Re-arranging Formulae

Question 0

Make y the subject of the formula:

w = 1 - y /2

Answer 0

1) you need to get y on its own
2) multiply both sides by 2 (2w=1-y)
3) add y to both sides (2w + y = 1)
4) subtract 2w from both sides
y = 1 - 2w

Question 1

Make x the subject of the formula:

y = 4 + b x

Answer 1

1) you need to get x on its own
2) subtract 4 from both sides (y-4=bx)
3) divide both sides by b and write x on the left hand side ( x = y - 4 /b)

Question 2

z = 4 ( 2 - x ) /7

Answer 2

x = 8 - 7z /4

Question 3

a + b = 2 /4 - 3y

Answer 3

y = 4/3 - 2 /3 ( a + b)

OR

4 ( a + b ) - 2 /3 ( a + b )

Question 4

Make w the subject of the formula:

2k = 12 - (sqr) w - 2

Answer 4

Make (sqr) w-2 the subject
After squaring both sides make e the subject:
w = [(12 - 2k) squared] + 2

Question 5

Make z the subject of the formula:

t = 1 - 3[(z + 1) squared]

Answer 5

Make [(z + 1) squared] the subject
After square rooting both sides, make z the subjects of the formula:
[(1- t /3) sqr] - 1

Question 6

Make a the subject of the formula:

x(a + 1) = 3 (1 - 2a)

Answer 6

1) expand the brackets by multiplying:
ax + x = 3 - 6a
2) rearrange the formula so all a’s are on one side:
ax + 6a = 3 - x
3) factorise the left hand side and rearrange to get a on its own:
a(x + 6) = 3 - x
Answer: a = 3 - x /x + 6

Question 7

Six steps applied to rearranging formulas

Answer 7

1) get rid of any square root signs by squaring both sides
2) get everything off the bottom by cross-multiplying up to every other term
3) multiply out any brackets
4) collect all subject terms on one side of the ‘=’ and all the non subject terms on the other. Remember to reverse +/- sign of any term that crosses the ‘=’
5) combine together the like terms on each side of the equation and reduce it to the form ‘ax = b’ a and b are the bunches of letters that don’t include the subject
6) slide a under b to give the subject answer (cancel if possible)