[{_id:ObjectId("50b59cd75bed76f46522c35a"),student_id:1,class_id:22,scores:[{type:"exam",score:47.38775906993299},{type:"quiz",score:9.963742963372834},{type:"homework",score:22.17993073237026},{type:"homework",score:33.7647119689925},{type:"homework",score:18.29543263797219}]}]

db.collection.aggregate([{"$match":{student_id:1,class_id:22,"scores.type":"exam"}},{"$set":{"data":{"$first":{"$filter":{"input":"$scores","cond":{"$eq":["$$this.type","exam"]}}}}}},{"$project":{"_id":0,"score":"$data.score","type":"$data.type"}}])