Can I Skip Math 1314 for Calculus I with a TSI Score of 350?

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coolsupermanfly
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I took the TSI in January this year. I scored ok in the English part, and I'm confused on the math part. Here is my math score from the TSI paper:

TSI Mathematic Placement: 350

MATH 1314, 1324, 1332, 1342
Enroll in Math 1314, College Algebra. You also qualify for Math 1324, 1332, 1342.

I'm trying to become a mechanical engineer and my college's Program Plan requires me to take Calculus I. The TSI says I should Enroll in Math 1314 but I want to go into Calculus I as soon as I start my fall college courses. Would it be a good idea for me to skip Math 1314 and go straight into Calculus I?

Note: I didn't study for the TSI, nor did I know I had to take it until a counselor at my high school asked me if I wanted to sign up for the TSI.

Edit:
Just enrolled in a Math 1314 class for the summer. Now I'm wondering if I could skip Pre-calculus.
 
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College Algebra and Precalculus may be separate courses. The "College Algebra" part of Precalculus should be the same or equivalent enough in both. Best to check with your school and how the actual content of either course prepares you for Calculus 1, but you should do at least ONE of them. One needs heavy-duty algebra skills and significant Trigonometry knowledge for Calculus.