Title: InkMaths / Spot the error
On every note of this deck, unless a note says otherwise:
Footer: Continue on inkmaths.co.uk · © 2026 InkMaths. All rights reserved.

Front: SPOT THE ERROR
Say what is wrong with this claim:
If sin x = 0.5 then x = 30° is the complete answer.
Back: Sine repeats: in 0° to 360° alone, x = 30° and x = 150° both work, and the general solution adds full turns to each. Always read the given interval and use the sine curve or CAST to find every solution inside it.

Front: SPOT THE ERROR
Say what is wrong with this claim:
In (x² + 5x)/x², the x² terms cancel to leave 1 + 5x.
Back: Only common factors of the whole numerator and denominator cancel. Factorise first: x(x + 5)/x² = (x + 5)/x, which is 1 + 5/x. Cancelling terms that are added, rather than factors that are multiplied, is the single most common algebra slip.

Front: SPOT THE ERROR
Say what is wrong with this claim:
√(a² + b²) simplifies to a + b.
Back: Square roots do not distribute over addition. Try a = 3, b = 4: the left side is 5, the right side is 7. Only √(a²b²) = ab behaves like that, because the inside is a product.

Front: SPOT THE ERROR
Say what is wrong with this claim:
(x + 3)² = x² + 9.
Back: Squaring a sum needs the cross term: (x + 3)² = x² + 6x + 9. The slip drops 2 × x × 3. Expanding the bracket term by term makes the middle term impossible to lose.

Front: SPOT THE ERROR
Say what is wrong with this claim:
ln(a)/ln(b) simplifies to ln(a/b).
Back: The quotient law is ln a − ln b = ln(a/b): a difference of logs, not a quotient of logs. ln(a)/ln(b) is the change-of-base form of log base b of a, and it does not simplify further.

Front: SPOT THE ERROR
Say what is wrong with this claim:
Dividing both sides of x² = 4x by x gives x = 4, done.
Back: Dividing by x silently assumes x ≠ 0 and throws away the solution x = 0. Move everything to one side and factorise: x(x − 4) = 0, so x = 0 or x = 4.