This paper estimates the effect of home internet speed on national test scores of students at age 14. We combine comprehensive information on the telecom network, administrative student records, house prices and local amenities in England in a fuzzy spatial regression discontinuity design across invisible telephone exchange catchment area boundaries. We find that increasing broadband speed by 1 Mbit/s raises test scores by 1.37 percentile ranks. This effect is sizeable, equivalent to 5% of a standard deviation in the national score distribution. Our results are not driven by school technological factors and do not fade out two years later.