The Federal Home Loan Mortgage Corp. yesterday reported an 18.2 percent drop in first-quarter earnings, down to $45 million from $55 million in the year-ago period.

The corporation, better known as Freddie Mac, became a taxpayer for the first time on Jan. 1, 1985. Its new status is reflected in the reduced first-quarter profits, which worked out to $34.86 per common share.

Freddie Mac's pre-tax earnings for the quarter were $83 million, which means that the company would have done 51 percent better than it did in the year-ago quarter had it not been subject to taxation.

On the other hand, if Freddie Mac had paid taxes in 1984 at a rate comparable to that paid in the three months of this year, earnings per share in the year-ago quarter would have amounted to $19.80.

The impact of taxation is "expected to have a continuing significant effect on the corporation's future earnings," said Kenneth J. Thygerson, Freddie Mac president and chief executive officer.

Freddie Mac, once a government-backed agency, is now a publicly chartered corporation whose business is to increase the available pool of mortgage money for home loans.

* Geico Corp., also known as the Government Employees Insurance Corp., yesterday reported first-quarter earnings of $31 million, a 4.6 percent drop from profits of $32.5 million in the same period last year.

Earnings per share were $1.04 for the quarter, compared with $1.20 in the year-ago quarter.

In an unusually blunt corporate statement, Geico Chairman Jack Byrne said that his company's lower earnings were the results of its "failure to learn yet how to manage . . . growth; a greater than anticipated uptick in both accident frequency and the cost of claim settlements; and allowing our prices to fall somewhat behind" rising costs.

* Reston-based Scope Inc., an industrial products and defense contracting firm, said yesterday that it lost $140,000 (12 cents a share) in the first quarter of 1985, compared with a loss of $146,000 (12 cents) in the same period last year. Sales for the quarter rose 31.7 percent to $3.5 million from $2.7 million in the year-ago period. The drag on net income is caused by a slowdown in capital spending by businesses, which has substantially affected the performance of Scope's Industrial Products Division, Scope officials said yesterday.

* Systematics General Corp., a computer products company in Sterling, Va., reported a 5 percent increase in the first quarter, up to $401,000 (15 cents a share) from $382,000 (14 cents) in the first quarter of 1984. The company's sales for the quarter were $7.2 million, compared with $6.9 million in the same period last year.