Jesus, himself, makes the connection between faith and prayer. Consider these scriptures:

Matthew 21:21-22 . . . And Jesus answered and said to them, "Truly I say to you, if you have faith, and do not doubt, you shall not only do what was done to the fig tree, but even if you say to this mountain, ‘Be taken up and cast into the sea,’ it shall happen. (22) And all things you ask in prayer, believing, you will receive." (Clear statement about faith / prayer)
Mark 11:20-25 . . . As they were passing by in the morning, they saw the fig tree withered from the roots up. (21) Being reminded, Peter said to Him, "Rabbi, look, the fig tree which You cursed has withered." (22) And Jesus answered saying to them, "Have faith in God. (23) "Truly I say to you, whoever says to this mountain, 'Be taken up and cast into the sea,' and does not doubt in his heart, but believes that what he says is going to happen, it will be granted him. (24) "Therefore I say to you, all things for which you pray and ask, believe that you have received them, and they will be granted you. (25) "Whenever you stand praying, forgive, if you have anything against anyone, so that your Father who is in heaven will also forgive you your transgressions. (Clear statement about faith / prayer)
Matthew 7:7-11 . . . "Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. (8) "For everyone who asks receives, and he who seeks finds, and to him who knocks it will be opened. (9) "Or what man is there among you who, when his son asks for a loaf, will give him a stone? (10) "Or if he asks for a fish, he will not give him a snake, will he? (11) "If you then, being evil, know how to give good gifts to your children, how much more will your Father who is in heaven give what is good to those who ask Him! (Implied statement about faith / prayer - if our children can trust us to give them good things, we can trust God)
John 14:12-13 . . . Truly, truly, I say to you, he who believes in Me, the works that I do shall he do also; and greater works than these shall he do; because I go to the Father. (13) Whatever you ask in My name, that will I do, so that the Father may be glorified in the Son. (Implied statement about faith / prayer - to pray in Jesus’ name requires faith in Jesus, himself - that he is who he says he is and he can do what he says he will do.)
(In the Jewish way of thinking, a person’s name is directly linked to the person’s character and prerogatives. "Prerogatives" refers to any exclusive right or privilege a person may hold. In Jesus case, his prerogative is the right to rule, to be the Master in relation to our being the servant. This means that prayer in Jesus name is prayer that fits within the boundaries of Christ’s character, seeks the will of Jesus, and is submissive to the authority of Jesus. This means that prayer in Jesus’ name is prayer offered in faith that Jesus is trustworthy, and therefore, worthy of the positions and authority he holds over us.)
John 15:16 . . . You did not choose Me but I chose you, and appointed you that you would go and bear fruit, and that your fruit would remain, so that whatever you ask of the Father in My name He may give to you. (Implied statement about faith / prayer - accepting the idea that we have been chosen by Jesus to build his kingdom, and living accordingly, requires faith - and that is the faith we bring to prayer when seeking from God what we need to accomplish the task before us.)
John 15:5-8 . . . I am the vine, you are the branches; he who abides in Me, and I in him, he bears much fruit; for apart from Me you can do nothing. (6) If anyone does not abide in Me, he is thrown away as a branch, and dries up; and they gather them, and cast them into the fire, and they are burned. (7) If you abide in Me, and My words abide in you, ask whatever you wish, and it will be done for you. (8) By this is My Father glorified, that you bear much fruit, and so prove to be My disciples. (Implied statement about faith / prayer - the praying and receiving is based on abiding in Jesus and living according to his word so that our prayers are in accordance with his will. Such a life is a life of faith - believing that Jesus is trustworthy and as good as his word.)

One of the important ideas that comes from these scriptures is that faith, in relation to prayer, is inseparably linked to understanding and trusting in Jesus and our Heavenly Father to the extent that we willingly cooperate with their purposes. What this implies is that faith is not a tool but a mindset. 

Faith, as it is related to prayer, is not a tool to obtain what we want but a mindset enabling us to pray as we ought. The difference between a tool and a mindset is this.

