AP CALCULUS – DIAGNOSTIC TEST - REASSESSMENTNON CALCULATOR SECTION

NAME: ___________________________________________ DATE: ______________

1. Create a set of coordinate axes and appropriate scale on the grids provided. Use what you know about translations and transformations to sketch the graph of the functions then state

the domain and range of each. Label x and y intercepts for each.

(a) g(x) = (x +1)2 + 2 (b) f(x) = -2x – 1

domain: ________________ domain: ________________ range: __________________ range: _________________

(c) f(x) = . (d) y = 2x

domain: ________________ domain: ________________ range: __________________ range: _________________

2. Consider the function f(x) = x2 – 7x + 12(a) Find the x-intercepts (if any) (b) Find the y-intercepts (if any)

5. Find the quadrant:

(a) cos > 0 and sin < 0 (b) tan < 0 and csc > 0

6. Find the trigonometric values

(a) (b)

7. Complete the trigonometric identity:

(a) 1 + cot2x = (b) sin2x - 1 =

8. Solve (a) for (b) 2sin2x – sinx = 0

9. Find an equation of the line perpendicular to the line 2x – y = 6 that passes through the point (-2, 3).

10. If f(x) = x2 +2 , find and simplify (where appropriate) the following:

(a) f(-4x3) = (b) f(x-1)

11. Solve 6x2 + 37x = -6 12. Simplify: (2x3y-2z)3

13. Rewrite using radical notation: (4x2)-1/3

14. Sketch a graph of the following, be sure to label axis, scale, and any intercepts:

f(x) =

15. Write your own piecewise function for the graph below:

g(x) =

15. Find the area of this trapezoid

Area =

16. Solve for x, leave your answers in exact form:

(a) 2xex - 6x = 0 (b)

17. Divide the polynomials using long division (3x3 + 2x2 – x + 2) (x – 2)