Do I really need to warm up before a workout?

Yes. To avoid injuries you need to warm up between 3 to 5 minutes for a person under 50 years old and 10 minutes if you are over 50 years of age.

Keep the warm up simple. Progressively increase activity intensity to warm up the synovial fluid in your joints and increase your muscle elasticity, heart rate,and core body temperature.

You can use a cardio machine or create a series of slow, light movements similar to the exercises and movements that you are planning to do for cardio and strength training. For example, you can do a combination of squats, burpees, lunges, walking push ups, side squats, jumping jacks, jumping rope, etc.