"Testament"="covenant"
"Hebrews 9:16"

Hebrews 9:16 16 For where a testament is, there must also of necessity be the death of the testator. KJV note: testament=covenant

   1. Under the Old Covenant (Testament), Gentiles were alienated from Israel, were called the "uncircumcision", were "strangers from the covenants of promise."
"Ephesians 2: 12"

Ephesians 2: 12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:

   2. But Jesus has united both into one by the New Covenant.
"Ephesians 2:14"

Ephesians 2:14 For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us;

   3. The New Covenant came into effect after Christ's death on the cross.
"Hebrews 9:17"

Hebrews 9:17 17 For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth. KJV

   4. Jesus died for all sins committed under the Old and New Covenant.
"Hebrews 9:15"

Hebrews 9:15 15 And for this cause He is the mediator of the New Testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance. KJV

  5. The first covenant is "old", "done away with" and places "a vail" over one's heart when he reads it.
"2 Corinthians 3:11, 15;

2 Corinthians 3:11, 15 11 For if that which is done away was glorious, much more that which remaineth is glorious. 15 But even unto this day, when Moses is read, the vail is upon their heart.

Hebrews 8:13"

Hebrews 8:13 In that he saith, A new covenant, he hath made the first old. KJV

  6. The first covenant is written for our learning for hope, to confirm Jesus as the Christ, and as a pattern for obedience.
"Romans 15:4";

Romans 15:4, For whatever things were written before were written for our learning, that we through the patience and comfort of the Scriptures might have hope.

"Luke 24:44";

Luke 24:44 Then He said to them, These are the words which I spoke to you while I was still with you, that all things must be fulfilled which were written in the Law of Moses and the Prophets and the Psalms concerning Me.

"1 Corinthians 10:11"

1 Cor. 10:11 Now all these things happened to them as examples, and they were written for our admonition, upon whom the ends of the ages have come.