The covenant of Jehovah with Israel was a covenant based on man's works to keep the law. Concerning this, Paul says in Galatians 2:16, "Knowing that a man is not justified out of works of law, but through faith in Jesus Christ, we also have believed into Christ Jesus that we might be justified out of faith in Christ and not out of the works of law, because out of the works of law no flesh will be justified."
The covenant with Israel is not like the covenant of promise given to Abraham, nor like the covenant of grace given to the New Testament believers (Rom. 6:14b). Actually the covenant of promise given to Abraham and the covenant of grace given to the New Testament believers are the same covenant. With Abraham this covenant was a matter of promise; with the believers it is a matter of fulfillment.
Jehovah's covenant with Israel was not by man's faith in God but by man's works in himself (Gal. 2:16). This covenant was altogether a matter that was wrapped up with the self instead of with God. The new covenant is different. The new covenant is based upon faith in God and it is wrapped up with God. If we do not have God, we do not have the new covenant. Without God, there is no way for us to experience the new covenant.
Israel became a total failure under the test of the law. They became such a failure that they might know certain things.