This document constitutes part of a prospectus covering securities that have been registered under the Securities Act of 1933 SIGMA-ALDRICH CORPORATION INCENTIVE STOCK OPTIONS – AGREEMENT

Exhibit 10 (b)

This document constitutes part of a prospectus covering securities that

have been registered under the Securities Act of 1933

SIGMA-XXXXXXX CORPORATION

2003 LONG-TERM INCENTIVE PLAN (As Amended)

INCENTIVE STOCK OPTIONS – AGREEMENT

The following terms (the “Terms”) outlined in this document (“Agreement”) govern the incentive stock options issued under the Sigma-Xxxxxxx Corporation 2003 Long-Term Incentive Plan, as amended, with respect to incentive stock options granted on or after February 7, 2011:

1. THIS IS TO CERTIFY THAT, in accordance with and subject to all of the terms, provisions and conditions of the Sigma-Xxxxxxx Corporation 2003 Long-Term Incentive Plan, as amended (the “Plan”), approved and adopted by the Board of Directors and shareholders of Sigma-Xxxxxxx Corporation, a Delaware corporation (the “Company”), and in accordance with and subject to the action relating to the Plan from time to time taken and authorized by the committee of directors appointed by the Board of Directors of the Company to administer the Plan (the “Committee”), including the rules from time to time promulgated by said Committee (copies of which are and will be maintained on file at the offices of the Secretary or Assistant Secretaries of the Company, subject to examination by any optionee holding options under the Plan (the “Optionee”), the Company has granted to the Optionee (who on the date of the grant of the option is an employee of the Company or of a subsidiary of the Company) the right and option to purchase from the Company the aggregate number of shares of the Company’s Common Stock, $1.00 par value per share, set forth in the Optionee’s 2003 Long-Term Incentive Plan Stock Option Letter (the “Letter”) at and for the purchase price per share set forth in the Letter, payable at the time of exercise of such option in cash or in the form of stock of the Company previously acquired by the Optionee or a combination thereof. Said option shall be an incentive stock option within the meaning of the Plan and Section 422 of the Internal Revenue Code of 1986, as amended. This Agreement and these Terms completely supersede and replace any prior form of terms, conditions, and agreements with respect to incentive stock options granted under the Plan on and after February 7, 2011.

2. The option granted pursuant to the Letter may be exercised, and the Common Stock may be purchased, by the Optionee as a result of such exercise, only within the period indicated in the Letter and subject to the limitations hereinafter set forth, namely:

(a) Except as provided in Section 2(d) below, no part of the option may be exercised, and none of the optioned shares may be purchased, prior to the date or dates on which such option, or portion thereof, as applicable, becomes vested as set forth in the Letter. Thereafter, all or portions of the option may be exercised and shares may be purchased in the share amounts indicated during the exercise periods stated in the Letter and as set forth herein. Notwithstanding anything in the Plan to the contrary, the Non-Exercise Period referred to in the Plan shall not apply to this option except to the extent specifically so stated in the Letter or in this Agreement.

(b) After the option, or portion thereof, as applicable, has vested, the shares underlying the vested portion of the option may be purchased as a whole at any time, or from time to time in part, by exercising this option until this option terminates

(c) At 5:00 P.M. (C.S.T.) on the expiration date indicated in the Letter (the “Expiration Date”), the right and option herein granted to purchase such shares in all events shall cease and terminate. Nothing in this Agreement or the Letter shall be construed to permit the exercise of the option beyond the Expiration Date.

(d) Except as provided below, the Optionee may not exercise any of the option rights hereunder unless at the time of exercise the Optionee is an employee of the Company or of a subsidiary of the Company, and has been in such employ continuously since the date of grant.

(1) Termination of Employment – General

Except as provided in Section 2(d)(2), if the Optionee’s employment with the Company and every subsidiary of the Company shall terminate for any reason, the Optionee’s right to exercise the unexercised portion of the option shall terminate and all rights hereunder shall cease.

(2) Termination of Employment

(A) By Retirement or Termination of Employment by the Company without Cause

(i) If the Optionee’s employment with the Company and every subsidiary of the Company shall have been involuntarily terminated by the Company and every subsidiary of the Company without Cause prior to the Optionee meeting the requirements for Retirement, and if the option has been granted and outstanding for a period of at least twelve (12) months, any portion of the option which is scheduled to vest under its terms after the date of such termination of employment and on or before the date that is twelve (12) months after the date of such termination of employment shall vest on the date of such termination of employment as if Optionee had remained employed by the Company for an additional twelve (12) months following termination of employment; provided that, any such vesting shall occur on the date of termination of employment. The Optionee shall have the right to exercise any vested and unexercised portion of the option at any time during a period of twelve (12) months after the date of such termination of employment, in whole or in part. If the Optionee dies within such twelve (12) month period at a time when the Optionee is not an employee, agent, or principal of a competitor of the Company or any subsidiary (or when the Company has consented to such relationship with a competitor), the option, to the extent it is vested and remains outstanding, may be exercised at any time by a Successor prior to the expiration of such twelve (12) month period after termination of employment during which the Optionee could have exercised the option had the Optionee survived. If the Optionee’s employment with the Company and every subsidiary shall have been terminated by the Company and every subsidiary without Cause at a time when the Optionee meets the requirements for a Retirement hereunder, such termination shall be deemed to be a Retirement.

