Of course you should work through your midterm review packet to study (and check your answers with the key I provided). You can also use all of your old tests and quizzes to study! (That's what I would do!)
Here's a list of exactly what topics are on the midterm: (I am literally typing these topics as I read through your exam...)
- Find the slope of a line given two points
- Find the equation of a line given a point and slope (in slope-intercept or point-slope form)
- Find the equation of a line parallel or perpendicular to a given line
- Challenge: find parallel and perpendicular line when the line you are given is vertical/horizontal
- Determine if lines are parallel, perpendicular, or neither
- Determine if a set of ordered pairs represents a function
- Evaluate functions (sub values for x)
- Find the domain of a function
- Graphically
- Rational functions (fractions), radical functions, and log functions
- Find the range of a function (graphically)
- Determine intervals of increasing, decreasing, constant (given a graph)
- Identify what type of function is shown (know the shapes of the parent functions!)
- Write equations of a function given different shifts/reflections
- Describe the shifts/reflections in a function
- Find compositions of functions
- Find the inverse of a function
- Given an equation
- Switch x and y, solve for y
- Given sets of ordered pairs
- Apply the horizontal line test
- Graph quadratic functions
- Find the vertex
- Find x-intercepts
- Find the y-intercept
- Determine shifts and if the parabola opens up/down
- Find the maximum/minimum value of a quadratic (the vertex!)
- Determine the end-behavior of a polynomial
- Use long division to divide polynomials
- Use synthetic division to divide polynomials
- Factor a polynomial (complete) given one of its factors
- Do (repeated) synthetic division given the factors to arrive at a quadratic, then factor the quadratic
- Determine possible rational zeros (rational zero test)
- Write complex numbers in standard form
- Add/subtract complex numbers
- Multiply complex numbers
- Divide complex numbers (multiply the numerator and denominator by the conjugate of the denominator)
- Simplify powers of I
- Find real zeros of a function
- Factor
- Graphing calculator
- Find all zeros of a function
- Factor (if possible) OR
- Find real zeros first
- Use repeated synthetic division (with the real zeros) to get to a quadratic, then factor or use the quadratic formula to find remaining zeros
- Graph rational functions
- Find horizontal asymptotes
- Find vertical asymptotes
- Find x and y-intercepts
- Substitute values of x to find "additional points"
- Graph!
- Use the laws of logs to expand and condense logarithmic expressions
- Find compound interest
- Continuously Compounded (Pe^rt)
- Compounded n times per year (P(1+r/n)^nt)
- Evaluate logs (with and without a calculator)
- Re-write in exponential form
- Graph logarithmic functions
- Graph exponential functions
- Use the change of base formula to evaluate logs
- Solve exponential equations
- Solve log equations
- Add/subtract functions
- Sketch the graph of a polynomial function
- Find zeros
- Determine multiplicity of zeros (bounce or cross?)
- End behavior
- Find "additional points"
- Evaluate exponential expressions
- BONUS:
- Find the inverse of a function like: y = (x+1)/(x-4)
- You may have to look up how to do this!
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