arith067 Simplifying a fraction
arith092 Using a common denominator to order fractions
arith230 Addition or subtraction of fractions with different denominators
arith053 Fraction multiplication
arith022 Fraction division
arith100 Fractional part of a circle
arith226 Converting between percentages and decimals
arith698 Applying the percent equation
arith074 Finding the sale price without a calculator given the original price and percent discount
arith031 Finding the original price given the sale price and percent discount
arith225 Finding the percentage increase or decrease: Advanced
arith228 Word problem on unit rates associated with ratios of whole numbers: Decimal answers
alge272 Solving a proportion of the form x/a = b/c
arith610 Word problem on proportions: Problem type 1
arith611 Word problem on proportions: Problem type 2
arith108 Integer addition: Problem type 2
arith690 Integer subtraction: Problem type 3
arith116 Signed fraction addition or subtraction: Basic
arith106 Signed fraction addition or subtraction: Advanced
arith234 Signed decimal addition and subtraction with 3 numbers
arith231 Integer multiplication and division
arith822 Signed fraction multiplication: Basic
arith105 Signed fraction multiplication: Advanced
arith702 Exponents and integers: Problem type 1
arith703 Exponents and integers: Problem type 2
arith704 Exponents and signed fractions
arith600 Order of operations with integers and exponents
alge005 Evaluating a linear expression: Integer multiplication with addition or subtraction
alge004 Evaluating a quadratic expression: Integers
arith071 Absolute value of a number
arith104 Operations with absolute value: Problem type 2
alge001 Identifying numbers as integers or non-integers
alge002 Identifying numbers as rational or irrational
alge187 Properties of addition
alge188 Properties of real numbers

alge010 Additive property of equality with integers
alge012 Multiplicative property of equality with signed fractions
alge006 Solving a two-step equation with integers
alge208 Solving a two-step equation with signed fractions
alge200 Solving an equation to find the value of an expression
alge011 Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution
alge061 Solving a linear equation with several occurrences of the variable: Variables on both sides and fractional coefficients
alge013 Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution
alge209 Solving a linear equation with several occurrences of the variable: Variables on both sides and two distributions
alge179 Solving a linear equation with several occurrences of the variable: Fractional forms with binomial numerators
alge742 Solving equations with zero, one, or infinitely many solutions
alge743 Algebraic symbol manipulation: Problem type 1
alge744 Algebraic symbol manipulation: Problem type 2
alge014 Solving a word problem with two unknowns using a linear equation
alge219 Solving a decimal word problem using a linear equation with the variable on both sides
alge173 Solving a decimal word problem using a linear equation of the form Ax + B = C
alge704 Solving a fraction word problem using a linear equation with the variable on both sides
alge794 Solving a value mixture problem using a linear equation
alge020 Solving a linear inequality: Problem type 2
alge021 Solving a linear inequality: Problem type 3
alge207 Solving a linear inequality: Problem type 4
alge166 Graphing a compound inequality on the number line
alge746 Solving a compound linear inequality: Graph solution, basic
alge747 Solving a compound linear inequality: Interval notation
alge729 Writing a multi-step inequality for a real-world situation
alge749 Solving a decimal word problem using a two-step linear inequality
alge750 Solving a decimal word problem using a linear inequality with the variable on both sides
alge270 Solving an absolute value equation of the form a|x| = b or |x|+a = b
alge103 Solving an absolute value equation of the form |ax+b| = c
alge167 Solving an absolute value equation of the form |ax+b| = |cx+d|
alge170 Solving an absolute value inequality: Basic

alge790 Evaluating expressions with exponents of zero
arith042 Evaluating an expression with a negative exponent: Positive fraction base
arith043 Evaluating an expression with a negative exponent: Negative integer base
arith029 Ordering numbers with positive exponents
