Step 1: Read the question. We must find the FALSE statement about coagulation.
Step 2: Check option A. Factor X (Stuart-Prower factor) is the first factor of the common pathway, where the intrinsic and extrinsic pathways converge, so it is shared by both. TRUE.
Step 3: Check option B. The EXTRINSIC pathway is triggered by tissue factor (Factor III) released from injured tissue, together with Factor VII. Activation by contact with a negatively charged surface (and plasma proteins such as Factor XII, prekallikrein, HMWK) is the hallmark of the INTRINSIC (contact) pathway, NOT the extrinsic pathway. This statement is therefore FALSE.
Step 4: Check options C and D. Calcium (Factor IV) is essential for multiple coagulation steps, so C is TRUE. The intrinsic (contact) pathway is indeed what gets activated in a glass tube in vitro, so D is TRUE.
Step 5: Select the exception. The incorrect statement is option B.
Answer: The extrinsic pathway is activated by contact with plasma and negatively charged surfaces (option B) is FALSE.