Recent advances in genomics are producing powerful DNA predictors of complex traits, especially cognitive abilities. Here, we leveraged summary statistics from the most recent genome-wide association studies of intelligence and educational attainment, with highly genetically correlated traits, to build prediction models of general cognitive ability and educational achievement. To this end, we compared the performances of multi-trait genomic and polygenic scoring methods. In a representative UK sample of 7,026 children at ages 12 and 16, we show that we can now predict up to 11% of the variance in intelligence and 16% in educational achievement. We also show that predictive power increases from age 12 to age 16 and that genomic predictions do not differ for girls and boys. We found that multi-trait genomic methods were effective in boosting predictive power. Prediction accuracy varied across polygenic score approaches, however results were similar for different multi-trait and polygenic score methods. We discuss general caveats of multi-trait methods and polygenic score prediction, and conclude that polygenic scores for educational attainment and intelligence are currently the most powerful predictors in the behavioural sciences.