arith024 Ordering numbers with negative exponents
alge024 Introduction to the product rule of exponents
alge030 Product rule with positive exponents: Multivariate
alge028 Product rule with negative exponents
alge026 Quotient of expressions involving exponents
alge755 Quotient rule with negative exponents: Problem type 1
alge754 Introduction to the power rules of exponents
alge027 Power rules with positive exponents
alge025 Power of a power rule with negative exponents
alge799 Power rules with negative exponents
alge756 Power and product rules with positive exponents
alge757 Power, product, and quotient rules with negative exponents
arith036 Scientific notation with positive exponent
arith037 Scientific notation with negative exponent
scinot002 Multiplying and dividing numbers written in scientific notation
alge758 Degree and leading coefficient of a univariate polynomial
alge031 Degree of a multivariate polynomial
alge663 Combining like terms: Advanced
alge798 Simplifying a sum or difference of two univariate polynomials
alge029 Simplifying a sum or difference of three univariate polynomials
alge735 Multiplying a univariate polynomial by a monomial with a positive coefficient
alge835 Multiplying a multivariate polynomial by a monomial
alge033 Multiplying binomials with leading coefficients of 1
alge764 Multiplying conjugate binomials: Univariate
alge032 Squaring a binomial: Univariate
alge180 Multiplication involving binomials and trinomials in two variables
alge736 Introduction to the GCF of two monomials
alge037 Greatest common factor of two multivariate monomials
alge738 Factoring out a monomial from a polynomial: Univariate
alge739 Factoring out a monomial from a polynomial: Multivariate
alge705 Factoring a quadratic with leading coefficient 1
alge040 Factoring a quadratic with leading coefficient greater than 1
alge041 Factoring a product of a quadratic trinomial and a monomial
alge624 Factoring a difference of squares
alge038 Factoring a polynomial by grouping: Problem type 1
alge042 Factoring with repeated use of the difference of squares formula
alge044 Factoring a sum or difference of two cubes
alge681 Solving an equation written in factored form
alge045 Finding the roots of a quadratic equation with leading coefficient 1
alge048 Finding the roots of a quadratic equation with leading coefficient greater than 1
alge211 Solving a quadratic equation needing simplification
alge781 Solving an equation that can be written in quadratic form: Problem type 1
alge092 Solving a quadratic equation using the square root property: Exact answers, basic
alge227 Solving a quadratic equation using the square root property: Exact answers, advanced
alge094 Completing the square
alge780 Solving a quadratic equation by completing the square: Exact answers
alge095 Applying the quadratic formula: Exact answers
alge214 Discriminant of a quadratic equation
alge163 Writing a quadratic equation given the roots and the leading coefficient
alge703 Solving a word problem using a quadratic equation with rational roots
alge524 Solving a word problem using a quadratic equation with irrational roots
alge784 Solving a quadratic inequality written in factored form
alge771 Solving a quadratic inequality

alge067 Plotting a point in the coordinate plane
alge066 Finding a solution to a linear equation in two variables
alge216 Determining whether given points lie on one, both, or neither of 2 lines given equations
alge197 Graphing a line given its x- and y-intercepts
alge194 Graphing a line given its equation in slope-intercept form
alge195 Graphing a line given its equation in standard form
alge196 Graphing a line through a given point with a given slope
alge198 Graphing a vertical or horizontal line
alge069 Finding the y-intercept of a line given its equation
alge210 Finding x- and y-intercepts of a line given the equation: Advanced
alge684 Finding slope given the graph of a line on a grid
alge685 Finding slope given two points on the line
alge631 Finding the slope of a line given its equation
alge070 Writing an equation of a line given the y-intercept and another point
alge071 Writing the equation of a line given the slope and a point on the line
alge072 Writing the equation of the line through two given points
alge073 Writing the equations of vertical and horizontal lines through a given point
