Murder Most Unladylike: A Murder Most Unladylike Mystery by Robin Stevens

Enhanced descriptions from Syndetics:

The first gripping, Agatha Christie-style mystery starring a brilliant new double act: feisty, funny schoolgirl detectives, Daisy Wells and Hazel Wong.
     When Daisy Wells and Hazel Wong set up their very own deadly secret detective agency at Deepdean School for Girls, they struggle to find any truly exciting mysteries to investigate. (Unless you count the case of Lavinia's missing tie. Which they don't, really.)
     But then Hazel discovers the Science Mistress, Miss Bell, lying dead in the Gym. She thinks it must all have been a terrible accident -- but when she and Daisy return five minutes later, the body has disappeared. Now the girls know a murder must have taken place... and there's more than one person at Deepdean with a motive.
     Now Hazel and Daisy not only have a murder to solve: they have to prove a murder happened in the first place. Determined to get to the bottom of the crime before the killer strikes again (and before the police can get there first, naturally), Hazel and Daisy must hunt for evidence, spy on their suspects and use all the cunning, scheming and intuition they can muster. But will they succeed? And can their friendship stand the test?