EOCT Study Guide Topic Checklist
Algebra Unit 1 –Unit 4 in Purple Book
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Be able to write the square root of a negative number in imaginary form
Solve quadratic equations that have imaginary solutions and be able to simplify the
answers
Add, subtract, and multiply complex numbers
Divide complex numbers (Use the complex conjugates to simplify)
Be able to simplify complex numbers such as i2 , i3, i4, i58, i99, etc
Graph a piecewise function given the equation
Write the rule for a piecewise function given the graph
Write a piecewise function to represent the graph of an absolute value function
Graph the greatest integer function (the “round down” function) and recognize that it is a
piecewise function
Identify the domain, range, and x and y intercepts of piecewise function
Identify intervals in which a function is constant, increasing, or decreasing
Solve absolute value equations and inequalities
Model real life situations using exponential functions
Use exponent rules to simplify expressions
Graph exponential equations. Find domain, range, asymptotes and intercepts
Use transformations to sketch exponential curves
Solve simple exponential equations and inequalities
Solve equations involving compound interest
Understand that and exponential function creates a geometric sequence (identify a
pattern in the outputs of and exponential function)
Graph quadratic functions by using transformations
Identify translations, stretches/ compressions, and reflections
Convert between standard form ax2 + bx + c and vertex form a(x-h)2 + k by completing
the square
For Quadratics: Identify Domain, Range, Zeroes, x and y intercepts, maximum/minimum
points, the axis of symmetry, and intervals of increase and decrease
Solve quadratic equations by factoring, graphing, or quadratic formula
Solve quadratic inequalities
Determine the pattern in an arithmetic sequence (linear sequence) and be able to find any
term
Find the sum of the first n terms of an arithmetic sequence
Be able to perform composition of functions
Find the inverse of a function and understand the relationship between a function and its
inverse
Recognize that the domain and range of a function’s inverse are the reverse of the
function’s domain and range, and that the graph of the inverse is a reflection of the
function over the line y = x
Use composition of functions to verify that two functions are inverses of each other
Be able to identify when a relation is a function
Know the term “one – to –one”. If a function is “one to one” its inverse is also a function
(the function passes the vertical and horizontal line test!)
Understand when to restrict the domain of a function or the function’s inverse
Geometry Unit 5 and 6 in Purple Book
□ Memorize and use the ratios of a 30-60-90 triangle ( x, x 3, 2 x )
□ Memorize and use the ratios of a 45-45-90 triangle ( x, x, x 2 )
□ Solve a right triangle using sine, cosine, and tangent
□ Be able to sketch a real life situation using angle of elevation and angle of
depression
□ Know all circle rules! See below
x
x
y
y
□ Find the length of an arc or area of a circle sector using proportions
□ Find the surface area and volume of a sphere
□ Determine the effect on surface area and volume of doubling, tripling, etc the
radius of the sphere
Data Analysis and Probability Unit 7 in Purple Book
□ Calculate mean, median, mode, standard deviation, and mean absolute deviation
□ Be able to estimate means and standard deviations from graphs and charts
□ Understand stem and leaf plots, histograms, box and whisker plot
□ Understand the central limit theorem (The standard deviation of a population is
larger than the standard deviation of a group of sample means taken form the
population  x 
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Model a data set using a linear or quadratic function. Be able to find the function
when given a table of values
Calculate the median-median line by hand
Understand positive and negative, weak and strong correlation
Distinguish between correlation and causation