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2 fractional coefficients Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and two distributions Solving a linear equation with several occurrences of the variable: Fractional forms with binomial numerators Solving equations with zero, one, or infinitely many solutions Algebraic symbol manipulation: Problem type 1 Algebraic symbol manipulation: Problem type 2 Solving a word problem with two unknowns using a linear equation Solving a decimal word problem using a linear equation of the form Ax + B = C Solving a value mixture problem using a linear equation Linear Inequalities (6 topics) Solving a linear inequality: Problem type 2 Solving a linear inequality: Problem type 3 Solving a linear inequality: Problem type 4 Graphing a compound inequality on the number line Solving a compound linear inequality: Graph solution, basic Solving a compound linear inequality: Interval notation Absolute Value Equations and Inequalities (3 topics) Solving an absolute value equation of the form a x = b or x +a = b Solving an absolute value equation of the form ax+b = c Solving an absolute value inequality: Basic Exponents and Polynomials (43 topics) Properties of Exponents (13 topics) Evaluating an expression with a negative exponent: Positive fraction base Evaluating an expression with a negative exponent: Negative integer base Introduction to the product rule of exponents Product rule with positive exponents: Multivariate Product rule with negative exponents Quotient of expressions involving exponents Quotient rule with negative exponents: Problem type 1 Introduction to the power rules of exponents Power rules with positive exponents Power of a power rule with negative exponents Power rules with negative exponents Power and product rules with positive exponents Power, product, and quotient rules with negative exponents Scientific Notation (2 topics) Scientific notation with positive exponent Scientific notation with negative exponent Polynomial Expressions (9 topics) Degree and leading coefficient of a univariate polynomial Combining like terms: Advanced Simplifying a sum or difference of two univariate polynomials Multiplying a univariate polynomial by a monomial with a positive coefficient Multiplying a multivariate polynomial by a monomial Multiplying binomials with leading coefficients of 1 Multiplying conjugate binomials: Univariate Squaring a binomial: Univariate Multiplication involving binomials and trinomials in two variables Factoring (9 topics) Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/10

4 Solving a value mixture problem using a system of linear equations Solving a distance, rate, time problem using a system of linear equations Solving a percent mixture problem using a system of linear equations Interpreting the graphs of two functions Functions and Graphs (34 topics) Sets, Relations, and Functions (10 topics) Union and intersection of finite sets Set builder and interval notation Union and intersection of intervals Identifying functions from relations Vertical line test Evaluating functions: Linear and quadratic or cubic Evaluating functions: Absolute value, rational, radical Evaluating a piecewise defined function Variable expressions as inputs of functions: Problem type 1 Domain and range from ordered pairs Graphs and Transformations (16 topics) Finding intercepts of a nonlinear function given its graph Finding local maxima and minima of a function given the graph Domain and range from the graph of a continuous function Writing an equation for a function after a vertical translation Writing an equation for a function after a vertical and horizontal translation Translating the graph of a function: One step Translating the graph of a function: Two steps Transforming the graph of a function by reflecting over an axis Transforming the graph of a function by shrinking or stretching Finding the x intercept(s) and the vertex of a parabola Graphing a parabola of the form y = ax 2 Graphing a parabola of the form y = (x h) 2 + k Graphing a parabola of the form y = ax 2 + bx + c: Integer coefficients Rewriting a quadratic function to find the vertex of its graph Graphing a cubic function of the form y = ax 3 Graphing an absolute value equation in the plane: Advanced Polynomial Functions (2 topics) Finding zeros of a polynomial function written in factored form Finding x and y intercepts given a polynomial function Combining Functions; Composite Functions; Inverse Functions (6 topics) Sum, difference, and product of two functions Quotient of two functions: Basic Composition of two functions: Basic Composition of two functions: Advanced Inverse functions: Linear, discrete Inverse functions: Rational Rational Expressions (30 topics) Rational Expressions (20 topics) Domain of a rational function: Excluded values Simplifying a ratio of polynomials: Problem type 1 Simplifying a ratio of polynomials: Problem type 2 Simplifying a ratio of multivariate polynomials Multiplying rational expressions involving multivariate monomials Multiplying rational expressions involving quadratics with leading coefficients of 1 Dividing rational expressions involving multivariate monomials Introduction to the LCM of two monomials Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 4/10

