Several major new contracts helped BDM International Inc. post record revenues, net income and earnings per share in the first quarter.

Earnings rose 38 percent to $922,000 (42 cents a share) on revenues of $24.3 million from $668,000 (30 cents) on revenues of $19.7 million during the first quarter of 1981.

Based in McLean, BDM is a diversified professional and technical services firm.

Sales at Scope Inc., a diversified electronics and technology company based in Reston, were flat for the first quarter, but the company posted a loss of $291,000 compared with profits of $487,000 (40 cents a share) last year.

Scope's figures indicate a continuation of the disappointing results the company reported last year, which officials attributed to the recession. They also cited first-quarter costs associated with Scope's decision to spin off its two largest subsidiaries, Repco and National Controls. Because of the spin-offs, Scope will not pay a third-quarter cash dividend.

Revenues at LogEtronics Inc. jumped 53 percent this quarter from the first quarter of 1981, and company officials attributed this to the acquisition of Dunn Systems Inc. LogE had revenues of $11.4 million compared with $7.4 million last year.

Earnings of the Springfield firm in the quarter were $213,000 (16 cents a share) compared with $1.2 million ($1.01) the year before. Results from 1981, however, included nearly a million dollars (81 cents) of a reversal of deferred income taxes and foreign currency translation gains.

Increases in noninterest income and in earnings from short-term investments gave Financial General Bankshares Inc. a 3.2 percent gain in income for the first quarter of 1982. The D.C.-based bank holding company had profits of $5.07 million (69 cents a share) compared with $4.9 million (68 cents) during 1981.

Assets increased to $2.4 billion, deposits were up to $1.9 billion, and loans increased to $1.3 billion.