Download Practice Test 2 – Topics

Practice Test 2 – Topics - College Algebra Exam 2
1. Be able to tell the difference between a linear, quadratic and cubic equation and know
the techniques for solving each:
a. Linear: One solution  isolate x
b. Quadratic: One solution, 2 complex solutions, 2 real solutions.  Set polynomial to zero in
descending order of power.
i. Methods of solving:
1. Factoring: Only in special cases  two terms, three terms, four terms  2 real
roots/solutions only  set factors = 0 independently
2. Quadratic formula  Can be used on any quadratic equation 0, 1, 2 real or
complex roots/solutions
3. Completing the square  Can be used on any quadratic equation but not advisable if
b/a not a whole number or simple fraction  0, 1, 2 real or complex roots/solutions
4. Square root method  Only used when bx is missing  0, 1, 2 real or complex
roots/solutions Examples: ax2 + c = 0 or (x + b)2 + c = 0
c. Rational: Solutions depend on whether fraction terms simplify to a linear or quadratic equation.
You must check your answers to make sure they are in the domain of the equation!!
i. Solve by multiplying through the numerators by the LCD. Finish solving as linear or
quadratic depending on how the numerators simplify.
d. Third, fourth and fifth degree polynomials:  Can have as many solutions as the highest power.
i. Solve by factoring out the variable as a GCF and then solve as quadratic. Set GCF and any
factors = 0 independently
e. Radical: Solutions depend on whether radical terms simplify to a linear or quadratic equation
i. Solve by isolating the radical and squaring both sides of the equation.
2. Use the discriminant only to determine the number and type of solutions for a quadratic equation
3. Complete the square in the form of (x +A)2 + B = 0 (used for circles and solving quadratic equations)
4. Use quadratic equations to solve area of rectangle, triangle, etc.
5. Complex numbers:
a. Complex number operations – Multiply, divide, addition and subtraction, rationalize the
denominator
b. Simplify ix as i, -i, 1, -1
c. Simplify complex imaginary square roots with multiplication, division, addition and subtraction
6. Given a shape, find the distance/length of the sides and determine if one or more corners are perpendicular.
(See homework)
7. Circles:
a. Find the midpoint
b. Find the equation of a circle given a radius and center or diameter (find the midpoint)
c. Find the center and radius given an equation of a circle
8. Two variable linear equations and graphing
a. Find the equation of the line given:
i. Two points,
ii. y-intercept and slope
iii. Picture of a graph,
iv. Parallel or perpendicular lines
v. Vertical or horizontal line
b. Model a contextual problem with a linear applications
9. Functions
a. Determine if a graph or set of points is a function (vertical line test)
b. Be able to explain in sentence form why an equation or graph is or is not a function
c. Be able to write an equation in function notation.
d. Determine the domain of a function.
i. Find the values for which a rational function is undefined and when a square root function is
undefined.
ii. Find the domain and range of a continuous graph, a graph of points, ordered pairs.
iii. Be able to write domain in interval notation.
e. Given a graph, determine when f(x) has a positive or negative function value and find any relative
maximum or minimum points.
f. Find f(a) and f(x) = b, from a continuous or graph of points.
g. Given a function find f(a), f(a + h),
h. Be able to find the average rate of change of a function
f ( x  h)  f ( x )
h
i. Find f(a) and f(x) = b, from a continuous or graph of points.
10. Symmetry
a. Show algebraically whether or not a function is even, odd or neither
b. Determine even or odd symmetry based on the look of a graph.