UCAT Quantitative Reasoning - Practice & Free Samples

The UCAT Quantitative Reasoning subtest assesses one’s ability to implement standard numerical skills (GCSE standard) to solve quantitative problems. The questions in this section test you on your problem-solving skills, as opposed to your numerical ability.

The UCAT Quantitative Reasoning section is specifically designed to give everyone an equal opportunity to successfully complete it. A-level math is not required, but most of the questions on the Quantitative Reasoning section are at least GCSE-level.

On the UCAT Quantitative Reasoning section, you must draw out the pertinent information from numerical presentations (such as tables). Each numerical presentation will have four questions that relate to it, each with five possible answer choices, from which you must select the best answer. The Quantitative Reasoning subtest is comprised of nine data sets, making a total of 36 questions.

You have 24 minutes to complete this section (plus one minute for instructions). You will be provided with a simple on-screen calculator for this part of the test.

UCAT Quantitative Reasoning Sample Questions

The example questions below demonstrate the types of questions you will experience in this test. By going through it with you, we highlight some of the challenges you will come up against in this section.

Sample Question 1:

A teacher brings their chemistry class a semi-filled 2L canister of distilled water, which is equivalent to 1kg of water. She introduced the class to the Mole (mol) unit, which measures amounts of chemical substances. 1 mol represents an amount of substance which includes 6.02 x 1023 particles.

For example, 1 mol of water molecules (H2O) contains 2 mol hydrogen atoms (12.04 x 1023 particles) and 1 mol oxygen atoms. 1 mol of distilled water weighs 18 grams.

The teacher measured the weight of 9 grams of water.
How many atoms of oxygen did she weigh?

A. 3.01 X 10^23

B. 1.505 X 10^23

C. 6.02 X 10^23

D. 3.01 X 5^23

E. 6.02 X 5^23

View Explanation

The correct answer is A.

9 grams of water equals half a mole. 9/18 = 0.5
Since in any mole of water there is 1 mole of oxygen particles, then in 9 grams there is half the amount of particles that there is in a mole.

We need to divide 6.02 x 1023 by 2.The outcome is 3.01 x 1023.
1023 is an expression of a power. It represents a sequence of 23 multiplications by 10; therefore a division by 2 won't change it to be 523.

Note that even if you were given a more complex and unfamiliar mathematical expression, there would usually be some sort of a clue in the supplemental information, which will assist in the solution. In our case it was mentioned that 2 moles of hydrogen contain 12.04 x 1023 particles. The multiplication action did not affect the power; hence, we can deduce that neither division will.

Sample Question 2:

The spring-migration route of a flock of storks returning from Africa to Europe covers a distance of 12,600km.

On the next day, the flock soared and gained speed uniformly for one hour from 0km/h to 60km/h, and then continued in that fixed velocity to cover a total flight distance of 360km.
How much time did the flock's journey last that day?

A. 5.5 hours

B. 6 hours

C. 6.5 hours

D. 6.75 hours

E. 7 hours

View Explanation

The correct answer is C.

The key concept of this question is "uniform acceleration", which is likely to appear in some speed-time-distance problems. In general, an average speed for a time period of uniform acceleration is the average of the initial speed and the final speed, as expressed in a formula:
[average speed on acceleration = (initial speed + final speed)/2].

For example, if someone drives a car and accelerates uniformly from 50km/h to 100km/h, then while accelerating he'll be going at an average speed of (50+100)/2 = 75km/h.

Back to our question,
The flock of birds increased speed from 0km/h to 60km/h in one hour. It means that for one hour it flew at an average speed of (0+60)/2 = 30km/h and thus covered 30km. The flock travelled the remaining 330km at a fixed velocity of 60km/h, which took 330/60 = 5.5 hours. Together it sums to 6.5 hours of flight.

Let's reassess the distracters. Note that both options A and B suggest a time frame of 6 hours or less. 6 hours is when 360km will be covered at a fixed velocity of 60km/h. Since we face acceleration at the first phase of the flight, the accumulated time cannot be 6 hours or less; therefore, you can exclude these distracters as possible answers.
Spotting these clues while solving UKCAT exams will help decrease the chance you make a mistake, even when you don't figure out the exact answer.

On the UCAT Quantitative Reasoning subtest, you will be provided with an on-screen calculator. The calculator may be helpful on the test, but it can also present challenges and slow you down. Here are some helpful tips:

The UCAT calculator is a TI-108, which is the most basic calculator. It includes the four basic functions as well as square root and percentage keys. In each Quantitative Reasoning question, there is a link to the online calculator on the top left-hand side of the screen. When you click on this link, the UCAT calculator will appear on your screen. You may either click the buttons using your mouse or by using the number buttons on your keyboard.

You may find using a calculator while you practise for the UCAT Quantitative Reasoning section to be beneficial. Make sure to use the same type of basic calculator so that you can get acquainted with it before the test. Here are some tips to consider regarding the UCAT calculator:

It is good to know and understand what you can and can’t do with a basic calculator. Brushing up on the different functions you can perform with the calculator will save you time on the test.
Preparing with the calculator will help you answer questions more accurately. Some of the common problems with using a basic calculator include inputting the equation into the calculator in the wrong order or getting confused about how to calculate a percentage or a decimal point.
You will have to perform more difficult calculations without the help of a calculator. Prepare for these in advance so that you will know how to perform these tasks correctly, quickly, and easily on the test.
Practising will help you to become familiar with the calculator, making it quicker for you to input necessary information (numbers, functions, etc).

UCAT Quantitative Reasoning Test

What is the UCAT Quantitative Reasoning Test?

UCAT Quantitative Reasoning Sample Questions

Sample Question 1:

Sample Question 2:

4 Tips to Use the UCAT Calculator