Refer to figures. 
EASA learning objective 022.08.01.01.07 states: 'Define ‘Mach trim’ and state that the Mach-trim system can be independent.'

At high subsonic speeds aircraft will eventually reach a point where some airflow around the aircraft will reach supesonic speeds, this speed is known as M_crit. Above M_crit shockwaves will start to form causing turbulent airflow and the centre of pressure of the wing will start moving rearwards. This rearward centre of pressure and shockwave movement coupled with airflow changes over the tailplane will cause a nose down pitching movement which will need to be counteracted to avoid speed instability or loss of control.

Mach trim is an automatic system which controls the tailplane trim to counteract this nose down tendency, it's a separate system so the autopilot doesn't need to be engaged for it to operate.

is activated by the pilot when reaching the limiting Mach number to trim attitude --> INCORRECT. It's fully automatic and requires no pilot input.

compensates for Mach tuck by trimming the stabiliser down --> INCORRECT. It trims the horizontal stabiliser up to counteract the nose down effect.

compensates for Mach tuck caused by the rearward movement of the aircraft centre of pressure as an aircraft accelerates --> CORRECT. Rearward movement of the shockwave and centre of pressure cause 'Mach Tuck'

compensates for the forward movement of the centre of pressure, due to the forward movement of the shock wave, as speed increases --> INCORRECT. The shockwave and centre of pressure move. rearwards

Note: Some versions of this question will have 'rearward movement of the shockwave' as the correct answer option instead of 'rearward movement of the centre of pressure', either option is correct.