The following diagram demonstrates the format of the UCAT calculator, annotated with functions and usage of each key.

Adapted from: http://questions.ukcat.ac.uk/pages/calculator-ti108.aspx

Keys | Notes on operations |

+ / – | Function: Toggles back and forth between the positive and negative of a value. The number must be on display for this function to work. |

√ | Function: Calculates the square root of the number. The number must be on display for this function to work. |

M+ | Function: adds the number to memory. The number must be on display for this function to work. You must first clear the memory if this function was used previously. Note: more on this key here. |

MRC | Function: Recalls the number from memory. The calculator will remember the same number until you manually clear the memory with the M- key. The number will be shown on screen. You can directly use it in your calculations. Note: more on this key here. |

M- | Function: Clears the number from memory. Must first use the MRC button to recall the number onto the display. |

ON/C | Function 1: Turns the calculator on. Function 2: Clears the input. Note: If you press this button, or backspace on your keypad, you will lose your calculation! |

= | Function: Equals key. Completes the calculation. Can be accessed by pressing “enter” on the keypad |

You can practice using the UCAT calculator here.

It is common to hear that the calculator should be avoided as much as possible. On the contrary, we would advise to use it with certain rules:

**Use it when you need to.**You will only be able to mentally calculate certain questions. Do not pressure yourself into doing everything in your head. Each individual has their own mental maths limits. Although it is beneficial to work on your mental maths, know your limits and adapt to them by practicing using the calculator as well.**Avoid using your mouse!**Use the keypad for as many buttons as possible. This may seem obvious, but it will save you a**lot**of time.**Practice keying in the numbers quickly and accurately.**If you can key in the numbers without looking down at the keypad, you will be able to watch the screen instead. This will allow you to ensure accuracy of your calculations and instantly correct your mistakes when necessary.**Use the memory key if necessary.**It will remember the number you input and save you time from recalculating or writing it down. Alternatively, you can keep the numbers in the whiteboard or scratchpad.**Only use the “equals” function at the end, if possible.**Try to make continuous calculations as much as possible. This is much faster than putting your answers onto the whiteboard/scratchpad. For example, you are asked to calculate the following:

1080 – 679 – 28 – 9

Instead of taking down the answer after 1080 – 679, then subtracting 28 from your answer, know that you don’t have to stop! The calculator is able to carry out continuous calculations, so you can input the numbers and functions exactly as shown above, pressing the equals button, or “enter” on your keyboard, only at the end. Again, this simple tip will save you a lot of time! However, if there are multiple steps and functions in the calculation, be wary of this strategy. The calculator is not scientific and thus it does not follow the rules of BODMAS.

## Limitations of the Calculator

**This is not a scientific calculator.** Therefore, it will carry out calculations in the exact order you key in the numbers and will not obey the mathematical laws of order, or “BODMAS”. Thus, you must be careful of the order of operations.

**There is no power button.** Because there is no function to square or cube a number, you must repeatedly multiply by that number to achieve this. However, there is a square root button, so you can use this to double check you have done it correctly if you have any doubt.

*Note 1:* Learning some square and cube numbers will save you a lot of time in the exam. See the tables below.

*Note 2:* If you learn the square numbers but not the cube numbers, you can simply multiply the square number by the number being squared in order to reach the cube number.

- E.g. 5
^{3}= ?

5^{2} is 25, so 5^{3 }= 25 x 5

= 125

**First 20 Square Numbers**

1^{2} | 2^{2} | 3^{2} | 4^{2} | 5^{2} | 6^{2} | 7^{2} | 8^{2} | 9^{2} | 10^{2} |

1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 |

11^{2} | 12^{2} | 13^{2} | 14^{2} | 15^{2} | 16^{2} | 17^{2} | 18^{2} | 19^{2} | 20^{2} |

121 | 144 | 169 | 196 | 225 | 256 | 289 | 324 | 361 | 400 |

**First 10 Cube Numbers**

1^{3} | 2^{3} | 3^{3} | 4^{3} | 5^{3} | 6^{3} | 7^{3} | 8^{3} | 9^{3} | 10^{3} |

1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 | 729 | 1000 |

**There are no backspaces.** If you make a mistake and/or press the delete button in the middle of your calculations, you will have to restart. Therefore, practice entering them correctly! If you make a mistake with a single function, you may not need to restart. Consider the example below.

