I agree with the other comments about 1X 10X probes. I really do not like the 1X 10X probes,they can cause problems if you unintentionally have them set at 1X, Sometimes the switch can go wonky also. In general they do not work as well as unswitched probes, maybe stray capacitance?
I spent years with inadequate probes that did not match the scopes I was using. In retrospect, that was stupid. At the really cheap prices that are common today there is little reason not to get the correct probes. Usually good to get probes that are rated higher than your scope. since your scope is 40 MHz this should not be a problem. You do have a calibrator connector just under the screen for calibrating your new probes. Should be nice square wave.The BNC connector part of the probe should have an adjustment (really just an adjustable cap) that is used to make the wave square. This is what "matches" the capacitance of the probe with the input capacitance of the scope.
About max freq....in analog scopes this is usually the frequency where the trace is 80% of what is should be. The scope can go higher, sometimes much higher, but the amplitude of the trace will not be accurate. Sometimes there is a "hole" in the freq range just above the Max where the scope has low response then maybe the scope gets back on track with even higher freq.
That is a real nice scope. Much more than a "beginner" scope.
Don't clean the surface with any solvents, could erase the lettering, use soap if necessary