Algebra Topics
This is a list of topics that may be tested on the Algebra exam, along with a few examples of what types
of questions we might ask to test them. It is meant to be roughly complete but may not be exhaustive.
The sections on the exam may not mirror these sections or the ones used on the example exam. Topics
and assessment ideas listed under one section here could be combined with those under other sections.
Any of these topics could be tested via word problems.
Each section also includes links to some study materials from Khan Academy – there’s lots of material,
so pick and choose what you need to review. If you’re looking for a full course of study, the first 6
sections of the Algebra II course (https://www.khanacademy.org/math/algebra2) cover about 90% of
what you need (skipping imaginary & complex numbers, conic sections, and matrices).
Basics of Algebra & Geometry
Topics:
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Rules of algebra
Linear equations
Coefficients and variables
Graphing
Area and volume
Example assessment:
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Simplify expressions using the rules of algebra.
Solve equations of one variable, and solve equations of multiple variables for one of the variables.
Perform algebraic manipulations on equations with coefficients expressed as parameters rather
than as specific values.
Graph equations of two variables.
Calculate and interpret the slope of a line.
Calculate distances between points.
Express the equation of a line in multiple forms.
Find the intercepts for any line.
Identify parallel and perpendicular lines based on their slopes.
Given two points, determine the line through the points.
Resources:
Manipulating expressions: https://www.khanacademy.org/math/algebra-basics/core-algebraexpressions/core-algebra-manipulating-expressions/v/combining-like-terms
Linear equations: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-tofunctions/standard-form (see the earlier videos in this sequence if you need to review point-slope form,
the meaning of slope, or other aspects of linear equations)
Distance & midpoint: https://www.khanacademy.org/math/geometry/analytic-geometry-topic/ccdistances-between-points
Parallel & perpendicular lines: https://www.khanacademy.org/math/geometry/analytic-geometrytopic/parallel-and-perpendicular/v/equations-of-parallel-and-perpendicular-lines
Rational expressions: https://www.khanacademy.org/math/algebra2/rational-expressions
The following resources cover topics we assume most students have already mastered, but that some
students may find helpful to review. We link to the first video in each sequence; you will find more
advanced videos on the left of the screen.
Exponents: https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/world-ofexponents-college-readiness/v/introduction-to-exponents
Order of operations: https://www.khanacademy.org/math/algebra-basics/core-algebrafoundations/algebra-foundations-order-of-operations/v/introduction-to-order-of-operations
Radicals (roots): https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/squareroots-for-college/v/understanding-square-roots
Fractions: https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebrafoundations-fractions/v/adding-fractions-with-unlike-denominators-word-problem
Systems of equations
Topics:
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Solving by substitution
Solving by addition (elimination)
Systems of 2 and 3 variables
Graphical interpretation of systems
Example assessment:
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Solve particular systems, including nonlinear equations
Graph linear systems
Interpret graphs of systems
Convert a graphical system into an algebraic system
Solving by substitution: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systemstopic/cc-8th-systems-with-substitution
Solving by elimination: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systemstopic/cc-8th-systems-elimination
Graphical systems: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systemstopic/cc-8th-systems-graphically
Special cases: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8thsystems-solutions/v/inconsistent-systems-of-equations and https://www.khanacademy.org/math/cceighth-grade-math/cc-8th-systems-topic/cc-8th-systems-solutions/v/infinite-solutions-to-systems
Three variables:
https://www.khanacademy.org/math/algebra2/systems_eq_ineq/fancier_systems_precalc
Non-linear systems: https://www.khanacademy.org/math/algebra2/systems_eq_ineq/non-linearsystems-tutorial
Exponents & Logarithms
Topics:
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Rules of algebra with exponents & logarithms
Expressing roots as exponents / fractional exponents
Negative exponents / expressing division using exponents
Exponents with base 𝑒
Logarithms as the inverse of exponents
Using logarithms to solve problems with variables in the exponent
Logarithms of different bases
The natural log, 𝑙𝑛
Example assessment:
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Simplify expressions with logarithms
Solve equations and inequalities with variables in the exponent
Solve equations with a variable inside a logarithm
Use the rules of algebra with logarithms to expand or contract the terms inside a logarithm
Resources
There’s much more material here than in most of the other sections, because we’ve found that some
students need substantial review on these topics, particularly logarithms. Pick and choose what you
need.
