Variance of parts equal to variance of whole?

Good morning,

I ran a hierarchical regression to test if variables A and B (established in the literature) are mediated by variable C (my research question) when predicting overall performance in a university unit. Block 1 was variables A and B using enter method. Block 2 included variable C into the regression model. In Model 1, variable B did not predict performance, but variable A did (p=.003). In model 2, variable B still did not predict performance and now variable A was non-significant (p=.699). Variable C was significant (p<.001). I concluded that variable A was entirely mediated by variable C.

In the literature, variable A is related to concept learning and variable B is related to fact learning. Overall performance was calculated by the sum of in-semester performance, which required fact learning, and exam performance, which required concept learning. This prompted a further research question. Does the predictive value of variables A and B differ for in-semester and exam performance? I ran the same regressions as before, but once with in-semester performance and once with exam performance as the dependent variable. Essentially, the same thing happened. In Model 1, variable A was significant and variable B was non-significant. In Model 2, both were non-significant and variable C was significant.

The adjusted R2 values of Model 2 are as follows:
Overall R2=.23
In-sem R2=.13
Exam R2=.13

This is where I need some advice.
Overall score = in-semester score + exam score
Does the variance follow the same simple rule [R2(in-sem) + R2(exam) = R2(overall)]?
If so, we have .13 + .13 = .23
Can it be concluded that Model 2 predicts 13% of variance in in-semester performance and 13% of variance in exam performance, and 3% of that is overlapping such that a total of 23% of variance in overall performance is explained?
Are these assumptions beyond the assumptions of regression?

Your advice will be greatly appreciated!