<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


[X]          QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(D) OF THE
                        SECURITIES EXCHANGE ACT OF 1934

For the Quarterly Period Ended        March 31, 1998
                                ---------------------------

                                       OR

[ ]          TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934


For the transition period from                 to
                               ----------------   ------------------


Commission file number       0-21682
                       -------------------


                                  SPARTA, Inc.
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)


                    Delaware                                     63-0775889
        (State or other jurisdiction of                       (I.R.S. Employer)
        incorporation or organization)


      23041 Avenida de la Carlota, Suite 325, Laguna Hills, CA 92653-1595
--------------------------------------------------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)


                                 (949) 768-8161
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)


                                 Not Applicable
--------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act or 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports) and (2) has been subject to such filing
requirements for the past 90 days.

Yes  X         No
    ---

As of April 5, 1998, the registrant had 5,733,914 shares of common stock, $.01
par value per share, issued and outstanding.



<PAGE>   2

                                  SPARTA, Inc.

              QUARTERLY REPORT FOR THE PERIOD ENDED MARCH 31, 1998

                                      INDEX


PART I  FINANCIAL STATEMENTS

ITEM 1  Quarterly Financial Statements

        Statements of Income for the Three Months Ended March 31, 1998 and March
        31, 1997 (Unaudited)

        Balance Sheets as of March 31, 1998 and December 31, 1997 (Unaudited)

        Statement of Cash Flows for the Three Months Ended March 31, 1998 and
        March 31, 1997 (Unaudited)

        Notes to Consolidated Financial Statements (Unaudited)

ITEM 2  Management's Discussion and Analysis of Financial Condition and
        Results of Operations

PART II OTHER INFORMATION

SIGNATURE

EXHIBIT 11  Computations of Earnings per Share



<PAGE>   3

ITEM 1.  FINANCIAL STATEMENTS
-----------------------------

                                  SPARTA, INC.

                        CONSOLIDATED STATEMENT OF INCOME
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                      THREE MONTHS ENDED MARCH 31
                                     ------------------------------
                                        1998               1997
                                     -----------        -----------
<S>                                  <C>                <C>
SALES                                $22,944,000        $18,834,000
                                     -----------        -----------

COSTS AND EXPENSES:

  Labor costs and related
    benefits                          12,441,000         10,176,000

  Subcontractor & other costs          5,865,000          4,526,000

  Facility costs                       1,813,000          1,872,000

  Travel and other                       640,000            802,000

  Interest expense, net                   82,000             35,000
                                     -----------        -----------

                                      20,839,000         17,411,000
                                     -----------        -----------

INCOME BEFORE PROVISION FOR
  TAXES ON INCOME                      2,103,000          1,423,000

PROVISION FOR TAXES ON INCOME            883,000            598,000
                                     -----------        -----------

NET INCOME                           $ 1,220,000        $   825,000
                                     ===========        ===========

BASIC EARNINGS PER SHARE             $      0.14        $      0.09
                                     ===========        ===========

DILUTED EARNINGS PER SHARE           $      0.13        $      0.08
                                     ===========        ===========
</TABLE>


* EARNINGS PER SHARE AMOUNTS PRESENTED FOR PRIOR YEARS HAVE BEEN RESTATED IN
  ACCORDANCE WITH STATEMENT OF FINANCIAL ACCOUNTING STANDARDS NO. 128, "EARNINGS
  PER SHARE".



    The accompanying notes are an integral part of the financial statements
<PAGE>   4
                                  SPARTA, INC.

                         CONSOLIDATED BALANCE STATEMENT
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                            MARCH             DECEMBER 31,
                                                            1998                  1997
                                                         ------------         ------------
                                                         (Unaudited)            (Audited)
<S>                                                      <C>                  <C>
ASSETS

CURRENT ASSETS
  Cash                                                   $     86,000         $    198,000
  Accounts receivable                                      24,026,000           23,557,000
  Prepaid expenses                                            669,000              448,000
                                                         ------------         ------------
    TOTAL CURRENT ASSETS                                   24,781,000           24,203,000

  Equipment and improvements, net                           7,775,000            7,321,000
  Other assets                                              1,544,000            1,685,000
                                                         ------------         ------------
    TOTAL ASSETS                                         $ 34,100,000         $ 33,209,000
                                                         ============         ============


LIABILITIES AND STOCKHOLDERS' EQUITY
CURRENT LIABILITIES
  Accrued compensation                                   $  2,632,000         $  5,723,000
  Accounts payable and other accrued expenses               1,315,000            3,005,000
  Current portion of notes payable                            461,000              477,000
  Income tax payable                                          821,000              199,000
  Deferred income taxes                                     1,394,000            2,446,000
                                                         ------------         ------------
    TOTAL CURRENT LIABILITIES                               6,623,000           11,850,000

