The University Clinical Aptitude Test (UCAT), formerly known as the UKCAT, includes a Quantitative Reasoning section designed to test your ability to use critical thinking and numeracy skills to solve problems.
Given the time pressure, we understand why quantitative reasoning is often the section that so many students are apprehensive about.
Having sat my UCAT in 2019, achieving in the top 1% of my cohort, and scoring 880 in QR, here are my top 19 tips to ensure that you are excellently prepared to sit your quantitative reasoning UCAT section!
Check out our free guides to other sections to aid your UCAT preparation, and check out our expert UCAT tutoring services if you need a bit more guidance!
UCAT Quantitative Reasoning Tips Summary:
Get To Know GCSE Maths
Know The Question Types You Will Face
Get To Grips With Compound Interest
How To Expertly Tackle Tax Brackets
Estimate Where Appropriate
Hone Your Mental Maths Skills
Learn The Formulas For Common Shapes
Keep An Eye Out For Sneaky Unit Changes
Practice Using The On-Screen Calculator
Build Muscle Memory For The Numerical Keypad
Keyboard Shortcuts Will Save You Time
Get To Know Your Weaknesses
Reflective Studying
Utilise The Whiteboard
Watch Out For Multi-Step Calculations
Use The Skip Strategically
Answer Every Single Question
Practice To Timed Conditions
Use The Official UCAT Mocks
Quantitative Reasoning Tip 1: Get To Know GCSE Maths
The level of understanding that UCAT examiners expect you to have is that of GCSE Mathematics.
However, we know that not everybody has sat or passed Maths exams, therefore we recommend taking a look at the current curriculum to familiarise yourself with the skills that you’ll be required to demonstrate during your UCAT.
This will also be helpful if you don’t currently take maths at A-level and haven’t used your mathematical skills since secondary school level.
👉🏻 Read more: How To Pick The Perfect UCAT Exam Date
QR Tip 2: Know The Question Types You Will Face
There are a limited number of question types that the UCAT examiners can give you, so with practice, you can reduce the risk of having an unwanted surprise during the exam!
Being confident with every question type puts you in a strong position to sit your exam, and the only way to reach this position is through regular practice of each question type.
The question types that you might face in the QR subtest of the UCAT exam include:
Speed, distance and time calculations
Percentages
Ratios and proportions
Conversions between units
Probability calculations
Interpretation of tables and diagrams
Geometry questions including volume, area, perimeter
Combination type questions
👉🏻 Read more: Answering Data Interpretation Questions
UCAT QR Tip 3: Get To Grips With Compound Interest
One of the hardest types of questions you’ll face in the UCAT is compound interest.
For some students, it might be worth skipping this question, but if you want to score highly, it’s worth revising how to answer these questions before your exam.
Some students are more confident with calculating the interest built up in one year, multiplying this new value by the interest value for the following year until they reach the number of years passed.
However, for larger periods, students might find it more helpful to memorise the formula for compound interest, which will lead them to the correct answer more quickly.
A = P(1 + r/n) ^(nt)
Where:
A = final amount
P = previous amount
r = annual interest rate as a decimal
n = number of times interest is compounded
t - time interested compounds for
👉🏻 Read more: Answering Calculation Questions
Tip 4: How To Expertly Tackle Tax Brackets In The Quantitative Reasoning Subtest
Tax brackets are yet another one of the UCAT’s most feared QR questions, therefore it’s worth getting to grips with how to answer these questions to maximise your marks.
In your exam, you’ll likely face at least one question where you’re asked to interpret or calculate a value pre- or post-tax.
The most important factor to remember when facing tax questions is that tax isn’t a flat value calculated from what’s been earned. It is calculated in portions.
Income (£) | Rate | Explanation | Example |
0 - 12,500 | 0% | This means that you will pay no tax on the first £12,500 you earn. | Salary = £8,000 Tax paid = 0 Take Home Pay = £8000 |
12,501 - 50,000 | 20% | This means that any amount that is earned over £12,500 is taxed at a rate of 20%. | Salary = £42,000 Tax paid = 12500 x 0 = 0 29,500 x 0.2 = 5900 Take Home Pay = £36,100 |
50,001 - 150,000 | 40% | This means that any amount earned over £50,000 is taxed at a rate of 40% | Salary = £82,000 Tax paid = 12500 x 0 = 0 37500 x 0.2 = 7500 32000 x 0.4 = 12800 Total tax = £20,300 Take Home Pay = £61,700 |
Quantitative Reasoning Tip 5: Estimate Where Appropriate
Having strong estimation skills is very beneficial for maximising your speed in this section. However, it’s important to recognise which questions are appropriate and not appropriate to use estimation and approximation.