Exponents: https://www.khanacademy.org/math/algebra/exponent-equations
Logarithms: https://www.khanacademy.org/math/algebra2/logarithms-tutorial (skip the last section on
scale & patterns)
Exponential functions:
https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/exp_growth_decay
Logarithmic functions & equations:
https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/log_functions and
https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/logarithmicequations
Summation Notation
Topics:
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Using summation notation to express series and sequences
Formulae for calculating infinite sums
Simplifying complex sums
Calculating sums
Example assessment:
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Compute a numerical sum or expand an abstract sum (finite or infinite)
Simplify a complex expression in summation notation
Express a sequence of terms using summation notation
Translate a scenario described in words to an expression in summation notation
Sigma notation: https://www.khanacademy.org/math/integralcalculus/sequences_series_approx_calc/calculus-series/v/sigma-notation-sum
Writing a series in summation notation: https://www.khanacademy.org/math/integralcalculus/sequences_series_approx_calc/calculus-series/v/writing-series-sigma-notation
Inequalities & Absolute Values
Topics:
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Rules of algebra for inequalities & absolute values
Solving inequalities
Solving equations and inequalities with absolute values
Graphing sets (used to express the solution to an inequality)
Example assessment:
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Solve and graph the solution to equations and inequalities, including those with absolute value
(where the variable may be inside the absolute value, outside the absolute value, or both)
Represent the solutions to inequalities and absolute value problems graphically
Resources
Solving inequalities:
https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-usingmultiplication-and-division
Solving absolute value equations: https://www.khanacademy.org/math/algebra/solving-linearequations-and-inequalities/absolute-value-equations/v/absolute-value-equations
Inequalities with absolute value:
https://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/
v/compound-inequalities
Graphing linear inequalities: https://www.khanacademy.org/math/algebra-basics/core-algebragraphing-lines-slope/core-algebra-graphing-linear-inequalities/v/graphing-inequalities
Quadratic inequalities:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq
Systems of inequalities:
https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_inequalities_precalc
Graphing absolute values:
https://www.khanacademy.org/math/algebra2/functions_and_graphs/piecewise-functionstutorial/e/graphs-of-absolute-value-functions
Functions
Topics:
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The nature of a function
Domain, range
Common functional forms, including polynomial, radical, exponential, logarithmic and
rational
Composite functions
Inverse functions
Example assessment:
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Evaluate a function at a point
Find the 𝑥- and 𝑦- intercepts of the graphs of a function
Find the domain or range of a function
Find a composite
Break a composite function into constituent functions
Based on the graph of a function, quickly determine how the graph changes as the function is
shifted and/or reflected (sum, difference, product, quotient)
Find the inverse of a function where one exists
Resources:
Basics of functions (most people can skip this):
https://www.khanacademy.org/math/algebra2/functions_and_graphs/function-introduction
Domain & range: https://www.khanacademy.org/math/algebra2/functions_and_graphs/domain_range
Composites of functions:
https://www.khanacademy.org/math/algebra2/functions_and_graphs/composing-functions
Inverses of functions:
https://www.khanacademy.org/math/algebra2/functions_and_graphs/function_inverses_2
Shifting & reflecting functions:
https://www.khanacademy.org/math/algebra2/functions_and_graphs/shifting-reflecting-functions
Polynomials
Topics:
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Factoring polynomials
Distributing factored polynomials
Quadratic formula
Solving / roots of polynomials
Binomial theorem
Example assessment:
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Find and interpret the roots of a polynomial
Find intercepts of factored polynomials
Factor a polynomial
Identify the degree of the polynomial
Use the above approaches to solve inequalities and absolute value problems
Identify the maximum number of roots of a generic polynomial
Use the binomial theorem to expand (𝑥 + 𝑦)𝑛 or determine a particular coefficient of the
expansion
Resources
Quadratic factoring: https://www.khanacademy.org/math/algebra/introduction-to-polynomials-andfactorization/factoring-polynomials-2-quadratic-forms and
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring
Quadratic formula:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/v/usin
g-the-quadratic-formula (see later videos in this sequence for more example problems)
Binomial theorem:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/binomia
l-theorem (the subsequent two videos may also be helpful)