NOTES PAYABLE                                               5,342,000            2,658,000
SUBORDINATED NOTES PAYABLE                                    525,000              646,000
DEFERRED INCOME TAXES                                       2,645,000            1,677,000

Commitments and contingencies

REDEEMABLE PREFERRED STOCK
  Preferred stock, $.01 par value; 2,000,000
    shares authorized; 569,039 and 569,039 shares
    issued and outstanding                                  4,376,000            3,926,000
STOCKHOLDERS' EQUITY
  Common stock, $.01 par value, 25,000,000 shares
    authorized; 13,383,529 and 13,070,700 shares
    issued                                                    134,000              131,000
  Additional paid-in capital                               28,539,000           26,340,000
  Retained earnings                                        25,923,000           25,152,000
  Treasury stock                                          (40,007,000)         (39,171,000)
                                                         ------------         ------------
    TOTAL STOCKHOLDERS' EQUITY                             14,589,000           12,452,000
                                                         ------------         ------------

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY               $ 34,100,000         $ 33,209,000
                                                         ============         ============
</TABLE>



    The accompanying notes are an integral part of the financial statements
<PAGE>   5
                                  SPARTA, INC.

                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                             THREE MONTHS ENDED MARCH 31
                                                            -------------------------------
                                                               1998                1997
                                                            -----------         -----------
<S>                                                         <C>                 <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net Income                                                $ 1,220,000         $   825,000
  Adjustments to reconcile net income to net
    cash provided by operating activities:
      Depreciation and amortization                             370,000             290,000
      Loss on sale of equipment                                   1,000              86,000
      Employee compensation paid in stock                     1,467,000             905,000
      Changes in assets and liabilities:
        Accounts receivable                                    (470,000)          2,614,000
        Prepaid expenses                                       (221,000)           (138,000)
        Other assets                                            141,000             (96,000)
        Accrued compensation                                 (3,091,000)         (1,658,000)
        Accounts payable and other accrued expense           (1,690,000)         (1,238,000)
        Income taxes payable                                    821,000             362,000
        Deferred income taxes                                  (283,000)           (283,000)
      Tax benefit relating to stock plan                        115,000               8,000
                                                            -----------         -----------
          NET CASH PROVIDED BY OPERATING ACTIVITIES          (1,620,000)          1,677,000
                                                            -----------         -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
    Capital expenditures                                       (825,000)           (624,000)
    Cost of acquisition, net of cash acquired                         0                   0
                                                            -----------         -----------
          NET CASH USED IN INVESTING ACTIVITIES                (825,000)           (624,000)
                                                            -----------         -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Proceeds from issuance of stock                               620,000             511,000
  Cash purchases of treasury stock                             (425,000)         (1,544,000)
  Net (repayments) proceeds line-of-credit agreement          2,685,000            (173,000)
  Principal payments on debt                                   (548,000)            171,000
                                                            -----------         -----------
          NET CASH USED IN FINANCING ACTIVITIES               2,332,000          (1,035,000)
                                                            -----------         -----------

NET DECREASE IN CASH                                           (112,000)             18,000
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                198,000             151,000
                                                            -----------         -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                  $    86,000         $   169,000
                                                            ===========         ===========

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:
  Cash paid during the period for:
    Interest                                                $    83,000         $    36,000
                                                            ===========         ===========
    Income taxes                                            $ 1,251,000         $   524,000
                                                            ===========         ===========
</TABLE>


    The accompanying notes are an integral part of the financial statements
<PAGE>   6

                                  SPARTA, INC.

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)


NOTE A - BASIS OF PRESENTATION

The accompanying financial information has been prepared in accordance with the
instructions to Form 10-Q and therefore does not necessarily include all
information and footnotes necessary for a fair presentation of financial
position, results of operations and cash flows in conformity with generally
accepted accounting principles.

The Company's fiscal year is the 52 or 53 week period ending on the Friday
closest to December 31. The Company's last fiscal year ended on January 2, 1998;
and, its first quarter ended April 5, 1998 and corresponding first quarter last
year on April 4, 1997. To aid the reader of the financial statements, the year
end has been presented as December 31, 1996 and the quarters and three months
ended March 31, 1997 and March 31, 1998.

In the opinion of management, the unaudited financial information for the
three-month periods ended March 31, 1998 and March 31, 1997 reflects all
adjustments (which include only normal, recurring adjustments) necessary for a
fair presentation thereof.