(ii) If the Optionee’s employment with the Company and every subsidiary of the Company shall terminate because of the Retirement (as defined herein) of

2

the Optionee from the Company and all subsidiaries, the option shall be one hundred percent (100%) vested, and the Optionee shall have the right to exercise the unexercised portion of the option at any time during a period of five (5) years after the date of Retirement, in whole or in part. If the Optionee dies within such five (5) year period at a time when the Optionee is not an employee, agent or principal of a competitor of the Company or any subsidiary (or when the Company has consented to such relationship with a competitor), the option, to the extent it remains outstanding, may be exercised at any time by a Successor prior to the expiration of such five (5) year period after termination of employment during which the Optionee could have exercised such option had the Optionee survived.

(iii) Notwithstanding anything in the Plan to the contrary, the term “Retirement” shall mean the termination of the Optionee’s employment on account of death, Disability, involuntary termination by the Company without Cause, or voluntary termination by the Optionee, in each event, after the date on which the Optionee either (x) attains age sixty five (65) or (y) both attains age fifty five (55) and completes seven (7) years of service with the Company and its affiliates, whether or not such service is consecutive. In no event shall a termination of the Optionee’s employment for Cause be deemed to be a Retirement.

(B) By Death or Permanent and Total Disability

If the Optionee dies or is totally and permanently disabled (within the meaning of Section 422(c)(6) of the Internal Revenue Code) while in the employ of the Company or any subsidiary and prior to meeting the requirements for Retirement, the option shall be one hundred percent (100%) vested and may be exercised by the Optionee or by the Optionee’s Successor at any time during the twelve (12) month period after the date of such death or disability for the total number of shares subject to the Optionee’s options. If the Optionee dies during such twelve (12) month period after the date of such disability, the option, to the extent it remains outstanding, may be exercised at any time by a Successor prior to the expiration of such twelve (12) month period after disability during which the Optionee could have exercised such option had the Optionee survived. If the Optionee dies or terminates employment on account of a disability while in the employ of the Company or any subsidiary at a time when the Optionee meets the requirements for a Retirement hereunder, such termination of employment on account of death or disability shall be deemed to be a Retirement.

(C) By Termination of Employment for Cause

If the Optionee’s employment is terminated by the Company and every subsidiary for Cause, any unexercised portion of any option granted to the Optionee, whether or not vested, shall terminate immediately with his or her termination of employment.

(D) By Voluntary Termination of Employment

If the Optionee voluntarily terminates his or her employment with the Company and every subsidiary for any reason other than his or her Retirement, any unexercised portion of his or her option, whether or not vested, shall terminate immediately with his or her termination of employment.

(E) Certain Corporate Transactions

3

Upon the occurrence of a Change in Control, the entire option shall become vested and exercisable, and the shares may be purchased at any time by exercising this option in accordance with all other terms and conditions hereof, without regard to Section 6(g)(i) of the Plan. Any unexercised portion shall terminate immediately if and when the Optionee becomes an employee, agent or principal of a competitor of the Company, or of any subsidiary of the Company, without the consent of the Company. Notwithstanding anything herein or in the Plan to the contrary, Section 6(f)(i)(H) of the Plan shall not apply to this option; except that, this option shall not be affected by any change in employment responsibilities so long as the Optionee continues to be an employee of the Company or a subsidiary thereof.

(3) Tax Treatment of Incentive Stock Options

Notwithstanding the foregoing, in the event an incentive stock option is exercised more than three months after the date of the termination of the Optionee’s employment, the incentive stock option will generally be treated as a non-qualified stock option, unless the Optionee’s employment was terminated as a result of disability or death. Accordingly, the Optionee will be required to recognize income upon exercise of the stock option. The Optionee should consult his or her personal tax advisor regarding the tax implications and consequences of this option and the exercise thereof.

3. This option may be exercised in such form and manner and otherwise pursuant to such procedures as may be established by the Company from time to time. The Company has the right to require payment of any taxes before issuing to the Optionee any stock under the option and will deduct any required minimum taxes from any payment of any kind due to the Optionee. The Committee may permit the Optionee to satisfy withholding obligations by delivering previously owned shares or by electing to have shares withheld to meet the statutory required minimum withholding requirements.

4. This option shall not be transferred by the Optionee otherwise than by will or the laws of descent and distribution, nor may the Optionee pledge, hypothecate or otherwise create any lien thereupon. During the lifetime of the Optionee, the option shall be exercisable only by the Optionee or, if he or she is legally incompetent, by his or her legal representative.

5. The option hereby incorporates by reference the terms and conditions of the Plan, and the option is issued to and received by the Optionee subject to all such terms and conditions. In the event of any conflict or inconsistency between the provisions of Section 6(f) of the Plan and these Terms or the Letter, the provisions of these Terms and the Letter shall control. In the event of any conflict or inconsistency between any other provisions of the Plan and these Terms or the Letter, the provisions of the Plan shall control, except to the extent specifically contemplated otherwise herein. Notwithstanding anything herein or in the Plan or the Letter to the contrary, the option is subject to the Company’s Financial Restatement Policy as amended from time to time.

6. These terms are an integral part of the Letter and should be read in conjunction therewith.

4