7 Converting between degree and radian measure: Problem type 1 Sketching an angle in standard position Reference angles: Problem type 1 Coterminal angles Arc length and central angle measure Right Triangle Trigonometry (7 topics) Sine, cosine, and tangent ratios: Variables for side lengths Using a trigonometric ratio to find a side length in a right triangle Using a trigonometric ratio to find an angle measure in a right triangle Finding trigonometric ratios given a right triangle Solving a right triangle Solving a triangle with the law of sines: Problem type 1 Solving a triangle with the law of cosines Unit Circle Trigonometry (7 topics) Finding coordinates on the unit circle for special angles Trigonometric functions and special angles: Problem type 1 Trigonometric functions and special angles: Problem type 2 Trigonometric functions and special angles: Problem type 3 Finding values of trigonometric functions given information about an angle: Problem type 1 Finding values of trigonometric functions given information about an angle: Problem type 2 Finding values of trigonometric functions given information about an angle: Problem type 3 Graphing Trigonometric Functions (2 topics) Sketching the graph of y= a sin(x+c) or y= a cos(x+c) Sketching the graph of y= a sin(bx) or y= a cos(bx) Inverse Trigonometric Functions (1 topics) Values of inverse trigonometric functions Trigonometric Identities (1 topics) Simplifying trigonometric expressions Trigonometric Equations (4 topics) Finding solutions in an interval for a basic equation involving sine or cosine Finding solutions in an interval for a basic tangent, cotangent, secant, or cosecant equation Finding solutions in an interval for a trigonometric equation using Pythagorean identities: Problem type 1 Solving a basic trigonometric equation involving sine or cosine Other Topics Available(*) (125 additional topics) Real Numbers (8 topics) Fractional part of a circle Finding the percentage increase or decrease: Advanced Word problem on unit rates associated with ratios of whole numbers: Decimal answers Exponents and integers: Problem type 2 Identifying numbers as integers or non integers Identifying numbers as rational or irrational Properties of addition Properties of real numbers Equations and Inequalities (7 topics) Solving an equation to find the value of an expression Solving a decimal word problem using a linear equation with the variable on both sides Solving a fraction word problem using a linear equation with the variable on both sides Writing a multi step inequality for a real world situation Solving a decimal word problem using a two step linear inequality Solving a decimal word problem using a linear inequality with the variable on both sides Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 7/10

9 Rationalizing a denominator: Quotient involving higher radicals and monomials Using i to rewrite square roots of negative numbers Simplifying a product and quotient involving square roots of negative numbers Adding or subtracting complex numbers Multiplying complex numbers Dividing complex numbers Simplifying a power of i Solving a quadratic equation with complex roots Exponentials and Logarithms (7 topics) Change of base for logarithms: Problem type 2 Solving an equation involving logarithms on both sides: Problem type 1 Solving an exponential equation by finding common bases: Linear and quadratic exponents Finding the initial or final amount in a word problem on exponential growth or decay Finding the rate or time in a word problem on continuous exponential growth or decay Graphing an exponential function and its asymptote: f(x) = a(e) x b + c Graphing a logarithmic function: Advanced Geometry (13 topics) Areas of rectangles with the same perimeter Finding a side length given the perimeter and side lengths with variables Finding the radius or the diameter of a circle given its circumference Circumference ratios Area involving rectangles and circles Word problem involving the area between two concentric circles Volume of a cone: Exact answers in terms of pi Volume of a sphere Word problem involving the rate of filling or emptying a cylinder Ratio of volumes Midpoint of a line segment in the plane Writing an equation of a circle given its center and a point on the circle Writing an equation of a circle given the endpoints of a diameter Trigonometry (20 topics) Area of a sector of a circle Using trigonometry to find a length in a word problem with one right triangle Using trigonometry to find angles of elevation or depression in a word problem Amplitude and period of sine and cosine functions Amplitude, period, and phase shift of sine and cosine functions Composition of a trigonometric function with its inverse trigonometric function: Problem type 1 Composition of a trigonometric function with the inverse of another trigonometric function: Problem type 2 Composition of a trigonometric function with the inverse of another trigonometric function: Problem type 3 Using cofunction identities Sum and difference identities: Problem type 1 Sum and difference identities: Problem type 2 Double angle identities: Problem type 1 Double angle identities: Problem type 2 Product to sum and sum to product identities: Problem type 1 Solving a basic trigonometric equation involving tangent, cotangent, secant, or cosecant Plotting a point in polar coordinates Converting rectangular coordinates to polar coordinates: Special angles Converting polar coordinates to rectangular coordinates Converting an equation written in rectangular form to one written in polar form Converting an equation written in polar form to one written in rectangular coordinates Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 9/10

10 Limits and Continuity (15 topics) Estimating a limit numerically Finding limits from a graph Finding limits for a piecewise defined function Finding a limit by using the limit laws: Problem type 1 Finding a limit by using the limit laws: Problem type 2 Finding a limit by using the limit laws: Problem type 3 Squeeze Theorem Determining points of discontinuity from a graph Determining a parameter to make a function continuous Limits at infinity and graphs Limits at infinity and rational functions Infinite limits and graphs Infinite limits and rational functions Finding a limit of a trigonometric function by using continuity Finding a limit by using special trigonometric limits Other Topics Available By default, these topics are NOT included in the course, but can be added using the content editor in the Teacher Module. Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 10/10

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