The provided document outlines the Trigonometry course curriculum from ALEKS (McGraw Hill), which consists of 465 core topics and 533 additional topics available for customization (p. 1).
The curriculum is divided into several primary mathematical domains:
Core Curriculum (465 Topics)
Algebra and Geometry Review (98 topics): Covers foundational skills including real numbers, exponents, polynomial and rational expressions, and basic geometry like the Pythagorean Theorem (pp. 1-2).
Equations and Inequalities (55 topics): Focuses on linear equations, complex numbers, and radical/quadratic equations (pp. 2-3).
Graphs and Functions (101 topics): Includes the coordinate plane, slopes, linear applications, and various function types (absolute value, square root, and piecewise) (pp. 3-4).
Trigonometric Functions (48 topics): The heart of the course, covering angle measures, the unit circle, right triangle trigonometry, and arc length (p. 5).
Trigonometric Graphs (29 topics): Detailed study of sine, cosine, and other trigonometric functions, including transformations, amplitude, and period (p. 6).
Identities and Equations (64 topics): Covers inverse functions, verifying identities, sum/difference formulas, and solving complex trigonometric equations (pp. 6-7).
Triangles, Vectors, and Polar Coordinates (57 topics): Includes the Laws of Sines and Cosines, vector operations, dot products, and polar equations (pp. 7-8).
Additional Topics Available (533 Topics)
These are optional modules that instructors can add to customize the course scope (pp. 8, 16):
Advanced Algebra & Geometry: Expanded review of proportions, volume/surface area, and complex inequalities (pp. 8, 11-12).
Advanced Functions: Deeper dives into difference quotients, average rate of change, and function composition (pp. 13-14).
Conic Sections: Detailed graphing and equations for parabolas, ellipses, and hyperbolas (p. 15).
Exponential and Logarithmic Functions: A large section (62 topics) covering growth/decay models, logarithmic properties, and solving exponential equations (pp. 15-16).
Trigonometry
This course covers the topics shown below.
Students navigate learning paths based on their level of readiness.
Institutional users may customize the scope and sequence to meet curricular needs.
Curriculum (465 topics + 533 additional topics)
Algebra and Geometry Review (98 topics)
Real Numbers and Algebraic Expressions (14 topics)
Signed fraction addition or subtraction: Basic
Signed fraction subtraction involving double negation
Signed fraction multiplication: Basic
Signed fraction division
Computing the distance between two integers on a number line
Exponents and integers: Problem type 1
Exponents and signed fractions
Order of operations with integers
Evaluating a linear expression: Integer multiplication with addition or subtraction
Evaluating a quadratic expression: Integers
Evaluating a linear expression: Signed fraction multiplication with addition or subtraction
Distributive property: Integer coe
ffi
cients
Using distribution and combining like terms to simplify: Univariate
Using distribution with double negation and combining like terms to simplify: Multivariate
Exponents (9 topics)
Introduction to the product rule of exponents
Product rule with positive exponents: Univariate
Introduction to the power of a power rule of exponents
Introduction to the power of a product rule of exponents
Power rules with positive exponents: Multivariate products
Power rules with positive exponents: Multivariate quotients
Simplifying a ratio of multivariate monomials: Basic
Introduction to the quotient rule of exponents
Simplifying a ratio of univariate monomials
Polynomial Expressions (8 topics)
Simplifying a sum or di
ff
erence of two univariate polynomials
Multiplying a univariate polynomial by a monomial with a positive coe
ffi
cient
Multiplying a univariate polynomial by a monomial with a negative coe
ffi
cient
Multiplying binomials with leading coe
ffi
cients of 1
Multiplying binomials with leading coe
ffi
cients greater than 1
Multiplying conjugate binomials: Univariate
Squaring a binomial: Univariate
Multiplying binomials with negative coe
ffi
cients
Factoring Polynomials (11 topics)
Greatest common factor of 2 numbers
Factoring a linear binomial
Introduction to the GCF of two monomials
Factoring out a monomial from a polynomial: Univariate
Factoring a quadratic with leading coe
ffi
cient 1
Factoring out a constant before factoring a quadratic
Factoring a quadratic with leading coe
ffi
cient greater than 1: Problem type 1
Factoring a quadratic with leading coe
ffi
cient greater than 1: Problem type 2
Factoring a perfect square trinomial with leading coe
ffi
cient 1
Factoring a di
ff
erence of squares in one variable: Basic
Factoring a di
ff
erence of squares in one variable: Advanced
Rational Expressions (28 topics)
Restriction on a variable in a denominator: Linear
Simplifying a ratio of factored polynomials: Linear factors
Simplifying a ratio of polynomials using GCF factoring
Simplifying a ratio of polynomials by factoring a quadratic with leading coe
ffi
cient 1
Simplifying a ratio of polynomials: Problem type 1
Multiplying rational expressions involving linear expressions
Multiplying rational expressions involving quadratics with leading coe
ffi
cients of 1
Dividing rational expressions involving linear expressions
Dividing rational expressions involving quadratics with leading coe
ffi
cients of 1
Least common multiple of 2 numbers
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Least common multiple of 3 numbers
Introduction to the LCM of two monomials
Finding the LCD of rational expressions with linear denominators: Relatively prime
Writing equivalent rational expressions with polynomial denominators
Introduction to adding fractions with variables and common denominators
Adding rational expressions with common denominators and monomial numerators
Adding rational expressions with common denominators and binomial numerators
Adding rational expressions with common denominators and GCF factoring
Adding rational expressions with common denominators and quadratic factoring
Adding rational expressions with di
ff
erent denominators and a single occurrence of a variable
Adding rational expressions with denominators ax and bx: Basic
Adding rational expressions with denominators ax and bx: Advanced
Adding rational expressions with linear denominators without common factors: Basic
Complex fraction without variables: Problem type 1
Complex fraction without variables: Problem type 2
