necessary in a complex calculation question, or if a question requires you to calculate each answer, such as when the answer choices are ratios written with a colon.

You should aim to limit your notebook use in QR as you practise – it will tend to slow you down on Test Day – but it may have its uses.

Better to jot down a number than to try to remember it but forget and then recalculate.

QR questions may focus on missing data in a few ways:

• The missing data value is the correct answer, so you must solve for it.
• You must solve without the missing data, using a roundabout approach to find the correct answer. In many cases, this would be more straightforward if you could use the missing data value.

Do not stress when you first spot blank cells or missing bars. Instead, wait for the question that relates to the missing data, then set up mentally before you calculate.

Some Quantitative Reasoning questions will allow you to use your work from a previous question later in the set.

In a few special cases, you will be able to use the correct answer from an earlier question to save time later in the set.

Don’t hesitate to click backwards and check earlier questions if you think there might be a shortcut to avoid re-doing calculations.

Wrong answer traps are waiting to catch you out in many QR questions. You can fall for a wrong answer trap by:

• Using the wrong numbers from the data
• Skipping the final step and selecting the value from the next-to-last step
• Inverting the values in a fraction
• Using the right formula but with one or more wrong values
• Omitting a factor or unit conversion

You may think you will avoid traps because you are good at maths, but remember – the vast majority of UCAT students are very good at maths. The fast pace of QR means that you are vulnerable to errors that would not happen in a conventional maths exam.

Be aware and be prepared to spot wrong answer traps as you practise. Learn from your mistakes when you revise mocks and practice questions, and you can dodge the traps more effectively on Test Day.

You can practise these techniques to avoid wrong answer traps in QR:

• Read the question first to find the goal
• Keep the goal front of mind as you select the relevant data
• Confirm that your answer matches the goal before you click it

You might also double check the units of your answer. For example, if you calculated a value in kilometres, are the answer choices in the same units? This can be very subtle when the answers are numbers with the units given in the question itself. (‘What is the distance…in miles?’)