UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, DC 20549

FORM 10-K

(Mark One)

For the fiscal year ended December 31, 2012

or

For the transition period from              to             

Commission file number of issuing entity: 333-164557-01

Commission file number of depositor: 333-164557

SLC STUDENT LOAN TRUST 2010-1

(Exact name of issuing entity as specified in its charter)

SLC STUDENT LOAN RECEIVABLES I, INC.

(Exact name of depositor as specified in its charter)

THE STUDENT LOAN CORPORATION

(Exact name of sponsor as specified in its charter)

Registrant’s telephone number, including area code: (469) 220-4928

Securities registered pursuant to Section 12(b) of the Act: NONE.

Securities registered pursuant to Section 12(g) of the Act: NONE.

Indicate by check mark if the registrant is a well-known seasoned issuer, as defined in Rule 405 of the Securities Act.    Yes  ¨    No  x

Indicate by check mark if the registrant is not required to file reports pursuant to Section 13 or Section 15(d) of the Act.    Yes  ¨    No  x

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 of 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  ¨

Indicate by check mark whether the registrant has submitted electronically and posted on its corporate Web site, if any, every Interactive Data File required to be submitted and posted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit and post such files).    Yes  ¨    No  ¨

Indicate by check mark if disclosure of delinquent filers pursuant to Item 405 of Regulation S-K (§229.405 of this chapter) is not contained herein, and will not be contained, to the best of registrant’s knowledge, in definitive proxy or information statements incorporated by reference in Part III of this Form 10-K or any amendment to this Form 10-K.  x

Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, or a smaller reporting company. See the definitions of “large accelerated filer,” “accelerated filer” and “smaller reporting company” in Rule 12b-2 of the Exchange Act:

Indicate by check mark whether the registrant is a shell company (as defined in Rule 12b-2 of the Act).    Yes  ¨    No  x

State the aggregate market value of the voting and non-voting common equity held by non-affiliates computed by reference to the price at which the common equity was last sold, or the average bid and asked prices of such common equity, as of the last business day of the registrant’s most recently completed second fiscal quarter.

REGISTRANT HAS NO VOTING OR NON-VOTING COMMON EQUITY OUTSTANDING HELD BY NON-AFFILIATES.

Indicate the number of shares outstanding of each of the registrant’s classes of common stock, as of December 31, 2012.

NOT APPLICABLE.

List hereunder the following documents if incorporated by reference and the Part of the Form 10-K (e.g., Part I, Part II, etc.) into which the document is incorporated: (1) Any annual report to security holders; (2) Any proxy or information statement; and (3) Any prospectus filed pursuant to Rule 424(b) or (c) under the Securities Act of 1933. The listed documents should be clearly described for identification purposes (e.g., annual report to security holders).

NOT APPLICABLE.

PART I

The following Items have been omitted in accordance with General Instruction J to Form 10-K:

Item 1. Business.

Item 1A. Risk Factors.

Item 2. Properties.

Item 3. Legal Proceedings.

None.

Not applicable.

The following substitute information is provided in accordance with General Instruction J to Form 10-K:

Item 1112(b) of Regulation AB. Significant Obligors of Pool Assets.

No single obligor represents 10% or more of the asset pool held by SLC Student Loan Trust 2010-1 (the “Trust”).

Item 1114(b)(2) of Regulation AB. Credit Enhancement and Other Support, Except for Certain Derivatives Instruments.

No entity or group of affiliated entities provides any external credit enhancement or other support with respect to either payment on the pool assets held by the Trust or payments on the notes (the “Notes”) or the certificate (the “Certificate”) issued by the Trust.

Item 1115(b) of Regulation AB. Certain Derivatives Instruments (Financial Information).

No entity or group of affiliated entities provides any external derivative instruments to either payment on the pool assets held by the Trust or payments on the Notes or the Certificate.

Item 1117 of Regulation AB. Legal Proceedings.

There are no legal proceedings that would be material to investors that are pending against the depositor, the issuing entity or, to the knowledge of the registrant, the sponsor, Deutsche Bank Trust Company Americas, Citibank, N.A. or Sallie Mae, Inc., nor does the registrant know of any such proceeding contemplated by any governmental authorities.

PART II

The following Items have been omitted in accordance with General Instruction J to Form 10-K:

Item 5. Market for Registrant’s Common Equity, Related Stockholder Matters and Issuer Purchases of Equity Securities.

Item 6. Selected Financial Data.

Item 7. Management’s Discussion and Analysis of Financial Condition and Results of Operations.

Item 7A. Quantitative and Qualitative Disclosures About Market Risk.

Item 8. Financial Statements and Supplementary Data.

Item 9. Changes in and Disagreements with Accountants on Accounting and Financial Disclosure.

Item 9A. Controls and Procedures.

Item 9B. Other Information.

Nothing to report.

PART III

The following Items have been omitted in accordance with General Instruction J to Form 10-K:

Item 10. Directors, Executive Officers and Corporate Governance.

Item 11. Executive Compensation.

Item 12. Security Ownership of Certain Beneficial Owners and Management and Related Stockholder Matters.

Item 13. Certain Relationships and Related Transactions, and Director Independence.

Item 14. Principal Accountant Fees and Services.

The following substitute information is provided in accordance with General Instruction J to Form 10-K:

Item 1119 of Regulation AB. Affiliations and Certain Relationships and Related Transactions.

The depositor, SLC Student Loan Receivables I, Inc., is a wholly-owned, special-purpose subsidiary of Citibank, N.A., which is the eligible lender trustee. There are no business relationships, agreements, arrangements, transactions or understandings entered into outside the ordinary course of business or on terms other than those that would be obtained in an arm’s length transaction with an unrelated third party that are material to noteholders other than as described in the prospectus supplement and the accompanying base prospectus (previously filed with the Securities and Exchange Commission on July 6, 2010 pursuant to Rule 424, file number 333-164557-01) between or among the sponsor and the issuing entity and any other principal party.

Item 1122 of Regulation AB. Compliance with Applicable Servicing Criteria.

The reports required by Item 1122(a) and (b) of, or relating to, all parties determined by the registrant to be participating in the servicing function with respect to the issuing entity are attached to this Form 10-K as Exhibits 33.1, 33.2, 33.3, 34.1, 34.2 and 34.3.

Item 1123 of Regulation AB. Servicing Compliance Statement.

The statements required by Item 1123 are attached to this Form 10-K as Exhibits 35.1 and 35.2.

PART IV

Item 15. Exhibits and Financial Statement Schedules.

1. Not applicable.

2. Not applicable.

3. See Item 15(b) below.

SIGNATURES

Pursuant to the requirements of Section 13 or 15(d) 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.

SUPPLEMENTAL INFORMATION TO BE FURNISHED WITH REPORTS FILED PURSUANT TO SECTION 15(d) OF THE ACT BY REGISTRANTS WHICH HAVE NOT REGISTERED SECURITIES PURSUANT TO SECTION 12 OF THE ACT.

No annual report to security holders, proxy statement, form of proxy or other proxy soliciting material has been sent to security holders or is anticipated to be furnished to security holders subsequent to the filing of this annual report on Form 10-K.

INDEX TO EXHIBITS