geom807 Finding slopes of lines parallel and perpendicular to a line given in the form Ax + By = C
geom808 Writing equations of lines parallel and perpendicular to a given line through a point
alge701 Writing an equation and drawing its graph to model a real-world situation: Advanced
alge805 Application problem with a linear function: Finding a coordinate given the slope and a point
alge806 Application problem with a linear function: Finding a coordinate given two points
alge018 Graphing a linear inequality in the plane: Standard form
alge225 Graphing a linear inequality in the plane: Vertical or horizontal line
alge725 Graphically solving a system of linear equations
alge751 Solving a system of linear equations using substitution
alge076 Solving a system of linear equations using elimination with multiplication and addition
alge753 Solving a 3x3 system of linear equations: Problem type 1
alge752 Solving a 2x2 system of linear equations that is inconsistent or consistent dependent
alge078 Solving a word problem involving a sum and another basic relationship using a system of linear equations
alge184 Solving a value mixture problem using a system of linear equations
alge224 Solving a distance, rate, time problem using a system of linear equations
alge192 Solving a percent mixture problem using a system of linear equations
alge172 Solving a tax rate or interest rate problem using a system of linear equations
alge793 Solving a word problem using a 3x3 system of linear equations: Problem type 1
alge263 Interpreting the graphs of two functions
alge079 Graphing a system of two linear inequalities: Basic

set001 Set builder notation
set002 Union and intersection of finite sets
set004 Set builder and interval notation
set005 Union and intersection of intervals
fun032 Identifying functions from relations
fun010 Vertical line test
pcalc760 Evaluating functions: Linear and quadratic or cubic
pcalc682 Evaluating functions: Absolute value, rational, radical
fun030 Evaluating a piecewise-defined function
fun033 Variable expressions as inputs of functions: Problem type 1
fun016 Domain and range from ordered pairs
pcalc761 Finding inputs and outputs of a function from its graph
pcalc750 Finding intercepts of a nonlinear function given its graph
pcalc751 Finding where a function is increasing, decreasing, or constant given the graph: Interval notation
pcalc752 Finding local maxima and minima of a function given the graph
fun024 Domain and range from the graph of a continuous function
fun025 Domain and range from the graph of a piecewise function
alge185 Writing an equation for a function after a vertical translation
fun020 Writing an equation for a function after a vertical and horizontal translation
pcalc769 Translating the graph of a function: One step
pcalc770 Translating the graph of a function: Two steps
pcalc771 Transforming the graph of a function by reflecting over an axis
pcalc772 Transforming the graph of a function by shrinking or stretching
alge277 Finding the x-intercept(s) and the vertex of a parabola
pcalc793 Using a graphing calculator to find the x-intercept(s) and vertex of a quadratic function
alge252 Graphing a parabola of the form y = ax2
alge253 Graphing a parabola of the form y = (x-h)2 + k
pcalc746 Graphing a parabola of the form y = ax2 + bx + c: Integer coefficients
pcalc747 Graphing a parabola of the form y = ax2 + bx + c: Rational coefficients
pcalc774 Rewriting a quadratic function to find the vertex of its graph
pcalc762 Range of a quadratic function
alge702 Classifying the graph of a function
alge262 Graphing a cubic function of the form y = ax3
alge168 Graphing an absolute value equation in the plane: Advanced
fun031 Graphing a piecewise-defined function: Problem type 1
pcalc764 Finding zeros of a polynomial function written in factored form
pcalc765 Finding x- and y-intercepts given a polynomial function
pcalc782 Determining the end behavior of the graph of a polynomial function
pcalc738 Inferring properties of a polynomial function from its graph
pcalc795 Using a graphing calculator to find zeros of a polynomial function
pcalc704 Using a graphing calculator to solve a word problem involving a polynomial of degree 3
pcalc794 Using a graphing calculator to find local extrema of a polynomial function
pcalc115 Using a graphing calculator to solve a word problem involving a local extremum of a polynomial function
