Math Placement Questions

So you want to major in math, engineering, computer science, biology, or chemistry. What math course should you start in? With a solid math background and strong test scores, you should start in MA 131 Accelerated Calculus. With a weaker background and lower test scores, but with precalculus preparation, you should take your calculus over a full year with the MA 121 – MA 122 sequence. Without a background in precalculus (strong algebra and trigonometry), you should take MA 117 Difference Equations and Linear Algebra, followed by MA 112 Precalculus.

What if you’re not sure how strong your background is or how ready you are for an accelerated calculus course? Use the questions below as a guide. It’s reasonable to need to look up a few things to refresh your memory. If you don’t have too much trouble with these problems (only need to look up a few things, or easily remember the ideas once you’ve looked them up), then you’re probably going to be in good shape in MA 131. If you have to look up several things and still have trouble with a few of the questions, but you know you have seen all of this material before, then you would be best off in the MA 121 – MA 122 sequence for calculus. This sequence will begin with a precalculus review before launching into calculus. If, however, you look at these questions and see concepts that you really don’t understand, or that you have never seen before, then you should start with MA 117 followed by MA 112 to be sure that you have the proper background before taking a calculus course.

  1. Solve the equation for x: .
  2. Write the equation of the line with slope 3 through the point (-1, 1).
  3. Write the equation of the line through the points (-2, 1) and (2, -2).
  4. A car starts from point P at time t = 0 and travels at 45 mph.
  5. Write an expression d(t) for the distance the car travels from P in t hours.
  6. Graph d(t).
  7. Express the side length of a square as a function of the length d of the square’s diagonal. Then express the area as a function of the diagonal length.
  8. Find the domain and range of the function .
  9. For a curve to be symmetric about the x-axis, the point (x, y) must lie on the curve if and only if the point (x, -y) lies on the curve. Explain why a curve that is symmetric about the x-axis is not the graph of a function, unless the function is y = 0.
  10. If f (x) = x – 1 and g(x) = 1/(x + 1), find f (g(3)).
  11. Simplify .
  12. The number of bacteria in a petri dish culture after t hours is B = 100e0.693t.
  13. What was the initial number of bacteria present?
  14. How many bacteria are present after 6 hours?
  15. When will the number of bacteria be 200? Determine this algebraically and confirm your answer graphically.
  16. Sketch, by hand, the graphs of sin(x) and cos(x).
  17. A person’s shadow is 40 inches long. An ant stands at the tip of the shadow and looks up from the ground at an angle of 50 degrees to exactly see the top of the person’s head. How tall is this person?

Math Placement Questions

Answers

  1. x = –6 or x = 2
  2. y = 3x + 4
  1. a. d(t) = 45t

b.

  1. ;
  1. Domain: [-2, 2]; Range: [0, 2]
  1. Unless y = 0, a curve that is symmetric about the x-axis has two y-values for each x-value (two outputs for each input).
  1. x5
  1. a. 100 bacteria
  1. 6394 bacteria
  2. 1 hour

The person is 47.8 inches tall.