Ohio Northern University
Department of Mathematics and Statistics
CALCULUS READINESS TEST
A graphing calculator may be used for this test; however, the majority of
the problems should be understood without relying on the graphing
capabilities of the calculator.
Allow yourself 45 minutes to complete this test.
Round answers to the nearest thousandths where necessary.
A link to the answers is provided at the end of the test.
A score of 15 or more out of 25 will indicate readiness to enroll in
Calculus 1, or Math 1631, at Ohio Northern University.
1.
Find the point of intersection in the first quadrant of the line y
the curve y x 2 .
2.
If f is a function whose graph is the parabola
shown, then find when f x 0.
1
3x 3 2 and g x
2
3
3.
Suppose f x
4.
Find x if 2 5000 10 x .
5.
Sketch a graph of y
6.
Find x if
7.
The population of Ada increases by a factor of 1.4 every year. (If there are
100 people now, next year there will be 140 people.) Find the factor the
population increases by over a 20 year period.
8.
A box has a square base and an open top.
Express its surface area in terms of x (width
of the base) and h (height of the box).
2x 3 x 2
x 3
x2
x 1 . If h x
4 x 2 and
f g x , then find h 1.7 .
ax 1.
0.
h
x
9.
Definition: A function is odd if f x
f x for each x in the domain of f.
Use the definition to determine all of the odd functions.
(A).
f x x 6
(B).
f x 3x 3 4x
(C).
f x 9 5x 2
(D).
f x x 4
(E).
f x
x3
10. Sketch a graph of f x
a x , where a 1.
11. In the figure shown, what is the
distance between the points
A and B?
B(2,5)
A(-3,1)
12. Given f x
5x 2
, find f a 3 .
x 1
13. The graph of the equation y
(A).
(B).
(C).
(D).
(E).
C(2,1)
3
x b is
5
a vertical line
a line falling to the right
a horizontal line
a line rising to the right
not a line
14. Using the figure shown, find the sum of
the areas of the shaded rectangles.
(Note: the upper left-hand corners of
rectangles should intersect the curve.)
y
1
2
3
4
5
x
15. The quantity
a2
(A).
a2
(B).
a3
(C).
a3
(D).
a b is a factor of which of the following?
b2
b2
b3
b3
16. Solve the inequality x 5
7 for x.
17. If the length x of a rectangle is doubled and the width y is tripled, find the
amount the area of the rectangle is increased by in terms of x and y.
18. Approximate the number approached by the sequence
4
6
8
2n
3
4
5
n 1
,
,
,...,
.
2
3
4
n
19. The length of a rectangle is 5 ft. more than twice its width. Find the width of
the rectangle if the perimeter of the rectangle is 163 ft.
20. The domain of the function whose
graph is shown is 0,6 . At which
of the numbers does the function
appear to have a maximum value.
1
21. Find tan
4
5
accurate to the nearest thousandths.
3
5
22. Find the measure in radians of the angle
.
(4,5)
23. Use trigonometric properties and/or identities to simplify 1 tan 2 .
24. Find the area of the rectangle that
is formed by the origin and the
intersection of the functions
y asinx and y acosx
y
y
a sin x
a cos x
25. Use trigonometric properties and/or identities to simplify sin
tan
csc 2 .
There is a link to the answers on the Mathematics Department home page. A
score of 15 or more out of 25 will indicate readiness to enroll in Calculus 1, or
Math 163, at Ohio Northern University.