- E.g. 3.95 + 1.25 – 0.75 + 6.25 =

If you get to the fourth step ( + 6.25) and accidentally hit ( – 6.25), you would simply just need to hit ( + 6.25) twice to fix the problem, rather than restarting the entire calculator. You can apply the same rule to multiplying and dividing.

# Saving Time

## Avoid Clearing

E.g. Publisher A in London has 6834 books that require printing. They printed 3802 of these last week, and the capacity of the printer this week is 4000. If Publisher B uses the remaining printer capacity after Publisher A finishes printing, how many books can Publisher B print this week?

Here, the steps would be:

- Number of books Publisher A has left to print:

6834 – 3802 = 3032

2. (Printer capacity) – (Number of books Publisher A needs to print) = (Number of books Publisher B can print)

4000 – 3032 = 968

You might be tempted to clear the 3032 from the first step, or even write it on your whiteboard before starting the second step. Consider this method to speed up your calculations:

6834 – 3802 = 3032

3032 – 4000 = -968

This method saves a lot of time! You are solving for a magnitude, so you just need to ignore, or reverse, the “ – “ sign in front of 968. However, make sure you understand the question so you do not confuse yourself or make errors while using this tip.

Alternatively, you could use the “ +/- “ sign to change the sign on 3032 to -3032, then add 4000. This would give you the exact value, as ( – 3032 + 4000 ) is the exact same as ( 4000 – 3032 ). However, this would take longer than the first suggestion as you would need to switch from your number pad to your mouse in order to use the +/- sign, and so, the first technique is a far more superior method of solving this question.

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## Memory Key

E.g. Mickie recently bought a rare car for £125,925. The car increases in value by 9.5% each year as Mickie takes good care of it.What will the value of the car be after four years?

As the value increases by 9.5% annually, the *rate* at which the car would increase in value is 109.5%, or 1.095. This would be the multiplier of this question.

*Note:* If you simply multiply the car’s value by 9.5%, you will get the value of the increase, but not the total value of the car after the increase! Thus, you must add 100% to the multiplier in order to obtain the value of the car.

To save yourself from entering the multiplier 4 times to obtain the value of the car in 4 years, you can simply add the multiplier to the calculator’s memory. To answer this question using the memory key, you would make the following entries into your calculator:

1. | Start with the number you wish to save in your calculator’s memory: 1.095 |

2. | Press M+ to store it in memory |

3. | Multiply by the value of the car (125925) to obtain the value after 1 year: 1.095 x 125925 |

4. | Multiply by the memory (1.095) three more times to obtain the value in 4 years’ time. x MRc x MRc x MRc |

5. | = £181,037 |

## Eyeballing Strategies

When you are short of time, you might need to calculate a question as quickly as possible. Sometimes, this is done without actually knowing the exact answer – what we call eyeballing. This strategy usually only works if the numbers are different enough. If they are all very close together, you may not be able to eyeball.

**Round the numbers to make them easily calculable**

E.g. 18 x 21 (378) can be rounded to 20 x 20 (400)

This strategy will provide you with a close answer which may help you eliminate choices and make a more accurate guess.

**Read the question to rule out impossible answers.**

For example, if the question is asking for an answer in miles, and some answers are given in kilometres, you can easily rule these out. Further, if the question has a number and asks for a positive increase, whereas some answers have a lesser value than the original number, you can easily rule these out.

**Order the numbers into ranges**

E.g. Try to order the following numbers into 3 ranges based on their closeness in value.

- 55
- 98
- 60
- 100
- 32

It is clear that there are three distinct ranges into which the numbers can be separated.

**Range 1:**32**Range 2:**55, 60**Range 3:**98, 100

This may appear to be slightly pointless, but once you are familiar with this technique, you will be able to apply it in seconds to improve your ability to eyeball the answer. Based on the numbers given in the question and the calculations needed, your options will be:

- Guess any answer within the range that appears to be correct. For example, if you know which range the answer must in and there are only two numbers in the range, selecting one of them will give you a 50% chance of guessing the correct answer.
- Work backwards. For example, if 60 seems to be too large, you can easily cancel out the other number within the same range. You would then choose an answer in a lower range. In this case, there is only one number in the lower range (32), so hopefully you would have the correct answer! This would allow you to narrow down your guesses and is especially useful for long-winded, graph analysis questions.
- Eyeball to double-check your answer. If you have completed a multi-step calculation and want to make sure you got the correct answer, rather than conducting the entire calculation again, you can estimate by looking at the question again and trying to eyeball the answer.