Actually no.
The Greek words translated "faith" and "believe" in the New Testament come from the Greek pistis. The Greek term is equivalent to the Hebrew word 'emunah.
These words do not refer to a mental assent or acknowledgement of a claim, a creed, or to credulity. Rather they signify a type of behavior or response. The Jehovah's Witnesses are not very far off in their offering of the term "exercise faith" in the NWT. It is merely redundant however.
The words pistis and 'emunah mean "faithfulness." They can also be rendered as "trust" and even "loyalty" in some instances.
Originally with the New Testament writers being Jewish (except for Luke), the terminology never meant to have mere "belief" in a premise or teaching, as it does now where Christians are asked to guard against doubting lest they lose their mental grasp of a stand or theological view. While the Church Fathers only slightly began to give the meaning of "assent to a creed or doctrine" to pistis in the early church, it would be the Reformation that would give new meaning to the terms, especially as they appear in Pauline writings, notably that of Romans more than anywhere else.
But in reality the terms refer to walking according to a set type of behavior as an expression of loyalty, to a concept yes, but not merely the mental grasping or believing aspect that is generally understood today. The original meanings can greatly alter the text if read directly from the Greek.
For instance, Matthew 17:20 is now meaningless due to the current view of the word "faith." The verse reads in the NRSV: "Truly I tell you, if you have faith the size of a mustard seed, you will say to this mountain, ‘Move from here to there,’ and it will move; and nothing will be impossible for you."
Because people think the word "faith" means "belief" this is generally applied as merely asking God for help and sitting back, waiting for God to do something. Yet the word pistis is not that static at all. A more precise way to render this verse would be: "If you were as faithful as a mustard seed, should you tell this mountain, 'Move from here to there,' it will move. Thus nothing will be impossible for you."
Mustard in Israel is notorious for overgrowing wildly, taking over the land where other crops and vegetation lives, choking the life out of them, and taking their place. There were thus laws in ancient Israel regarding restrictions on how and where it could and could not be planted because of this plant's behavior.
The text in Matthew 17:20 does not have the Greek word "size" in it at all. Because of how the Reformation has changed Christian views on pistis, it is now read as if the context is implying the "size" of a mustard seed, to read the text as if it saying that if you have even a little amount of "mental assent" or "belief" in something, God will make it happen for you.
Read the other way around the words of Jesus mean that he didn't expect his disciples to just sit around after praying for something to happen. Like the mustard seed, they would act faithfully in their resolve and take over the situation for themselves. If you want the mountain to move, you don't sit by and wait for God to do it. You start pushing on the mountain. Jesus is saying that God will only help you out if you start pushing.
This fits in with the Jewish teaching: "Pray as if everything depends upon God, but act as if everything depends upon you."
This is also why Judaism is said to be "practiced" while Christianity is "believed." Some practicing Jews are atheist, and myself, even though I consider myself to be theist cannot honestly reduce my response to the concept of God to the term "belief." I don't subscribe to the notion of belief in doctrines, a common stand among Jews.
But one can right say that according to the belief of some, mostly Christians, it is all about having "belief." At the same time one cannot say that this stand is immediately taken from Scripture. It's more theology than anything else because membership in Christian movements often demand adherents to mentally assent to a creed or a theology. Most Christian movements will expel members that refuse to mentally assent or believe in certain things too, even though almost all of these concepts are supposed to be transcendent in nature.