fun019 Sum, difference, and product of two functions
alge786 Quotient of two functions: Basic
fun022 Composition of two functions: Basic
alge129 Composition of two functions: Advanced
fun011 Horizontal line test
pcalc777 Determining whether two functions are inverses of each other
fun012 Inverse functions: Linear, discrete
alge130 Inverse functions: Rational

alge715 Domain of a rational function: Excluded values
alge710 Simplifying a ratio of polynomials: Problem type 1
alge682 Simplifying a ratio of polynomials: Problem type 2
alge034 Simplifying a ratio of multivariate polynomials
alge059 Ordering fractions with variables
alge053 Multiplying rational expressions involving multivariate monomials
alge620 Multiplying rational expressions involving quadratics with leading coefficients of 1
alge054 Dividing rational expressions involving multivariate monomials
alge766 Dividing rational expressions involving quadratics with leading coefficients of 1
alge737 Introduction to the LCM of two monomials
alge055 Least common multiple of two monomials
alge056 Adding rational expressions with common denominators and binomial numerators
alge057 Adding rational expressions with different denominators: ax, bx
alge226 Adding rational expressions with multivariate monomial denominators: Advanced
alge622 Adding rational expressions with different denominators: x+a, x+b
arith695 Complex fraction without variables: Problem type 1
arith696 Complex fraction without variables: Problem type 2
alge058 Complex fraction involving multivariate monomials
alge767 Complex fraction: GCF and quadratic factoring
alge768 Complex fraction made of sums involving rational expressions
alge759 Dividing a polynomial by a monomial: Univariate
alge761 Polynomial long division: Problem type 1
alge762 Polynomial long division: Problem type 2
alge060 Solving a rational equation that simplifies to linear: Denominator x
alge205 Solving a rational equation that simplifies to linear: Denominator x+a
alge206 Solving a rational equation that simplifies to linear: Unlike binomial denominators
alge769 Solving a rational equation that simplifies to linear: Denominators a, x, or ax
alge212 Solving a rational equation that simplifies to quadratic: Binomial denominators, constant numerators
alge062 Solving a rational equation that simplifies to quadratic: Binomial denominators and numerators
alge047 Solving a rational equation that simplifies to quadratic: Proportional form, advanced
pcalc812 Partial fraction decomposition with distinct linear factors
pcalc813 Partial fraction decomposition with repeated linear factors
pcalc814 Partial fraction decomposition with an irreducible quadratic factor
pcalc681 Writing an equation that models variation
alge175 Word problem on direct variation
alge176 Word problem on inverse variation
alge772 Word problem on combined variation
alge220 Word problem on inverse proportions
arith612 Word problem involving multiple rates
pcalc815 Sketching the graph of a rational function: Constant over linear
pcalc816 Sketching the graph of a rational function: Linear over linear
pcalc819 Sketching the graph of a rational function: Quadratic over linear
pcalc792 Graphing rational functions with holes

pcalc763 Domain of a square root function: Advanced
pcalc781 Graphing a square root function
arith601 Square root of a rational perfect square
arith094 Cube root of an integer
arith093 Simplifying the square root of a whole number less than 100
alge264 Square root of a perfect square monomial
alge080 Simplifying a radical expression with an even exponent
alge275 Simplifying a radical expression with two variables
alge273 Simplifying a higher root of a whole number
alge811 Simplifying a higher radical expression: Multivariate
arith032 Square root addition or subtraction
alge084 Simplifying a sum or difference of radical expressions: Multivariate
arith039 Square root multiplication: Advanced
alge640 Simplifying a product of radical expressions: Multivariate
alge276 Simplifying a product involving square roots using the distributive property: Advanced
alge774 Special products of radical expressions: Conjugates and squaring
alge086 Rationalizing the denominator of a radical expression
alge088 Rationalizing the denominator of a radical expression using conjugates
alge775 Rationalizing a denominator: Quotient involving higher radicals and monomials
