The subject says it all. At the end of playing each record the needle screeches across the record. There is no skating setting on this AKAI AP-X1 that I can see in my owner's manual.
There have been quite a few turntables designed without a skating adjustment. While not the hottest topic to decide future national elections, the issue of skating and how to best correct for its undeniable effect has been discussed since the 1950's when variable pitch grooves came into production. Everyone agrees skating compensation is more often wrong than right since the amount of compensation is a dynamic function which changes constantly. However, since everyone agrees skating effects exist, they also agree skating compensation must be taken into account.
If your table has no anti-skating adjustments, the most common way to add skating compensation is to increase the downforce on the stylus by about 15-25%. In other words, if your cartridge is now tracking at 1.5 grams, increase the tracking force to about 2 grams. There is also no doubt among those who know best that your stylus will do more groove damage by tracking too lightly than it will by tracking at a heavier downforce. The discussion is too complicated to take on here but don't be afraid to track the cartridge at its highest recommended tracking force or even a bit above.
More important though, is how you have set the tracking force initially. If you are having the problem of the arm skating across the disc at the lead out groove, I have to think you've not done a good job of establishing a proper downforce to begin with. There are numerous youtube sites which describe the process along with just as many websites which describe the process. Most people screw up in the process of establishing a neutral balance and then not turning the counterweight without changing other settings.
On inexpensive tables, neutral balance is difficult to achieve due to the excessive amount of friction in the arm bearings. If you can't get to a true neutral balance with the arm, you will never get to a proper tracking force without more assistance from a scale.
The resulting downforce for an arm not initially set to neutral is then off by a pretty good amount. Add in the misguided concept many people have of tracking too lightly and the arm is really just shattering around in the groove without actually touching the area of the groove walls where the real music exists and the stylus follows the groove movement as intended.
Even if you bought this table from a shop and they set up the table for you, I simply wouldn't personally trust someone, who probably doesn't know diddly about tables, to do anything. Do it yourself and do it right and you'll probably be OK.
Check the web for the instructions and try your balance set up again. Contact MusicDirect for this balance scale; http://www.musicdirect.com/p-7523-shure-sfg-2-stylus-force-gauge.aspx Tracking your stylus too lightly will result in permanent damage to the record groove. What you pay to ensure the proper downforce will pay for itself in records which last and sound good for decades.
Alternately, if you have an audio shop which is actually in the business of selling audio equipment, ask if they won't balance your arm for you. Most should do this at no cost as a simple courtesy. Once the arm has been balanced, take pains to make sure the adjustment doesn't move while transporting the table back home.
And, yes, the table you own is a plastic toy. If it's all you can afford, that's one thing. But your records are being damaged by this table due to its poor design. Look into buying a decent table ASAP if you want to have good sound that lasts. There are always a good selection of pre-owned tables to choose from as people step up into a more sophisticated design. Set up matters too. Particularly if you play your music at loud listening levels.
If the rebalancing doesn't solve your problem and you can't afford a better table at the moment, check back and tell us how you have the table situated. What's it sitting on and so forth and how loudly you listen to music.
This is, as I now see, a semi-automatic turntable meaning the arm should trip a lift device as it moves across the lead out groove and hits a predetermined point on the disc surface. On an inexpensive table this is typically nothing more than a series of shafts and levers which determine the lift point and another set of levers which will lift the arm and possibly move the arm back to its rest position. There is the possibility one of these pieces of stamped metal levers might be bent or somehow maladjusted. This is not an uncommon situation when the table has been transported (even a very short distance) without the arm and plinth being tied down. It does take a bit of force to bend the levers but I have seen semi and fully automatic tables with this problem. It only takes a very small amount of damage to the levers to create problems.
In addition, since these arms and levers are coated with grease for smooth operation, if the table has been stored for any amount of time or simply not in use, the grease can harden which would foul the mechanism. The best repair for this would be a dis-assembly of the automatic functions and new grease being applied before re-assembly. It's a slow, rather tedious process which not many techs looked forward to performing and charged accordingly. If you get either the dis-assembly or the re-assembly wrong, you'll have more problems to deal with.
If either of these is the case with your table, the result can be the arm doesn't lift straight up but moves at an angle which appears to drag the stylus across the lead out groove resulting in a good bit of noise. There's not much a user can do to correct this since you'll need a shop manual and the tools required to perform service on the table. There's likely no tech who would care to look at an Akai table so you are rather on your own on this.
Should this prove to be the case with your table, the best option, IMO, is to physically disconnect the automatic mechanisms and turn the table into a straight, fully manual system. As always, be very careful when dealing with the arm and its mechanics. It's quite easy to do damage to the arm bearings which would result in even worse problems. It's not unheard of for a table that doesn't lift the arm properly to snap the bonded stylus off the cartridge which will put you in a very bad place.