This can be determined by looking at the closeness of the given answers. If the answers are close together, it shows that you’ve got a very small room for error, therefore through approximation, you’re likely to reach the wrong answer when using round numbers.
However, when appropriate, rounded estimates allow you to quickly eliminate illogical answers and reach the correct answer more quickly.
QR Tip 6: Use Mental Maths Skills To Save Time
With the time pressures of this subtest, choosing to use the calculator for every question may lead to you running out of time in the exam.
We recommend practising using your mental maths skills as much as possible, such that on the day you are confident in completing simple maths calculations in your head, rather than relying on the calculator.
To help you revise this, we recommend looking over your times tables grids up to 15 and improving recall speed.
👉🏻 Read more: Making a UCAT Revision Strategy
Top Tip 7: Learn The Formulas For Common Shapes
One of the common categories of UCAT quantitative reasoning questions involves the use of geometry. In the exam, you likely won’t be given any formulas, so it’s worth learning these in advance.
Shape | Perimeter | Area |
Square | 4 x side length | (Side length)^2 |
Rectangle | (2 x length) + (2 x width) | Width x height |
Triangle | Addition of side lengths | ½ (base x height) |
Regular Polygon | Side length x number of sides | ½ (number of sides x length of side x distance to middle) |
Circle | 2πr | πr^2 |
3D Shape | Surface Area | Volume |
Cube | 6 x (length of side)^2 | (length of side)^3 |
Prism | 2 x base area x side area | Base area x height |
Pyramid | Side area x number of sides | ⅓ (base area x height) |
Sphere | 4πr^2 | 4/3πr^3 |
Tip 8: Keep An Eye Out For Sneaky Unit Changes
Units are very easy to forget, especially after you’ve already taken several steps to reach an answer, but always double-check the units of your answer compared to the units of the question answers!
Examiners may include the answer pre-unit conversion to trick you out. Read the question carefully after you've chosen an answer to double-check this!
👉🏻 Read more: Avoiding UCAT Burnout During Revision Periods
Quantitative Reasoning Tip 9: Use The Calculator
The on-screen UCAT calculator is notoriously clunky and time-consuming to use, so the earlier that you become familiar with it, the better.
It is guaranteed that you’ll be required to use the UCAT calculator at least once during your exam. Unlike a scientific calculator which you may be used to, the UCAT calculator cannot save any previous answers, nor raise numbers to a power.
Make sure that you practice this!
Tip 10: Build Muscle Memory For The Numerical Keypad
It is well known that students who use a numerical pad to type into the UCAT calculator save time and answer QR UCAT questions faster.
A numerical number pad follows the shape and layout of a number pad on a mobile phone, with 3 rows of 3 numbers, so you must move your fingers less to reach the desired numbers. With practice, this can massively improve your speed in the UCAT QR section and help deal with the time pressure of the exam.
The keyboards in the exam centre where you will take your exam will have a numerical keypad on the right side of the keyboard, therefore it’s worth practising using this if you can.
👉🏻 Read more: Strategic UCAT Applications
QR Tip 11: Keyboard Shortcuts Will Save You Time
Several validated keyboard shortcuts work in the UCAT exam software. These are hugely beneficial for increasing your speed.
ALT-N - Next question
ALT-P - Previous question
ALT-C - Open calculator
ALT-F - Flag question
Tip 12: Get To Know Your Weaknesses
Every student revising mathematics will have different strengths and weaknesses, and struggle with different question types.
For instance, when I sat my exam, I knew that I struggled massively with Venn diagram questions if I wasn’t provided with a diagram.
Having insight into your weaknesses is hugely useful for the UCAT, as it highlights which questions might be worth skipping if you’ve got little time left.
Tip 13: Reflective Studying
Reflection is an important and often overlooked part of revision. When doing practice questions, you should be dissecting your incorrect answers until you fully understand the mistakes you have made. Through reflection, you will maximise your learning from practice questions and likely improve your quantitative reasoning score.
👉🏻 Read more: Reflective Practice
QR Tip 14: Use The Whiteboard
In the UCAT, you are provided with a whiteboard to make notes. We recommend that you use the whiteboard mostly in the decision-making and quantitative reasoning sections of the UCAT.
There are various applications in which the whiteboard may be useful for you in QR.
For instance:
Multi-step questions - In these questions, you may need to use a number that you previously calculated to do a further calculation. If this number is easily accessible on your whiteboard, it will save you time. It is sometimes helpful to write bigger numbers as round numbers.