A tool is something we possess and use to accomplish a task. A tool is under our control. Our use of a tool determines when the task will be accomplished and the quality of the product produced.

Some Christians hold a theological position which asserts that faith, as it is related to prayer, is like a tool. What this means is that when we have enough faith, or when we use our faith in the right way, our prayers will be answered according to our desires. And if our faith is strong enough, our prayers will be answered when desired.
It seems there are two problems with this view of faith in relation to prayer:

First, it puts the power of answered prayer in the hands of the one praying - and conversely, it places the blame for unanswered prayer on the one who prays without sufficient faith. In the end, this view establishes human faith as something God is expected to bow to. In fact, carried out to its logical end, it places God at the disposal or in the service of the one doing the praying. And how does it do all this? By making faith a tool to gain answers to prayer rather than looking to God’s love and grace as the means to answered prayer.
Second, it too easily leads to selfishness in prayer whereby we use God and prayer to achieve our personal interests and selfish desires. We see this happening among the "Name it and Claim it" folks who too often cross the line of good praying to using faith as a tool to get what they think they need - be it power, money, health, or fame.

It is my opinion that the scriptures are against treating faith as a tool when it comes to prayer. In relation to prayer, faith is to be a mindset. In its pure form, a mindset is a fixed or settled attitude or disposition which determines our approach to, our dealings with, and our interpretation or understanding of something. (A disposition is something you no longer have to think about because it is held as an absolute or as an accepted truth to be relied on.)

Faith, then, becomes the mindset with which we approach God in prayer and understand God’s dealings with us in relation to prayer.

In other words, faith is not a tool to be wielded in prayer as if it gives us some sort of power to control the outcome of our prayers. Faith is a mindset. And as a mindset, faith is the state of mind with which we come to God in prayer. Such a mindset creates a state of mind whereby our prayers most often, or more nearly line up with God’s character, His goals, and His methods of achieving His goals.
Get this picture clear in your mind: a mindset of faith (i.e., a fixed or settled attitude or disposition which determines our approach to, our dealings with, and our interpretation or understanding of something) - is essential to prayer according to the teachings of Christ.

Consider Jesus’ praying in the Garden of Gethsemane:

Matthew 26:38-39 . . . Then He said to them, "My soul is deeply grieved, to the point of death; remain here and keep watch with Me." (39) And He went a little beyond them, and fell on His face and prayed, saying, "My Father, if it is possible, let this cup pass from Me; yet not as I will, but as You will."
Jesus manifested a mindset of faith in this prayer. On this night of his betrayal and before his crucifixion, he did not approach prayer as if his faith were a tool to be used in obtaining the answer he sought. His prayers were not that of one who felt he had or even should have control over their outcome. Absolutely not! Christ’s prayers were prayers of great faith in the goodness and love of His Father.
Yet, according to Christ’s own teaching on prayer, it seems he should have been able to ask once and it be done according to what he asked. BUT that was not the case. He asked the same thing three times, and still God did not answer according to the thrust of the request. In fact, Jesus did not simply ask, he poured out his heart to God in such deep agony that his sweat became like drops of blood falling upon the ground. WHAT HAPPENED to praying in faith? What happened to believing you have what you ask for and receiving it? If this ‘praying in faith’ didn’t work for Jesus, how will it ever work for us? Is there something to be learned from Christ’s prayer?

In our examination of the relationship between faith and prayer - up to this point - we have discovered two important things. First, Jesus is the one who teaches us about faith and prayer. No where else in Scripture do we find such clear teaching about faith and prayer as we find in the words of Christ.Second, Christ’s teachings imply that faith is not a tool to be wielded in prayer as if by our faith we can control the outcome of our prayers. In fact, as we examine Christ’s teachings we see that faith in relation to prayer is a mindset, that is, a fixed or settled attitude and disposition which influences the way we approach prayer and the way we pray. However, the relationship between faith and prayer is not the only thing Jesus taught about in his teachings about prayer. In the Gospels, which are the first four books of the New Testament, Jesus presents two seemingly distinct approaches to prayer and an overriding principle governing all prayer.

