# Tutor profile: Kate B.

## Questions

### Subject: Basic Math

Whats a quick way to remember the 9 times tables?

Look at your hands. Each finger is called a number 1 - 10. Put down the finger of the number you want to know the multiple of 9 of. The number of fingers on either side give you the answer. To answer 3 x 9, hide your 3rd finger. You have two fingers on one side of your finger, and seven on the other. The answer is 27. To answer 5 x 9 hide your thumb. You have four fingers on the left, five on the right. The answer is 45.

### Subject: Biology

How do vaccinations work?

A vaccination is usually a killed, inactive version of the pathogen. It can also be a weakened version, one of its toxins or a surface molecule. The body recognises this as a 'non-self' molecule (an antigen), which stimulates the production of antibodies against the threat. Our immune system is able to produce specific antibodies against each antigen it encounters, and also keep a record of the specific antibodies it has produced. These so-called memory antibodies enable the immune system to quickly recognise and act against the same antigen if it comes across it again. So if we come across a pathogen that we have been vaccinated against, our bodies are able to very quickly produce the right antibodies to attack it.

### Subject: Calculus

Is there an easy way to remember how to differentiate?

The rule for differentiation is $$f(x) = ax^{n}$$ => $$f'(x) = anx^{n-1}$$ So you can think of it as multiplying by the index $$(n)$$ and reducing the index by one. For example when differentiating $$f(x) = 3x^{4} $$ you would multiply 3 x 4 to give 12, and then take one from 4 to give 3. Your answer would then be $$f'(x) = 12x^{3} $$ Remember when differentiating a value that is squared (e.g. $$x^{2}$$) taking one from the index gives $$x^{1} $$, which can be written simply as $$x$$

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