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To rearrange any equation, you must always do the same to both sides.
If you take a number from one side, you must also take it from the other. If you divide a side by one number you must divide the other by the same number (and this applies to the whole of both sides, not just part of the side).
7x + a = 3x + b, make x the subject:
Begin by collecting like terms on each side (so all the terms involving x on one side, and all the other terms on the other side).
1) Take 3x from both sides:
7x + a - 3x = 3x + b - 3x
4x + a = b
2) Take a from both sides:
4x + a - a = b - a
4x = b - a
3) Divide both sides by 4 (as x must be alone):
(4x)/4 = (b - a)/4
x = (b - a)/4 This is our answer
These problems can be worked out using the equation:
new = old x multiplier
new: is the new price of an item
old: is the old price of an item (before it was changed)
multiplier: is the percentage of the old price the new price represents
To calculate the multiplier, you must first know if there is an increase in price or a decrease in price:
Increase in price:
If the old price is increased to the new price
A t-shirt cost £10, it is sold for a 12% profit. What is it sold for?
Old = £10
New = ?
Multiplier = as there has been an increase, the new price is 100% + 12% = 112% of the old price. The multiplier is therefore (112%)/100 = 1.12
new = old x multiplier = 10 x 1.12 = £11.20
The question may also be asked as:
A t-shirt is sold for £11.20, which is a profit of 12% on the original price. What is the original price?
old = new/multiplier = 11.20/1.12 = £10
Or, a t-shirt is bought for £10 and sold for £11.20. What is the percentage profit?
multiplier = new/old = 11.2/10 = 1.12
percentage = multiplier x 100 = 1.12 x 100 = 112% <-- so the new is 112% of the old, which is a profit of 112 - 100 = 12% (as the old value is always 100% of the price)
Decrease in price:
If the old price is decreased to the new price
A t-shirt is on sale. The original price is £15, there is 20% off in the sale. How much does the t-shirt cost?
Old = £15
New = ?
Multiplier = the new is going to be 100% - 20% = 80% of the old. So the multiplier is 80/100 = 0.8
new = old x multiplier = 15 x 0.8 = £12
The question may also be asked as:
A t-shirt costs £12 in a 20% off sale. What is the original cost of the t-shirt?
old = new/multiplier = 12/0.8 = £15
Or, a t-shirt in a sale costs £12, the original price is £15. What percentage has been taken from the original price?
multiplier = new/old = 12/15 = 0.8
percentage = 0.8 x 100 = 80% <-- so the new price is 80% of the old price, which gives a percentage change of 80 - 100 = -20%, or a decrease of 20%.
So, there is 20% off in the sale.
In questions like this, you must set out your answer clearly (which makes it easier for the marker to give you marks).
One way of doing this is writing sentences such as:
_____ in the hormonal response, compared to ______ in the nervous response.
Often the mark scheme requires adjectives about both systems for each mark (like one being slow and the other being fast, not just that one is slow).
The main differences in these two systems lie in:
- Signal type
- Response: type, speed, duration
- Effector (what is carrying out the response)
So you could write something like:
Chemical signals carried by the bloodstream cause a response in the hormonal system. Whereas electrical signals carried by nerve cells and chemical signals between nerve cells cause a response in the nervous system.
(This covers signal type and transmission)
The response tends to occur much faster in the nervous system, but may last for a shorter period of time. In the hormonal system the response tends to be slower (as the chemical must be carried in the bloodstream to the target) and lasts for a longer period of time.
(This covers response speed and duration)
The nervous system causes effectors such as glands and muscles to secrete or contract respectively. The hormonal system causes a chemical change in specific target cells.
(This covers response type and effector)