 # UCAT Quantitative Reasoning Formulae and Equations

Advice & Insight From UCAT Specialists

Quantitative Reasoning contains 36 questions to be answered in 24 minutes (that’s 40 seconds per question). The questions vary in difficulty. Usually, easy questions can be solved by applying one calculation and harder questions will involve two or more.

You will need to use your prior GCSE knowledge of Maths including mental maths skills, problem solving and data analysis. Research has shown that there are about 17 different topic areas that come up each year. Of these, you will find that the application of formulae and equations will need to done in at least half of these so it is definitely worthwhile spending some time ensuring that you remember the main ones.

## What type of formulae will you need?

Certain formulae that you need to be aware of include how to calculate averages, percentages, fractions, ratios and conversions. Also, you will need to know geometric formulae such as how to calculate areas and volumes of shapes (especially circles), speed. You should also brush up how to perform currency conversions, calculate interest rates along with percentage changes.

## Formulae for 2D shapes:

 Shape Perimeter Area Square 4s s² Rectangle (2 x l) + (2 x w) l x w Parallelogram s1 + s2 + s3 + s4 b x h Circle 2πr πr² Triangle a + b + c ½ x b x h

s = side        l = length     h = height    b = base       w = width

## Formulae for 3D shapes:

 Shape Surface area Volume Box 2lw + 2lh + 2wh l x w x h Sphere 4πr 4/3 πr³ Parallelogram s1 + s2 + s3 + s4 b x h

s = side        l = length     h = height    b = base       w = width

## Circles:

 area πr² circumference 2πr diameter 2r

## Other useful formulae:

Pythagoras’ theorem = a² + b² + c²

“Speed, distance, time triangle” distance = speed x time

speed = distance ÷ time

time = distance ÷ speed

Acceleration = change in velocity
time taken

Mean (average) = sum of terms
number of terms

Percentage change = difference   x 100
original

Some useful conversions to remember to save time performing unnecessary calculations:

 1 metre (m) 100 cm 1 metre (m) 1000 mm 1 kilometre (km) 1000 metres
 1 gram (g) 1000 milligrams (mg) 1 kilogram (Kg) 1000 grams 1 tonne 1000 Kg
 1 litre (L) 1000 ml

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