Grammar JLPT Level N5 - Lesson 10

In order to make the negative past form of う-Verbs, you will need to change the last kana of the verb into the あ sound kana from the same column (or わ if the original kana was う). After this, the あ sound kana will be followed by ない (or ます), conjugated into their past forms. This will either be なかった (casual), or ませんでした (polite).
For the ませんでした (polite) form, rather than the final kana changing to the あ sound kana from the same column, it will change to the い sound kana from the same column.
The negative past form is used to convey that something 'did not happen', or 'was not'.

• 私(わたし)は公園(こうえん)で遊(あそ)ばなかった。
  I did not play at the park.
• あなたの車(くるま)は洗(あら)わなかった。
  I did not wash your car.
• そこに置(お)きませんでした。
  I did not place it there.
• そこには本(ほん)がありませんでした。
  The book was not over there.

A semi-polite form may also be used. This is constructed by using なかった, and then simply adding です. This form is not grammatically correct, but is so common that most sources (and native speakers) would consider it correct.

• 彼(かれ)とは話(はな)さなかったです。
  I did not talk with him. (Notice the use of と and は together. Double particle usage is common when presenting a topic in Japanese)

ある is an exception to the regular conjugation rules of う-Verbs. The casual past-negative is not あらなかった, but simply なかった. However, the polite past-negative form conjugates in the same way as would be expected for う-Verbs. ありませんでした.

• 紙(かみ)がなかった。
  There was no paper. (Casual Japanese past tense)
• 紙(かみ)がありませんでした。
  There was no paper. (Formal Japanese past tense)