Change the Vowel

The following puzzle contains a clue within each clue. The answer, of course, fits the clue, but each answer is also one of the words within the clue with its vowel sound changed. For instance, the clue “the distance from the top of your hat to the sole of your shoes” contains the word hat, and if you change the vowel sound from a short a to a long i, you get height, which fits the description.

As always, there’s a catch. Every answer to the clues below is a mathy word.

1. The number of permutations of three different colored socks.
   
2. This value is the same for 3 + 1 and 2 + 2.
3. Do this with two odd numbers and you’ll get an even number.
4. Three hours before noon.
5. You may fail to correctly expand (a + b)(c + d) if you don’t remember this mnemonic.
6. One represents this fractional portion of toes on the hoof of a deer.
7. The last element of a data set arranged in descending order.
8. The measure of central tendency made from the most common data points.
9. The number of contestants ahead of third place if there’s a tie for first place.
10. If the leader is forced to drop out of a race, the runner-up takes over this place.
11. The square root is needed to calculate the length of the hypotenuse in this type of triangle.
12. The graph of the declination of the Sun during a year can be approximated by this type of curve.

Answers

1. six
   
2. sum
3. add
4. nine
5. FOIL
6. half
7. least
8. mode
9. two
10. first
11. right
12. sine