NOTE B - RECEIVABLES

Unbilled accounts receivable include $1,293,649 of costs incurred on projects
for which the Company has been requested by the customer to begin work under a
new contract or extend work under a present contract, but for which final
contract negotiations or formal contracts or contract modifications have not
been executed at March 31, 1998.

NOTE C - INCOME TAXES

Income taxes for interim periods are computed using the estimated annual
effective rate method.


<PAGE>   7

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS

The Management Discussion and Analysis of Financial Condition and Results of
Operation contains forward-looking statements that involve risks and
uncertainties. The Company's actual results may differ significantly from
projections contained in forward-looking statements. For a more complete
discussion of the factors which could cause such a difference, the Company's
Form 10-K for the year ended December 31, 1997, should be consulted.

The following table sets forth, for the periods indicated, selected financial
results from the Company's continuing operations and audited Financial
Statements.

RESULTS OF OPERATIONS

<TABLE>
<CAPTION>
                                  Three months ended March 31,
                                  ----------------------------
                                     1998           1997
                                  ------------   -------------
<S>                               <C>            <C>
  Sales                           22,944,000     18,834,000
  Gross profit (1)                 2,219,000      1,536,000
  Gross profit as a % of costs         10.71%          8.88%
  Net income (2)                   1,220,000        825,000
  Number of staff                        647            543
</TABLE>


<TABLE>
<CAPTION>
                                                               Balance at
                                                ----------------------------------------
                                                 March 31,    December 31,   March 31,
                                                    1998          1997          1997
                                                -----------   ------------  ------------
<S>                                             <C>            <C>           <C>
  Funded 12 month backlog                        38,400,000    29,900,000    35,100,000
  Total 12 month contract backlog                88,200,000    93,200,000    81,500,000
  Stockholders equity                            14,589,000    12,452,000    10,860,000
  Equity per share (3)                                 2.35          1.89          1.71
  Stock repurchase notes                            986,000     1,123,000     1,901,000
  Line of credit                                  5,343,000     2,658,000       289,000
  Number in days sales in receivables                    97            93            88
  Current ratio                                         3.0           2.1           2.0
</TABLE>

-----------------
(1) The Company defines gross profits as sales less costs and expenses excluding
    interest costs and certain expenses which cannot be billed to its government
    customers.
(2) Prior to adjustments for interest and accretion on stock - See Exhibit 11.
(3) Equity per share based on weighted shares of common stock outstanding for 
    period ending, including weighted shares of preferred stock outstanding.

REVENUES

The Company's contract revenues for the first quarter were up 21.8% from the
corresponding three month period in 1997. Operating profitability for the three
month period ended March 31, 1998 was up 44.5% when compared to the
corresponding period in 1997. Operating profitability as a percent of costs
increased to 10.71% from 8.88% for the corresponding period in 1997, primarily
due to better than expected profits on fixed price contracts and strong award
fees on cost plus award fee contracts. Current profit rates are at historical
levels. Borrowings against the Company's line of credit totaled $5,343,000 as of
the end of the first quarter compared to a borrowing level of $289,000 at the
end of the corresponding period in 1997. The high level of borrowing for the
first quarter is the result of investments in the Company's product initiatives
and expenditures for independent research and development. The Company's current
plan is to scale back these costs after the first quarter.

ANNUALIZED BACKLOG

During the first quarter, the Company had no major new competitive contract
wins, but a few significant sole source contract awards. The only significant
losses in the quarter were bids where the Company was a proposed subcontractor
to

<PAGE>   8

prime contractors: a $10,000,000 share of the China Lake O&M contract bid
where the Company was a proposed subcontractor to AmComp, a $5,000,000 share of
an Army MISSI contract bid where the Company was a proposed subcontractor to
Computer Services Corporation, and a $2,400,000 share of a DARPA Information
Services contract bid where the Company was a proposed subcontractor to SRS.
These losses were all five year programs. Funding increments on existing
contracts were down from the same period last year. The Company received
contract funding of only $15,463,000 in the first quarter as compared to nearly
$21,000,000 in funding received for the same period last year.

Annualized contract backlog decreased 5.4% in the first quarter over backlog
starting the year. Backlog went from $93,200,000 to start the year to
$88,200,000 at the end of the first quarter. The Company plans to submit many
proposals in the next two quarters as the opportunity backlog is strong.

