The body’s current levels of muscle mass are determined by previous physical requirements and the
expectation of future demands.  The body also strives to maintain an additional reserve of ability to be accessed in emergencies.  To build muscle fast, exercise must be performed which draws on these reserve abilities.  An optimum training program produces constant progression.  This is an absolute requirement for increases in muscle size to be realized.

If exercises are regularly performed well within the current capabilities of the muscles involved, no muscle gains will be produced.  When you engage in an exercise program that forces your body to draw on its reserve ability, your body is forced to increase its current levels of strength and muscle mass in order to keep up.  Unless these demands are maintained and or increased, the body will not be capable of dealing with future demands.  All future demands must be greater than the previous.  This is achieved with the addition  weight and or more repetitions.

The ability for you to increase the quantity of exercise, via additional exercises and sets, is not really progress.  A muscle is capable of performing almost any amount of low intensity exercise.  True progression is stimulated by greater demands in power.  Increasing the level of intensity through the addition of weight is the secret key to gain muscle mass.

In practice, an effectively performed set of barbell curls would have a physical repetition limit of ten.  Once a you can perform ten full repetitions with ease, the number of repetitions should not be increased.  But, the amount of weight used should.  With increased weight, you may only be capable of performing eight repetitions.  You should then work towards  increasing the number of repetitions performed to ten.