alge812 Converting between radical form and exponent form
alge250 Rational exponents: Non-unit fraction exponent with a whole number base
alge251 Rational exponents: Negative exponents and fractional bases
alge773 Rational exponents: Products and quotients with negative exponents
alge249 Rational exponents: Powers of powers with negative exponents
alge089 Solving a radical equation that simplifies to a linear equation: One radical, basic
alge090 Solving a radical equation that simplifies to a linear equation: Two radicals
alge091 Solving a radical equation that simplifies to a quadratic equation: One radical
alge093 Solving an equation using the odd-root property: Problem type 1
alge778 Using i to rewrite square roots of negative numbers
alge779 Simplifying a product and quotient involving square roots of negative numbers
pcalc048 Adding or subtracting complex numbers
pcalc049 Multiplying complex numbers
pcalc050 Dividing complex numbers
pcalc053 Simplifying a power of i
pcalc051 Solving a quadratic equation with complex roots

alge108 Converting between logarithmic and exponential equations
pcalc799 Converting between natural logarithmic and exponential equations
alge232 Evaluating a logarithmic expression
pcalc708 Basic properties of logarithms
pcalc779 Expanding a logarithmic expression: Problem type 1
alge787 Writing an expression as a single logarithm
pcalc612 Change of base for logarithms: Problem type 1
pcalc613 Change of base for logarithms: Problem type 2
alge233 Solving an equation of the form logba = c
alge113 Solving an equation involving logarithms on both sides: Problem type 1
pcalc803 Solving a multi-step equation involving a single logarithm
pcalc804 Solving a multi-step equation involving natural logarithms
pcalc805 Solving an equation involving logarithms on both sides: Problem type 2
alge111 Solving an exponential equation by using logarithms: Exact answers in logarithmic form
alge112 Solving an exponential equation by finding common bases: Linear and quadratic exponents
alge789 Solving exponential equations by using logarithms and natural logarithms: Decimal answers
pcalc798 Evaluating an exponential function that models a real-world situation
alge177 Finding a final amount in a word problem on exponential growth or decay
alge178 Finding the time to reach a limit in a word problem on exponential growth or decay
pcalc614 Finding the initial or final amount in a word problem on exponential growth or decay
pcalc615 Finding the rate or time in a word problem on continuous exponential growth or decay
alge712 Graphing an exponential function and its asymptote: f(x) = a(b)x
pcalc797 The graph, domain, and range of an exponential function
pcalc103 Graphing an exponential function and its asymptote: f(x) = a(e)x-b + c
pcalc800 The graph, domain, and range of a logarithmic function
pcalc104 Graphing a logarithmic function: Advanced
pcalc102 Translating the graph of a logarithmic or exponential function

geom300 Perimeter of a square or a rectangle
geom019 Area of a square or a rectangle
geom340 Area of a piecewise rectangular figure
geom351 Areas of rectangles with the same perimeter
geom817 Finding a side length given the perimeter and side lengths with variables
geom217 Finding the side length of a rectangle given its perimeter or area
geom143 Finding the perimeter or area of a rectangle given one of these values
geom022 Area of a parallelogram
geom801 Area of a triangle
geom802 Circumference and area of a circle
geom218 Finding the radius or the diameter of a circle given its circumference
geom301 Perimeter involving rectangles and circles
geom838 Circumference ratios
geom302 Area involving rectangles and circles
geom036 Word problem involving the area between two concentric circles
geom214 Area involving inscribed figures
geom311 Volume of a rectangular prism
geom035 Volume of a cylinder
geom086 Volume of a cone: Exact answers in terms of pi
geom841 Volume of a sphere
geom092 Word problem involving the rate of filling or emptying a cylinder
geom133 Ratio of volumes
geom031 Surface area of a cube or a rectangular prism
geom034 Surface area of a cylinder: Exact answers in terms of pi
geom037 Similar polygons
geom337 Indirect measurement
geom044 Pythagorean Theorem
alge132 Distance between two points in the plane: Exact answers
alge191 Midpoint of a line segment in the plane
