Nobody marks your checker but you. Every mathematician you will ever meet runs one — a quiet second pass that catches errors before they matter — and the earlier you build yours, the sooner tests stop being scary. Four habits make up the whole machine.
Substitute back — into everything
Solved an equation? The equation itself will referee. Believe solves ? Substitute: — a true statement, and the equation has certified your answer, no key required. The same reflex checks a model: feed your tide equation an hour you did not use to build it, and see whether the depth it predicts matches the data. Evaluating at a chosen input is exactly the skill Function Notation hands you, and it costs less than a minute.
Estimate first, compare after
Before solving, write down a rough expected size — the reflex Estimation Duels trains. A balance compounding at 5% for ten years should grow by roughly half, not fifteen-fold; if the formula hands you from a deposit, one of you is wrong, and now you know to look. This check only works if the estimate came before the answer did.
Check the units
Units are a free error detector. If an interest answer arrives in years when the question asked for dollars, something upstream broke — and the units caught it without you rereading a single step. Carry them through every line, as Showing Your Thinking insists.
Ask whether the graph agrees with its own story
After modelling the Ferris wheel, put the numbers on a two-second sketch. An axis of 6 m with an amplitude of 5 m means the seat dips to 1 m above the ground — sensible for a loading platform. Had the amplitude come out as 7 m, the seat would swing a metre underground, and the sketch objects instantly. A model that disagrees with its own situation is the cheapest alarm in Sinusoidal Functions — and the question behind it is the one What Makes a Model Good asks of every model: does it tell the truth about the world it claims to describe?