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How to check your answers on a math test
Most points lost on math tests aren't from not knowing how. They're a dropped minus sign, a misread question, or an answer to something nobody asked. You can catch a lot of those in the last few minutes, if you check the right way.
Leave time for it
Plan to stop with five minutes left, or about a tenth of the time. As you go, put a small dot next to any answer you weren't sure of. Those are the ones you check first.
Don't just reread your working
When you reread your own lines, you see what you meant to write, not what you wrote. That's why the same mistake survives three rereads. Check the answer a different way instead.
1. Plug it back in
Put your answer into the original equation, not your last line. Solved 2x − 7 = 11 and got x = 9? Check: 2(9) − 7 = 11. It works. Got x = 2? 2(2) − 7 = −3, not 11, so something's off.
- Systems: plug both values into both equations.
- Factoring: multiply your factors back out.
- Multiple choice: you can plug the choices in, too. It's a fair way to check, and sometimes faster than solving.
2. Estimate
Round the numbers and get a rough answer in your head. 48 × 21 is about 50 × 20 = 1,000, so 1,008 looks right and 10,080 doesn't. On multiple choice, estimating often rules out two choices straight away.
3. Ask if it makes sense
- Lengths, prices, counts and times can't be negative.
- A probability is between 0 and 1.
- A discount makes the price smaller.
- The angles of a triangle add up to 180°.
4. Check the units
Area is in square units, volume in cubic, speed in distance per time. If the question gives minutes and you answered in hours, or it wants square feet and you wrote feet, a step got lost or the answer needs converting.
5. Reread the question, last
Read the final sentence again and compare it to what you wrote. This catches the costly ones:
- It asked for 2x, or x + 1, and you gave x.
- It said "round to the nearest tenth" or "leave in terms of π".
- It had two parts and you answered one.
- It asked for the width, and you found the length.
If a check fails
Don't erase everything. Go through your working one line at a time and ask "does this follow from the line above?" Look hardest at signs when a term moves across the equals sign, at distributing a minus, and at fractions. Fix the first wrong line and redo from there. If time's nearly up, fix what you can and leave your working visible: partial credit usually needs it.
Practise checking before the test
Checking is a habit, and the test is a bad place to start one. Do it on every homework problem for a week and it becomes automatic. More on that in how to check your math homework.
Where theoremEd fits
While you practise, theoremEd checks your working the same way a teacher would: it finds the first line that went wrong and asks you about it, without telling you the answer. Free to try, no account, in Chrome, on a Mac, or on the homepage.