pcalc605 Graphing a circle given its equation in standard form
pcalc064 Graphing a circle given its equation in general form
pcalc065 Writing an equation of a circle given its center and a point on the circle
pcalc066 Writing an equation of a circle given the endpoints of a diameter

pcalc002 Converting between degree and radian measure: Problem type 1
pcalc006 Sketching an angle in standard position
pcalc626 Reference angles: Problem type 1
pcalc622 Coterminal angles
pcalc005 Arc length and central angle measure
pcalc623 Area of a sector of a circle
pcalc600 Sine, cosine, and tangent ratios: Variables for side lengths
pcalc607 Using a trigonometric ratio to find a side length in a right triangle
pcalc610 Using trigonometry to find a length in a word problem with one right triangle
pcalc608 Using a trigonometric ratio to find an angle measure in a right triangle
pcalc611 Using trigonometry to find angles of elevation or depression in a word problem
pcalc008 Finding trigonometric ratios given a right triangle
pcalc642 Solving a right triangle
pcalc031 Solving a triangle with the law of sines: Problem type 1
pcalc033 Solving a triangle with the law of cosines
pcalc627 Finding coordinates on the unit circle for special angles
pcalc629 Trigonometric functions and special angles: Problem type 1
pcalc630 Trigonometric functions and special angles: Problem type 2
pcalc631 Trigonometric functions and special angles: Problem type 3
pcalc011 Finding values of trigonometric functions given information about an angle: Problem type 1
pcalc012 Finding values of trigonometric functions given information about an angle: Problem type 2
pcalc013 Finding values of trigonometric functions given information about an angle: Problem type 3
pcalc633 Amplitude and period of sine and cosine functions
pcalc634 Amplitude, period, and phase shift of sine and cosine functions
pcalc107 Sketching the graph of y=a*sin(x+c) or y=a*cos(x+c)
pcalc106 Sketching the graph of y=a*sin(bx) or y=a*cos(bx)
pcalc016 Values of inverse trigonometric functions
pcalc018 Composition of a trigonometric function with its inverse trigonometric function: Problem type 1
pcalc019 Composition of a trigonometric function with the inverse of another trigonometric function: Problem type 2
pcalc036 Composition of a trigonometric function with the inverse of another trigonometric function: Problem type 3
pcalc648 Simplifying trigonometric expressions
pcalc666 Using cofunction identities
pcalc029 Sum and difference identities: Problem type 1
pcalc663 Sum and difference identities: Problem type 2
pcalc030 Double-angle identities: Problem type 1
pcalc667 Double-angle identities: Problem type 2
pcalc124 Product-to-sum and sum-to-product identities: Problem type 1
pcalc650 Finding solutions in an interval for a basic equation involving sine or cosine
pcalc651 Finding solutions in an interval for a basic tangent, cotangent, secant, or cosecant equation
pcalc654 Finding solutions in an interval for a trigonometric equation using Pythagorean identities: Problem type 1
pcalc020 Solving a basic trigonometric equation involving sine or cosine
pcalc021 Solving a basic trigonometric equation involving tangent, cotangent, secant, or cosecant
pcalc055 Plotting a point in polar coordinates
pcalc056 Converting rectangular coordinates to polar coordinates: Special angles
pcalc057 Converting polar coordinates to rectangular coordinates
pcalc058 Converting an equation written in rectangular form to one written in polar form
pcalc059 Converting an equation written in polar form to one written in rectangular coordinates

pcalc901 Estimating a limit numerically
pcalc902 Finding limits from a graph
pcalc904 Finding limits for a piecewise-defined function
pcalc905 Finding a limit by using the limit laws: Problem type 1
pcalc906 Finding a limit by using the limit laws: Problem type 2
pcalc907 Finding a limit by using the limit laws: Problem type 3
pcalc911 Squeeze Theorem
pcalc903 Determining points of discontinuity from a graph
pcalc914 Determining a parameter to make a function continuous
pcalc910 Limits at infinity and graphs
pcalc908 Limits at infinity and rational functions
pcalc915 Infinite limits and graphs
pcalc909 Infinite limits and rational functions
pcalc913 Finding a limit of a trigonometric function by using continuity
pcalc912 Finding a limit by using special trigonometric limits