Ohio Northern University

Department of Mathematics

Calculus Readiness Test

General Instructions:   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 on the Mathematics Department home page.  A score of 15 or more out of 25  indicates readiness to enroll in Math 163 - Calculus 1 - at Ohio Northern University.

1.  Find the point of intersection in the first quadrant of the line y=4x+2 and the curve y = x^2.

2.  If f is a function whose graph is shown below, then find when f(x)>0.

[Maple Plot]

3.   Suppose f(x) = 3*x^3+2 and g(x) = (x-1)^2.  If  h(x) = f ( g ( x ) ), then find h(1.7).

4.   Find x if    2^5000 = 10^x .

5.   Describe as specifically as possible the graph of y = x^2+a*x-1 where a is an arbitrary constant.

6.   Find values of x satisfying     (2*x+3)*(x-2)/(x+3) = 0.

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).

[Maple Bitmap]

9.  Definition:  A function is odd  if f(-x) = - f(x)  for each x in the domain of  x.  Use this definition to determine which of these are odd functions:

a)  f(x) = x-6

b)  f(x) = 3*x^3+4*x

c)   f(x) = 9-5*x^2

d)   f(x) = x+4

e)   f(x) = -x^3

10.   Sketch the graph of f(x) = a^x ,  where a > 1.

11.   In the figure shown, what is the distance between the points A and B?  

[Maple Bitmap]

12.   Given f(x) = (5*x-2)/(x+1) , find f(a+3)

13.   The graph of the equation y = (-3/5)*x+b is:

a)  a vertical line

b)  a line falling to the right

c)  a horizontal line

d)  a line rising to the right

e)  not a line

14.   Using the figure shown below, find the sum of the areas of the three shaded rectagles under the curve y = sqrt(x)  .

[Maple OLE 2.0 Object]

15.   Which of the following has a-b as a factor ?

a)   a^2-b^2

b)   a^2+b^2

c)   a^3-b^3

d)   a^3+b^3

16.   Solve the inequality abs(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 following sequence:   (3/2)^4, (4/3)^6, (5/4)^8, ... , ((n+1)/n)^(2*n) , ...

19.  The length of a rectangle is 5 ft. more than twice its width.  Find the width of the rectangle if the perimeter is 163 ft.

20.   The graph of the function y = f(x)  is sketched below.  The domain of f is [0,6].  At what value of x does f(x) appear to achieve its maximum value?

[Maple OLE 2.0 Object]

21.   Find   tan(4*Pi/5) accurate to the nearest thousandth.

22.  Find the measure in radians of the angle alpha shown below.

[Maple OLE 2.0 Object]

23.   Use trigonometric properties and/or identities to simplify  1+ tan^2*theta .

24.   The rectangle shown below has one vertex at the origin and another vertex at the intersection of the curves y = a*cos(x) and y = a*sin(x).  Find the area of the rectangle.

[Maple OLE 2.0 Object]

25.   Use trigonometric properties and/or identities to simplify   sin*theta*tan*theta*csc^2*theta     

Please recall that a link to the answers may be found on the Mathematics Department home page!