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Exam Question Answers

January 2005 C1 OCR MEI

Firstly, it's usually easier to get the variable you want as the subject on the left-hand side, so we're just going to swap the sides around.

⁴⁄₃πr³ = V

Now we're going to get rid of the fraction. You can do this by turning the fraction upside down and carrying it to the other side.

πr³ = ^3V⁄₄

Next, we just need to take the π and take it over to the other side. Remember, it is multiplying the r³, so it will divide when it goes over to the other side.

r³ = ^3V⁄_4π

Finally, as the ³ is only on the r - what we need to have last, we need to get rid of it. So we need to find the cubic root of both sides.

r = ³√(^3V⁄4π)

June 2005 C1 OCR MEI

Similar to the above, we need to get x the subject.
To begin, we're going to get all the x's on one side.

3x + mx = y + 5y
3x + mx = 6y

Next, we're going to factorise the left-hand side.

x(3 + m) = 6y

All we need to do now, is carry the (3 + m) over to the other side. It needs to divide the 6y as it's multiplying the x.

x = ^6y ⁄ _{(3 + m)}

January 2006 C1 OCR MEI

As we want all the C's on the left hand side, we're going to take the C - 4 and take it over to the other side.

P(C - 4) = C
PC - 4P = C

Next we're going to get all the C's on one side.

PC - C = 4P

As we can't have the C's cancelling out, we need to factorise them.

C(1 - P) = 4P Now all we need to do is take the brackets out.

C = ^4P ⁄ _{1 - P}

June 2006 C1 OCR MEI

The first thing to do is get rid of the fraction.

3V = πr²h

Next we're going to collect the factors of r² and take them over to the other side.

3V = r²(πh)
^3V ⁄ _πh = r²

Now all we need to do is get rid of the ² and we can do this by taking the square root of both sides.

ą√^3V ⁄ _πh = r

Remember to put in the ą when you square root something!

January 2007 C1 OCR MEI

First, we're going to get all of the a's over to one side.

2a - af = 7c - 5c

As we need to get a on it's own, we need to get the factors of a to get rid of that f.

a(2 - f) = 2c

Next, we're going to take the brackets over to the other side to complete.

a = ^2c ⁄ _{2 - f}

January 2007 C1 OCR MEI

First we're going to split this equation up so that it looks a lot simpler.

3 × 4 × a³ × a² × b × b²

Remember, if the letter doesn't have a power, just think of it being to the power of 1. When you're multiplying, you have to add the powers together.

12 × a⁵ × b³

To finish, we just need to get rid of those × symbols.

12a⁵b³

June 2007 C1 OCR MEI

As usual, we get rid of the fraction first. You can do that by multiplying both sides by 2.

2s = at²

As both a and t are squared, we're going to square root both sides.

ą√2s = at

All that's left to do now is take away the a from the right-hand side.

ą√^2s ⁄ a = t
t = ą√^2s ⁄ a