Trained synthetic features were used with classification and regression trees (CART) and boosting methods to predict outcomes of categorical response variables in general. The trained synthetic features involved were synthetic features (Zieba, Tomczak, & Tomczak, 2016), principal component analysis (PCA), zero-one regression (ZO), logistic regression (LS), linear discriminant analysis (LDA), robust fitting of linear models (RLM), least trimmed squares (LTS), naive Bayes (NBAY), and univariate spline (SPL) using the statistical software R. To illustrate the trained synthetic features in this paper, they were applied to Polish companies' financial data, Fisher's Iris data, and skin lesion data. The objective of the research was to apply trained synthetic features to CART, stock boosting method that had been fitted with the synthetic features at the root node, and synthetic boosting method that was reweighted and refitted the synthetic features at each iteration, to improve on predictive accuracy for classes in a given data set rather than random guessing based on the prior probabilities.