The classical method of autonomous racing uses real-time localisation to follow a precalculated optimal trajectory. In contrast, end-to-end deep reinforcement learning (DRL) can train agents to race using only raw LiDAR scans. While classical methods prioritise optimization for high-performance racing, DRL approaches have focused on low-performance contexts with little consideration of the speed profile. This work addresses the problem of using end-to-end DRL agents for high-speed autonomous racing. We present trajectory-aided learning (TAL) that trains DRL agents for high-performance racing by incorporating the optimal trajectory (racing line) into the learning formulation. Our method is evaluated using the TD3 algorithm on four maps in the open-source F1Tenth simulator. The results demonstrate that our method achieves a significantly higher lap completion rate at high speeds compared to the baseline. This is due to TAL training the agent to select a feasible speed profile of slowing down in the corners and roughly tracking the optimal trajectory.