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
- Use algebra (not the calculator) to find the equation of a linear model going through any two points.
- Give the value of the slope of the linear model and interpret in context with correct units.
- 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:
- 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
- Interpret in context the coefficient a
- Interpret in context the base b
- Constructing the exponential model for a compound interest problem
- 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:
- 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:
- Identify the independent variable and its units
- Identify the dependent variable and its units
- 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
- Find the y-intercept of the model and interpret in context with correct units.
- 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)
- For a given x, find the y value
- For a given y, find the x-value
- Evaluate F(#) and interpret in context
- Find x when F(x) = #, and interpret in context