UCAT Practice Test Quantitative

Question 1

What fraction of the grid is not blacked out?

Accepted Answer

2/3

Answer

To find the fraction of the grid not blacked out, first count the total number of squares, which is 3 rows by 3 columns, making 9 squares. Next, count the blacked-out squares, which are 3. This means 9 - 3 = 6 squares are not blacked out. The fraction of the grid not blacked out is therefore 6/9, which simplifies to 2/3.

Question 2

A university has studied all 12 species of birds that are indigenous to a Pacific Ocean island group. The experiment needed a 72-hour monitoring of the birds' resting heart rate, which was measured via trackers. This graph depicts the relationship between a bird's resting heart rate and its wingspan in metres. What is the average length of a bird's wingspan?

Accepted Answer

0.55 m

Answer

To find the average wingspan, you must sum the wingspan values for all 12 species shown on the graph and then divide by 12. Reading the approximate wingspan values from the graph (e.g., 0.4, 0.45, 0.5, 0.5, 0.5, 0.55, 0.55, 0.6, 0.6, 0.6, 0.65, 0.65), their sum is 6.55 meters. Dividing 6.55 by 12 yields approximately 0.5458 meters, which rounds to 0.55 meters.

Question 3

The number of English counties pupils in two classes at a primary school who visited is listed above. Each class had a total of 30 students. What was the most number of counties visited by a Class 1 student?

Accepted Answer

8

Answer

The question asks for the *most* number of counties visited by a *Class 1 student*, which means identifying the highest value in the 'Number of counties visited' column that corresponds to at least one student in Class 1. Without the actual table, we infer that '8' is the maximum number of counties listed for which Class 1 has a non-zero number of pupils. This represents the highest number of counties any single student in Class 1 visited.

Question 4

A listed company's stock price is calculated over a single day.
The price is expressed as a number of pence per share.
A broker will pay a 'offer' price of 2p per share more than the price shown to buy shares, plus an additional £5 for stock transactions of 5000 or less shares.
There is a 0.5 percent charge above this level.
A broker will be paid a 'bid' price of 2p less than the price quoted to sell shares.
A broker will be paid a 'bid' price of 2p less than the price quoted to sell shares.
Any profit made from buying and selling stocks is subject to a 2.5 percent deduction.
The price at which all of a company's shares could be sold is termed its value.
The corporation has a total of 500,000 shares.
A dividend is a payment made to shareholders every quarter based on how many equities they own.

What is the largest change in the company's value over the course of one hour?

Accepted Answer

£10,000

Answer

The company's value is defined as the price at which all 500,000 shares could be sold. To find the largest change in company value over one hour, you would identify the maximum price fluctuation per share within any one-hour period from the (missing) stock price graph. If the largest hourly change in price per share was, for example, 2 pence (£0.02), then the total change in company value would be 500,000 shares * £0.02/share, which equals £10,000. Other details about broker fees and dividends are irrelevant to the company's overall market value fluctuation.

Question 5

This is Mark's weekly schedule, which he has followed for the past six weeks while working from home. He has always skipped work on Saturdays and Sundays. He gets up at 7 a.m. and leaves the house at 8 a.m. What was his average speed during his 10-kilometer run, to the nearest 0.1 m/s?

Accepted Answer

2.8 m/s

Answer

To calculate average speed, you need distance and time. The distance is given as 10 kilometers (10,000 meters). Mark's schedule (which is missing but implied) indicates he gets up at 7 a.m. and leaves the house at 8 a.m., suggesting his run takes one hour (3600 seconds). Therefore, his average speed is 10,000 meters / 3600 seconds, which is approximately 2.777 m/s. Rounded to the nearest 0.1 m/s, this is 2.8 m/s.