Complex fraction involving univariate monomials
Complex fraction: GCF factoring
Complex fraction made of sums involving rational expressions: Problem type 1
Perfect Squares and nth Roots (6 topics)
Finding all square roots of a number
Square root of a rational perfect square
Square roots of perfect squares with signs
Introduction to solving an absolute value equation
Cube root of an integer
Finding n
th
roots of perfect n
th
powers with signs
Rational Exponents (2 topics)
Rational exponents: Unit fraction exponents and whole number bases
Rational exponents: Non-unit fraction exponent with a whole number base
Radical Expressions (15 topics)
Simplifying the square root of a whole number less than 100
Simplifying a higher root of a whole number
Introduction to square root addition or subtraction
Square root addition or subtraction
Introduction to square root multiplication
Square root multiplication: Basic
Square root multiplication: Advanced
Introduction to simplifying a product involving square roots using the distributive property
Simplifying a product involving square roots using the distributive property: Basic
Simplifying a product involving square roots using the distributive property: Advanced
Simplifying a quotient of square roots
Simplifying a quotient involving a sum or di
ff
erence with a square root
Rationalizing a denominator: Quotient involving square roots
Rationalizing a denominator: Square root of a fraction
Rationalizing a denominator using conjugates: Integer numerator
Geometry (5 topics)
Area of a triangle
Circumference of a circle
Circumference and area of a circle
Introduction to the Pythagorean Theorem
Pythagorean Theorem
Equations and Inequalities (55 topics)
Linear Equations and Applications (19 topics)
Additive property of equality with signed fractions
Multiplicative property of equality with signed fractions
Solving a multi-step equation given in fractional form
Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution
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 two-step equation with signed fractions
Solving a proportion of the form (x+a)/b = c/d
Solving for a variable in terms of other variables using addition or subtraction: Basic
Solving for a variable in terms of other variables using addition or subtraction: Advanced
Solving for a variable in terms of other variables using multiplication or division: Basic
Solving for a variable in terms of other variables using multiplication or division: Advanced
Solving for a variable in terms of other variables using addition or subtraction with division
Solving for a variable inside parentheses in terms of other variables
Solving for a variable in terms of other variables in a linear equation with fractions
Translating a sentence into a one-step equation
Solving a word problem with two unknowns using a linear equation
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Solving a decimal word problem using a linear equation of the form Ax + B = C
Solving a one-step word problem using the formula d = rt
Linear Inequalities and Applications (5 topics)
Graphing a linear inequality on the number line
Graphing a compound inequality on the number line
Set-builder and interval notation
Solving a two-step linear inequality: Problem type 1
Solving a two-step linear inequality: Problem type 2
Rational Equations that Simplify to Linear (5 topics)
Solving a rational equation that simpli
fi
es to linear: Denominator x
Solving a rational equation that simpli
fi
es to linear: Denominator x+a
Solving for a variable in terms of other variables in a rational equation: Problem type 1
Solving for a variable in terms of other variables in a rational equation: Problem type 2
Word problem on proportions: Problem type 1
Complex Numbers (5 topics)
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
Quadratic Equations (13 topics)
Solving an equation written in factored form
Finding the roots of a quadratic equation of the form ax
2
+ bx = 0
Finding the roots of a quadratic equation with leading coe
ffi
cient 1
Finding the roots of a quadratic equation with leading coe
ffi
cient greater than 1
Solving an equation of the form x
2
= a using the square root property
Solving a quadratic equation using the square root property: Exact answers, basic
Solving a quadratic equation using the square root property: Exact answers, advanced
Completing the square
Applying the quadratic formula: Exact answers
Applying the quadratic formula: Decimal answers
Solving a word problem using a quadratic equation with irrational roots
Solving an equation using the odd-root property: Problem type 1
Solving an equation using the odd-root property: Problem type 2
Rational Equations that Simplify to Quadratic (1 topics)
Restriction on a variable in a denominator: Quadratic
Radical Equations (7 topics)
Introduction to solving a radical equation
Solving a radical equation that simpli
fi
es to a linear equation: One radical, basic
Solving a radical equation that simpli
fi
es to a linear equation: One radical, advanced
Solving a radical equation that simpli
fi
es to a linear equation: Two radicals
Solving for a variable in terms of other variables in an equation involving radicals
Solving an equation with a root index greater than 2: Problem type 1
Solving an equation with a root index greater than 2: Problem type 2
Graphs and Functions (101 topics)
The Coordinate Plane, Distance, and Midpoint (8 topics)
Reading a point in the coordinate plane
Plotting a point in the coordinate plane
Naming the quadrant or axis of a point given its coordinates
Naming the quadrant or axis of a point given the signs of its coordinates
Table for a linear equation
Distance between two points in the plane: Exact answers
Identifying solutions to a linear equation in two variables
Finding a solution to a linear equation in two variables
Graphs of Equations (13 topics)
Graphing a linear equation of the form y = mx
Graphing a line given its equation in slope-intercept form: Integer slope
Graphing a line given its equation in slope-intercept form: Fractional slope
Graphing a line given its equation in standard form
Graphing a vertical or horizontal line
Finding x- and y-intercepts given the graph of a line on a grid
Finding x- and y-intercepts of a line given the equation: Basic
Graphing a line by
fi
rst
fi
nding its x- and y-intercepts
Finding intercepts of a nonlinear function given its graph
Graphing an absolute value equation of the form y = A|x|
Graphing a parabola of the form y = ax
2
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