Welcome to the Differential Calculus Pretest. Attempt to complete all of the following questions in under 90 minutes. The solutions can be found by clicking this link: Differential Calculus Pretest Solutions.
Pretest (90 Minutes):
1. Given the equation of the linear line below, state the following: slope, x-intercept(s) and y-intercept(s).(1)
2. Determine the equation of a line that passes through the point (2, 6) and is perpendicular to the line below. Give your answer in the form of y = mx + b.(2)
3. Given the following quadratic equation, determine the x-intercept(s) if there are any, y-intercepts, as well as the vertex. Also determine if the quadratic equation opens up or down. You may need to utilize the quadratic formula which is provided below for reference.(3)
4. Determine the roots of the following expression:(5)
5. Simplify the following expression and state the equation(s) of any vertical asymptote(s).(6)
6. What is the area of the rectangle bounded by the lines x = 3, x = 7, y = 2, and y = -6?
7. State the value of the following without a calculator:(7)
8. For what value(s) of x does sin(x) = cos(x)?
9. Prove the following trigonometric identity:(8)
10. State the domain of the following functions:(9)
11. Determine the value of x without the use of a calculator.(12)
12. Determine the value of x without the use of a calculator.(13)