Another way that you can complete challenges and get more points is to become aggressive towards other racers in the event, and try to crash them and knock them out of the race. To get points by hitting enemy cars, you can shunt them by hitting them in their bumper, or you can rail/grind up against them by slamming into their side, and continually pushing them into the wall so that sparks start to fly. You can also just cause them to have a total takedown by driving with your turbo activated, and then ramming them into the wall. If you do these methods, you will get more points, but if you take out the car completely, then you will get a lot of points.
There are many, many ways that you can use to get some points during a race. I have taken the time to list the easiest methods that will give you points during a race. The first thing that you need to do, is to just drive dangerously. Take everything that they tell you about in driving school, and throw it out the window. You can Drive on the wrong side of the road and into oncoming traffic to get points, or you can narrowly avoid crashes with cars to get points. Another simple way to get points is to drift around corners and turn. If you use all three of these methods in a race, then you will get a lot of points.
It does not matter whether you are playing road rage, maniac mode, or even doing a regular race. By doing this one, simple and easy step, you can constantly get more points added to your total score while you simply drive. All you have to do is go into the left lane, where the cars on the opposite side of the road are driving, and drive that way. This way, you are driving into oncoming traffic. This will give you a constant sum of pints if you continue to drive on the wrong side, and if you nearly miss a crash with all the cars, then you will get more points.