Ummariyat Mirza, 21, of St Agathas Road, Birmingham, is charged with preparing for a terrorist attack in the UK by buying a knife and other items.
His sister, Zainub Mirza, 23, from Eastfield Road, Bordesley Green, is charged with sending Islamic State propaganda videos to others.
They were remanded in custody at Westminster Magistrates' Court.
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The siblings were ordered to appear on 28 April at the Old Bailey for a preliminary hearing.
It is alleged Ms Mirza sent the extremist material, including a picture of a man holding two severed heads, to encourage terror attacks.
Mr Mirza was arrested by counter-terror police in Alum Rock Road, Birmingham, as part of a series of raids on homes on 29 March.
He is also charged with possessing the bomb-making guide the Anarchist Cookbook and an extremist document called the Mujahideen Poisons handbook.
A man accused of plotting a terror knife attack has appeared in court alongside his sister.