Maths Detective: Formula Challenge

What’s inside

Choose the correct answer in each square to master formula rearrangement, substitution and factorisation.

1. Make x the subject of the formula y = x + 7. (Isolate x by undoing the addition.)
   x = 7 - y · x = y + 7 · x = y - 7 · x = y/7
2. Make x the subject of the formula y = 4x. (Use the inverse operation to isolate x.)
   x = 4/y · x = 4y · x = y - 4 · x = y/4
3. Make a the subject of the formula P = 2a + 6. (Subtract 6 first, then divide by 2.)
   a = (P + 6)/2 · a = (P - 6)/2 · a = 2P - 6 · a = P/2 + 6
4. Make x the subject of the formula y = 3x - 5. (Undo subtraction before dividing by 3.)
   x = (y + 5)/3 · x = (y - 5)/3 · x = 3y + 5 · x = y/3 - 5
5. Evaluate 2a + 3b when a = 4 and b = 5. (Substitute the values and follow the order of operations.)
   19 · 23 · 26 · 40
6. Evaluate x² + 2y when x = 3 and y = 4. (Remember that x² means x multiplied by itself.)
   13 · 17 · 25 · 49
7. The formula for the area of a triangle is A = 1/2 bh. Find A when b = 10 cm and h = 6 cm. (Substitute the base and height into the formula.)
   16 cm² · 20 cm² · 30 cm² · 60 cm²
8. The formula is v = u + at. Find v when u = 5, a = 3 and t = 4. (Substitute all three values into the formula.)
   12 · 17 · 20 · 32
9. Make h the subject of the formula V = lwh. (Divide both sides by lw to isolate h.)
   h = lw/V · h = V/(lw) · h = V/l + w · h = Vlw
10. Make x the subject of the formula y = (x - 4)/3. (Multiply both sides by 3, then add 4.)
    x = (y + 4)/3 · x = 3y + 4 · x = 3y - 4 · x = y/3 + 4
11. Make r the subject of the formula C = 2πr. (Divide both sides by 2π.)
    r = 2π/C · r = 2πC · r = C - 2π · r = C/(2π)
12. The formula is y = 2x + 3. Find y when x = 5. (Substitute x = 5 and calculate carefully.)
    10 · 13 · 16 · 25
13. The formula is A = πr². Find A when r = 2, using π = 3.14. (Square the radius before multiplying by π.)
    3.14 · 6.28 · 12.56 · 25.12
14. Factorise 6x + 12 fully. (Take out the highest common factor.)
    3(2x + 12) · 6(x + 2) · 6(x + 12) · 6x(1 + 2)
15. Factorise x² + 7x + 12 fully. (Find two numbers whose product is 12 and whose sum is 7.)
    (x + 2)(x + 6) · (x + 3)(x + 4) · (x - 3)(x - 4) · x(x + 7) + 12