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AP CALCULUS DIAGNOSTIC TEST

NON 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 statethe domain and range of each.

Label x and y intercepts for each.

(a) g(x) = (x 3)2 2 (b) f(x) = 3x 2

domain: ________________ domain: ________________

range: __________________ range: _________________

(c) f(x) = 4x + . (d) y = 3x

domain: ________________ domain: ________________range: __________________ range: _________________

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2. Consider the function f(x) = x2 4x + 3.

(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 sec > 0

6. Find the trigonometric values

(a) 5sin6 = (b) 5cos

3 =

7. Complete the trigonometric identity:

(a) 1 + tan2x = (b) sin(2x) =

8. Solve

(a) 2sin 2 = for0 2 < (b) 2cos2x cosx 1 = 0

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9. Find an equation of the line parallel to the line 4x 2y = -4 that passes through the point (0, l).

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

(a) f(3x2) = (b) f(x+2)

11. Solve 8x2 28x = -24. 12. Simplify: (3x2y-3z-1)-2

13. Rewrite using radical notation: (3xy)-2/3

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

f(x) =2

sin 0

0 2

3 2

x if x

x if x

x if x

<

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15. Find the area of this trapezoid

Area =

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

(a) 5xex -25x=0 (b)1 3

21 1x x

+ =

+

17. Divide the polynomials using long division (2x3 + 5x2 3x + 2) (x + 1)

CALCULATOR SECTION:

4 3 2 1 1 2 3 4 5

4321

1234

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NAME: _______________________________________ DATE: _______________

15. The position of one squash ball at time tis given by the function p1(t) = -.04t3 - .01t2 + 6t + 5. The position

of a second ball at time tis given by p2(t) = 13cos(2t). Find the time twhen the two balls collide (that is, thefirst time when their positions are equal).

16. Use your calculator to find the max of f(x)= 3sin2(x-1) 5 for 0