First, Jesus presents the strong relationship between faith and prayer with the implication that this approach to prayer fits into a specific context. And we will examine the scriptures to see just what that context is.
Second, Jesus presents the strong relationship between persistence and prayer with the implication that this approach also fits into a specific context. Here again, we will examine the scriptures to see what this context is.
Third, Jesus teaches in word and deed the inseparable link between God’s will and prayer. And though the following words are the words of John, he sums up Jesus’ teaching on this topic in I John 5:14, where he wrote: "This is the confidence which we have before Him, that, if we ask anything according to His will, He hears us." The opposite of this governing principle of prayer is found in James 4:3, which says: "You ask and do not receive, because you ask with wrong motives, so that you may spend it on your pleasures." Just like faith and persistence, which are mindsets taken into prayer, submission to the will of God is a mindset governing prayer.

To summarize, Jesus teaches that we need to exercise faith, persistence, and submission to the will of God when we pray. Faith, persistence, and submission to the will of God are mindsets which influence our praying and set boundaries for our prayers. To help us see each of these three mindsets we will examine the scriptures related to each one.

When it comes to Christ’s teaching on the relation of faith to prayer it seems the context for this relationship is ministry of some kind, be it acts of kindness, evangelism, missionary service, kingdom building, or some other form of public activity in which we are engaged for the purpose of joining God in accomplishing His purposes in our world. To see this, lets examine two teachings of Christ on this subject.

Matthew 21:21-22 . . . And Jesus answered and said to them, "Truly I say to you, if you have faith, and do not doubt, you shall not only do what was done to the fig tree, but even if you say to this mountain, ‘Be taken up and cast into the sea,’ it shall happen. (22) And all things you ask in prayer, believing, you will receive."
(Context - triumphal entry into Jerusalem, followed by casting the money changers out of the temple, followed by healing the sick who were at the temple, followed by being confronted by the religious leaders, followed by spending the night in Bethany, followed by returning to Jerusalem because this was where Jesus needed to be in order to become God’s sacrifical lamb. The context is that of doing God’s work in God’s way regardless of the consequences.The implication then is that we are to pray in faith for what we need, to do God’s work God’s way.)
John 14:12-13 . . . Truly, truly, I say to you, he who believes in Me, the works that I do shall he do also; and greater works than these shall he do; because I go to the Father. (13) Whatever you ask in My name, that will I do, so that the Father may be glorified in the Son.
(Context - Jesus is giving his farewell address to his disciples and he begins by reminding them that he and the Father are one. It is in this context of assuring them that the Son is in the Father and the Father is in the Son that he tells his disciples that if they pray in his name, he will do what they ask of him in order for them to see the glory of the Father in him. And why is this important? The rest of the address is spent speaking about service to God and love for one another in a manner that speaks so loud, the world will come to repentance and conversion. The context here is that of service to God, and the implication is that such service places the servant in a position of having and seeing needs which only God can meet. The solution to these needs is to go to God in the name of Jesus - which is equal to praying in faith - and Jesus, himself, will supply the need.)

These scriptures show that Christ’s teaching on the relationship between faith and prayer relates to prayer that is directed at asking God for what we believe is needed to be effective workers in God’s field for the purpose of building God’s kingdom. Such praying has nothing to do with personal interests. But it has everything to do with God’s interests. The context of Christ’s teaching about faith and prayer lead us to see the power of faith in prayer related to praying for that which is needed to accomplish God’s purposes in our world.

I am convinced that faith and prayer go together in all praying. But to take the principle of "Ask what you will, in faith believing, and it will be done according to what you ask." into praying for personal wants and desires and needs is, in my opinion, a misapplication of Christ’s teaching on prayer and faith. And I think the proof that this is a misapplication is in the number of Christians praying self-interested prayers with the hope of having or demonstrating enough faith in their praying to move God to give them what they want.
To summarize, when we are acting as God’s workers doing God’s work, or when we are praying for others who are doing God’s work, we are to ask in faith for what is needed, believing we have what we ask for, and it will be done according to our prayer. This is the context Jesus presents when he teaches about faith and prayer.