Title: InkMaths / Spot the error
On every note of this deck, unless a note says otherwise:
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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 both x = 30° and x = 150° work, and full turns can be added to either. Read the interval the question gives, then use the sine curve or CAST to collect every solution inside it. One answer where four are wanted is a three-mark loss.

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. A product does come apart, but as √(a²b²) = |ab|: with a = 1, b = −1 the root is 1 and not −1.

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, and the slip drops 2 × x × 3. Write the bracket out twice and multiply term by term. The middle term then becomes 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 wants a difference of logs, not a quotient of them. ln a − ln b = ln(a/b). What ln(a)/ln(b) actually equals is log base b of a, the change-of-base form, and it goes no 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.