Chapter 9 ends with an analogy to sports, running a race and boxing and then Paul says
27 But I keep under my body, and bring it into subjection: lest that by any means, when I have preached to others, I myself should be a castaway. (1Co 9:27 KJG)
This is not "castaway" from salvation but to be disapproved. Salvation is by grace and rewards by works. The race and sports competitions are in the context of reward. Paul takes this further in the next chapter.
KJG 1 Corinthians 10:1 Moreover, brethren, I would not that ye should be ignorant, how that all our fathers were under the cloud, and all passed through the sea;
2 And were all baptized unto Moses in the cloud and in the sea;
3 And did all eat the same spiritual meat;
4 And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ.
5 But with many of them God was not well pleased: for they were overthrown in the wilderness.
The first point that stands out is the confirmation of the Acts context where assemblies were made up of a mixture of Jews and Gentiles. Here the Jews are being addressed "all our fathers" -- the fathers of the gentile believers were not all baptized unto Moses neither did they all drink the same spiritual drink etc. Paul addresses the Jews with pictures from their own historical spiritual inventory. The race and sportsmanship were well known by all but were especially a part of the gentile historical context. They served the purpose of analogy in chapter 9, here the spiritual truths can be seen more diirectly for while the Jews drank and ate real material things they also had spiritual value and would serve directly as instruction for the Acts believers and especially the Jew first.
6 Now these things were our examples, to the intent we should not lust after evil things, as they also lusted.
7 Neither be ye idolaters, as were some of them; as it is written, The people sat down to eat and drink, and rose up to play.
8 Neither let us commit fornication, as some of them committed, and fell in one day three and twenty thousand.
9 Neither let us tempt Christ, as some of them also tempted, and were destroyed of serpents.
10 Neither murmur ye, as some of them also murmured, and were destroyed of the destroyer.
11 Now all these things happened unto them for ensamples: and they are written for our admonition, upon whom the ends of the world are come.
11 ταῦτα δὲ πάντα τύποι συνέβαινον ἐκείνοις· ἐγράφη δὲ πρὸς νουθεσίαν ἡμῶν, εἰς οὓς τὰ τέλη τῶν αἰώνων κατήντησεν. (1Co 10:11 TBT)
These things which happened were types (τύποι) and examples -- they really happened but functioned especially for the Jewish Acts believers as types. Further Paul identifies themselves (Paul and the Corinthians) as recipients of the goals of the ages. What the ages were declaring concerning God's outworking purposes were finding their fulfilment in the believers of the Acts age. This needs to be pondered. What were the goals of the ages? The prophets declared the coming of the Messiah who would suffer first and then afterward a glorious reigning Messiah -- it must be the latter visions and prophecy that relate to the ends (goals).
The Acts age governed by goals of the ages is a very different time to that wherein we live! Before the times governed by ages there was a purpose and plan made by God who kept it secret.
KJG 2 Timothy 1:9 Who hath saved us, and called us with an holy calling, not according to our works, but according to his own purpose and grace, which was given us in Christ Jesus before the world began,
TBT 2 Timothy 1:9 τοῦ σώσαντος ἡμᾶς καὶ καλέσαντος κλήσει ἁγίᾳ, οὐ κατὰ τὰ ἔργα ἡμῶν, ἀλλὰ κατ᾽ ἰδίαν πρόθεσιν καὶ χάριν τὴν δοθεῖσαν ἡμῖν ἐν Χριστῷ Ἰησοῦ πρὸ χρόνων αἰωνίων,
The last clause τὴν δοθεῖσαν ἡμῖν ἐν Χριστῷ Ἰησοῦ πρὸ χρόνων αἰωνίων = "which was given to us in Christ Jesus before the age times". The word αἰωνίων is an adjective, it modifies the times (χρόνων) -- when Paul writes to Timothy he says that the salvation and calling relates to a purpose that was designed in Christ before the age times. The Goals and purposes of this age do not find their roots in the ages but before them.
This implies that our age is NOT a continuation of the ACTS - for the age of THE MYSTERY has its roots deep within GOD before the age times.