LIQUIDITY AND CAPITAL RESOURCES

The Company's primary sources of liquidity are funds provided by operations and
the bank line of credit. The Company's line of credit limit is $8,000,000, but
is currently being renegotiated with the bank to increase it to $12,000,000. It
is anticipated that the increased amount may be needed to provide funds to
support the Company's investment in its product initiatives and anticipated
growth in 1999. Borrowings under the line of credit at March 31, 1998 totaled
$5,343,000. Days sales outstanding increased to 97 days at March 31, 1998, from
93 days at December 31, 1997, and from 88 days at March 31, 1997. The increase
is primarily due to slower than normal invoicing because of start-up problems
with the Company's new accounting system. The Company continues to actively
monitor receivables with emphasis placed on collection activities. The Company's
debt-to-equity ratio, as defined by the bank, was 0.7 at March 31, 1998 versus
0.8 at December 31, 1997 and 0.6 at March 31, 1997. All capital expenditures
were financed through operating funds and the revolving line of credit. The
Company's cash flow from operations plus borrowing under its line of credit are
expected to provide sufficient funds for the Company's operations, common stock
repurchases, capital expenditures, and future long-term debt requirements.

STOCKHOLDER EQUITY

The Company increased stockholder's equity from $12,452,000 at the end of 1997
to $14,589,000 at March 31, 1998. The Company's strong earnings and net proceeds
from the sale and repurchase of stock have accounted for this increase. The
Company is now repurchasing all the stock from terminating employees and intends
to continue to do so for the rest of the year.

STOCK PURCHASE AGREEMENT

In November, 1994, the Company entered into a Stock Purchase Agreement (the
"Agreement") with Science Applications International Corporation ("SAIC"), under
which SAIC was obligated to buy, during the first year of the Agreement, shares
of the Company's Preferred Stock with an aggregate price of $1,200,000. Under
the Agreement, SAIC also has the option, but not the obligation, to buy
additional shares of Preferred Stock, provided that SAIC's total purchases
during any quarter may not exceed $600,000 and provided further, that the total
number of shares of Preferred Stock purchases during any quarter may not exceed
the total number of shares of Common Stock offered to the Company for repurchase
by the Company's existing stockholders. The purchase price for all shares
purchased under the Agreement by SAIC is equal to the then current Formula Price
applicable to the Company's Common Stock. The Agreement grants SAIC the option
to require the Company to repurchase all of the Preferred Stock held by SAIC at
the Formula Price at time of option exercise. In the event the option is
exercised, the Company may issue SAIC a subordinated note bearing an interest
rate equal to the lesser of prime or 10%. SAIC suspended its purchase of Company
preferred stock in the last quarter of 1996 and has not purchased any stock
since. The total purchase as of March 31, 1998 of $2,400,000 of Company
Preferred Stock represents 9.03% of the Company's total outstanding stock.
Through March 31, 1998 accretion of Preferred Stock was $1,976,000.

EFFECTS OF FEDERAL FUNDING FOR DEFENSE PROGRAMS

The Company continues to have over 90% of its contracts with the Department of
Defense. The Company anticipates little or no effect on its anticipated sales
for 1998 as a result of the outcome of the November, 1998 federal elections for
the Senate and House of Representatives. However, sales in its government
business areas for 1999 and subsequent years could be impacted by this election
and the yet to be resolved federal budget for Government Fiscal Year 1999.


<PAGE>   9

PART II        OTHER INFORMATION

ITEM 1         LEGAL PROCEEDINGS

The Company has no investigations, claims, and lawsuits arising out of its
business, nor any known to be pending.

ITEM 2         CHANGES IN SECURITIES

Not Applicable

ITEM 3         DEFAULTS UPON SENIOR SECURITIES

Not Applicable

ITEM 4         SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

No matters were presented for shareholder vote in the quarter ended March 31,
1998. The Company's Annual Meeting will be held on May 1, 1998 at which time
proxies and shareholders present will vote on the proposed 1997 Stock Plan, the
Amended and Restated Certificate of Incorporation, the Directors and the
continuation of Price Waterhouse as auditor.

ITEM 5         OTHER MATERIALLY IMPORTANT EVENTS

Not Applicable

ITEM 6         EXHIBITS AND REPORTS ON FORM 8-K

No report(s) on Form 8-K were filed by the Company during the fiscal quarter for
which this report is filed.


<PAGE>   10

                                    SIGNATURE


Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                           SPARTA, INC.


Date: May 15, 1998                         /s/ B. Warren Knudson
                                           -------------------------------------
                                           B. Warren Knudson
                                           Vice President and Chief
                                           Financial Officer
                                           (Principal Finance and
                                           Accounting Officer)

<PAGE>   11

                                  EXHIBIT INDEX

                                  SPARTA, INC.

                          QUARTER ENDED MARCH 31, 1998

<TABLE>
<CAPTION>

Exhibit                                                                         Sequential
  No.             Description of Exhibits                                        Page No.
-------           -----------------------                                       ----------
<S>               <C>                                                           <C>
   11             Statement re:  Computation of Per Share Earnings

   27             Financial Data Schedule
</TABLE>