Summarising the question - unfortunately, some UCAT questions contain more text than needed. Writing down important numbers from the question on your whiteboard can help you retrieve important information more quickly when needed. This can take up too much time though!
Tip 15: Watch Out For Multi-Step Calculations
Multi-step quantitative reasoning questions require breaking down the problem into distinct steps and solving each component in sequence.
These are the most time-consuming questions in the QR section and may be worth skipping if you are low on time during this section.
Make sure that you read the question properly so that you know which part is relevant.
👉🏻 Read more: What To Expect On The Day - UCAT
Tip 16: Use The Skip Strategically
With 36 questions and only 24 minutes to answer them, to prepare for the UCAT quantitative reasoning questions, you should become comfortable with answering in just 40 seconds per question.
As discussed, through revision you should begin to identify which questions you find more challenging. As a result, you should begin to learn when to use the “strategic skip”, to avoid spending excessive time on difficult questions.
Given that all questions are worth the same number of marks, you are much better spending time on answering the easier questions correctly, than spending lots of time on a difficult question.
You can always flag these questions and come back later if time permits. In short, answer as many questions as you can, and guess the ones you can't!
Tip 17: Answer Every Single Question
You should attempt to answer every question in the quantitative reasoning topic subtest of the UCAT, even if you are not certain of the correct solution.
Given that the UCAT is not negatively marked, it’s worth choosing your best estimate or approximation, as leaving questions blank will guarantee zero marks.
👉🏻 Read more tips for UCAT success in our Free UCAT Guide
Number 18: Practice Sample Questions To Timed Conditions
In your quantitative reasoning preparation, it is crucial to practice answering sample questions and mock exams under timed conditions.
This allows you to realistically simulate the time pressure you will face on exam day and improve your pacing, increasing your chances of a high score and success in the UCAT.
Quantitative Reasoning Advice 19: Use The Official UCAT Practice Questions
The UCAT consortium has provided several free official Mock exams and practice questions. These are an invaluable resource to practice quantitative reasoning questions at the same difficulty as the real exam questions.
We recommend sitting these mock exams around a week before your UCAT exam to get a feel for how you would score in the real exam, and highlight any further weaknesses in your quantitative reasoning skills to brush up on before your exam!
👉🏻 Read more: Everything You Need To Know For The UCAT QR Section
UCAT Quantitative Reasoning Frequently Asked Questions
What is the UCAT Quantitative Reasoning section?
The UCAT Quantitative Reasoning section is one of the subtests in the UCAT (University Clinical Aptitude Test) examination. It assesses your ability to interpret, analyse, and solve problems involving numerical data.
How many questions are there in the UCAT Quantitative Reasoning section?
The UCAT Quantitative Reasoning section consists of 36 multiple-choice questions. Test-takers are given 25 minutes to complete this section.
What topics are covered in the Quantitative Reasoning section?
The Quantitative Reasoning section assesses your skills in basic arithmetic, applied mathematics, and data interpretation. Topics include percentages, ratios, proportions, basic algebra, and graph interpretation.
Are calculators allowed in the UCAT Quantitative Reasoning topic?
You are not allowed to bring calculators into the UCAT Quantitative Reasoning exam. However, there is an in-built calculator in the UCAT exam software, which you can use.
How should I prepare for the Quantitative Reasoning section?
Effective preparation involves practising mental calculations, reviewing basic mathematical concepts, and familiarising yourself with the question format. Utilise official UCAT practice materials and timed practice tests.
What is the scoring system for UCAT Quantitative Reasoning?
The Quantitative Reasoning section is scored on a scale from 300 to 900, with 600 being the average score. Your performance is measured against other test-takers.
Is there a negative marking in the UCAT Quantitative Reasoning subtest?
No, there is no negative marking. Therefore, it's important to manage your time effectively, answer questions you can, and guess the rest.
Can I go back to review or change the answers in the Quantitative Reasoning UCAT questions?
Yes, you can review previous answers. It is worth flagging the questions you have struggled with. However, the UCAT is a computer-based test, and once you move on to the next section, you cannot go back to review or change your answers.
Are there any specific strategies for tackling the UCAT Quantitative Reasoning questions?
Time management is crucial. Prioritise questions based on your confidence level, and don't spend too much time on a single question. Focus on understanding the problem and choose the most appropriate answer.
How does the Quantitative Reasoning section contribute to my overall UCAT score?
Each of the four UCAT subtests, including Quantitative Reasoning, contributes equally to your overall UCAT score. Your performance in this section, along with the others, will be used by medical schools as part of their selection process.
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