Math 117A – Study Guide for Competency Test

  • All problems in the test are story (word) problems.
  • Read carefully, and respect the instructions given in the problems. If they say YEARS SINCE ______, the x-values count the number of years after the given base year
  • Round as indicated, otherwise you will lose ½ a point (make sure you follow round off rules!!!)
  • If the round-off rule is not specified in the problem, use your criteria – no points will be deducted
  • Statements like this will appear on your test:

Use a complete sentence and correct units to interpret in context.

All interpretations should be given in context with correct units

  • Statements like this will be in your test:
  • Algebraic steps should be shown in parts b and c

If algebraic steps are required, show them. You will only be given one point for a correct answer which is not supported by algebraic process; the remaining points will be lost.

  • If algebraic work is not required, points will not be deducted if correct answers are given without supporting work

Question-types characteristic of Linear Functions F(x) = mx + b

  1. Use algebra (not the calculator) to find the equation of a linear model going through any two points.
  2. Give the value of the slope of the linear model and interpret in context with correct units.
  3. Find the average rate of change of y with respect to x and interpret in context with correct units.

Question-types characteristic of Exponential Functions:

  1. Use algebra (not the calculator) to find the equation of an exponential model going through two points with one of them being the y-intercept
  2. Interpret in context the coefficient a
  3. Interpret in context the base b
  4. Constructing the exponential model for a compound interest problem
  5. Given an exponential function with base e: , show algebraic steps to answer:

a)For a given x value, find the y-value

b)For a given y-value, find the x-value

Question-types characteristic of Quadratic Functions:

  1. Use algebra to find the vertex and interpret in context

The following types of questions apply to any of the three function-types mentioned above:

  1. Identify the independent variable and its units
  2. Identify the dependent variable and its units
  3. Use the regression feature of your calculator to find the best model that fits the data

a)You need to look at the scatter-diagram in order to decide which model to use: linear, exponential or quadratic (a grid will be provided on your paper)

b)Then, find the model equation by using LinReg, QuadReg, or ExpReg

  1. Find the y-intercept of the model and interpret in context with correct units.
  2. Find the x-intercept of the model and interpret in context with correct units (does not apply to exponential functions because the model that we studied does not have an x-intercept)
  3. For a given x, find the y value
  4. For a given y, find the x-value
  5. Evaluate F(#) and interpret in context
  6. Find x when F(x) = #, and interpret in context