Printable · GCSE Foundation · ages 14-16

Rearranging formulae worksheet — GCSE Foundation

Fifteen questions on "rearranging formulae" — DfE statement A5. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Rearranging formulae worksheet — GCSE Foundation

Maths · GCSE Foundation · A5 · Rearranging formulae · 15 questions

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1.Make x the subject of the formula y = 2x − 9.
y = 2x − 9
(a)x = (y + 9) / 2
(b)x = (y − 9) / 2
(c)x = 2(y + 9)
(d)x = y / 2 + 9
2.Make x the subject of the formula y = 5x + 3.
y = 5x + 3
(a)x = (y + 3)/5
(b)x = (y − 3)/5
(c)x = y/5 − 3
(d)x = 5(y − 3)
3.Make x the subject of the formula y = 3(x + 2).
(a)x = (y − 2)/3
(b)x = y/3 − 2
(c)x = 3y − 2
(d)x = y/3 + 2
4.Make x the subject of the formula y = 4x − 3.
y = 4x − 3
(a)x = 4(y + 3)
(b)x = y/4 + 3
(c)x = (y − 3)/4
(d)x = (y + 3)/4
5.Make x the subject of the formula y = (x − 4)/5.
(a)x = 5(y + 4)
(b)x = 5y − 4
(c)x = y/5 + 4
(d)x = 5y + 4
6.Make c the subject of the formula k = 6c.
(a)c = 6k
(b)c = k/6
(c)c = k − 6
(d)c = 6 − k
7.Make p the subject of the formula n = p/3.
(a)p = n/3
(b)p = 3n
(c)p = 3/n
(d)p = n − 3
8.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.
(a)4.6
(b)7.4
(c)90
(d)6
9.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.
(a)h = Vlw
(b)h = V − lw
(c)h = V / (lw)
(d)h = lw / V
10.Make m the subject of the formula w = m − 8.
(a)m = 8 − w
(b)m = w + 8
(c)m = w/8
(d)m = w − 8
11.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.
(a)r = A/π
(b)r = √A/π
(c)r = √(A/π)
(d)r = (A/π)²
12.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.
(a)30 m
(b)11 m
(c)22 m
(d)38 m
13.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.
y = 3x − 8
(a)x = 3(y + 8)
(b)x = (y − 8) / 3
(c)x = y + 8 / 3
(d)x = (y + 8) / 3
14.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.
(a)9 m
(b)18 m
(c)37 m
(d)16 m
15.Make x the subject of the formula y = x + 7.
y = x + 7
(a)x = y + 7
(b)x = y − 7
(c)x = 7 − y
(d)x = 7y

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