Will this help with my child's High School Precalculus homework?

Yes. StudyPug covers every Precalculus strand in the Alabama Course of Study Math, so your child can find step-by-step explanations and practice problems that match exactly what their teacher assigned.

How long are the video lessons for Precalculus?

Most video lessons are short and focused, typically running a few minutes each, so students can target a specific concept like the Law of Sines or matrix operations without sitting through a long lecture.

Is there a state test for High School Precalculus in Alabama?

Precalculus is not itself a dedicated ACAP assessment subject. Alabama's ACAP assessments focus on earlier grades. Check with your child's school for any end-of-course requirements that may apply locally.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and computers, so your child can practice Precalculus topics at home, at the library, or anywhere with an internet connection.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can see the content before committing, and every paid plan includes a 30-day money-back guarantee if you are not satisfied.

AL High School Precalculus Curriculum

Give your high schooler the support they need in Precalculus with lessons and practice problems matched to what Alabama classrooms teach, from complex numbers to trigonometry and statistics.

AL High School Precalculus Curriculum

IDStandardStudyPug Topic

CC.HSN.CN.B.4Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
- Polar form of complex numbers
CC.HSN.CN.B.5Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
- Operations on complex numbers in polar form
CC.HSN.CN.B.6Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
- Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
CC.HSA.CED.A.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- Point-slope form: y - y_1 = m(x - x_1)
- Graphing quadratic inequalities in two variables
- Graphing systems of quadratic inequalities
CC.HSA.REI.D.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
- Graphing linear functions using table of values
- Graphing exponential functions
- Graphing logarithmic functions
- The inverse of 3 x 3 matrices with matrix row operations
- The inverse of 3 x 3 matrix with determinants and adjugate
CC.HSF.TF.A.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- Converting between degrees and radians
- Trigonometric ratios of angles in radians
- Radian measure and arc length
CC.HSF.TF.A.2Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
- Unit circle
CC.HSF.TF.A.3Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
- Find the exact value of trigonometric ratios
- Solving expressions using 45-45-90 special right triangles
- Solving expressions using 30-60-90 special right triangles
CC.HSF.TF.B.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
- Graphing transformations of trigonometric functions
- Determining trigonometric functions given their graphs
CC.HSF.TF.B.6Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- Finding inverse trigonometric function from its graph
- Finding inverse reciprocal trigonometric function from its graph
- Inverse reciprocal trigonometric function: finding the exact value
CC.HSF.TF.B.7Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
- Evaluating inverse trigonometric functions
CC.HSF.TF.C.8Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
- Pythagorean identities
CC.HSF.TF.C.9Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
- Sum and difference identities
- Double-angle identities
- Cofunction identities
CC.HSG.SRT.D.9Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
- Area of triangles: 1/2 a*b sin(C)
CC.HSG.SRT.D.10Prove the Laws of Sines and Cosines and use them to solve problems.
- Law of sines
- Law of cosines
CC.HSG.SRT.D.11Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
- Applications of the sine law and cosine law
CC.HSA.APR.C.4Prove polynomial identities and use them to describe numerical relationships.
- Solving polynomials with unknown coefficients
- Multiplicities of polynomials
- Imaginary zeros of polynomials
CC.HSA.APR.C.5Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
- Pascal's triangle
- Binomial theorem
- Determining the equation of a polynomial function
CC.HSA.APR.D.7Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
- Negative exponent rule
- Multiplying rational expressions
- Dividing rational expressions
- Descartes' rule of signs
CC.HSN.VM.A.1Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
- Use sine ratio to calculate angles and sides (Sin = o / h)
- Introduction to vectors
- Magnitude of a vector
- Direction angle of a vector
CC.HSN.VM.A.2Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
- Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- Scalar multiplication of vectors
- Equivalent vectors
CC.HSN.VM.A.3Solve problems involving velocity and other quantities that can be represented by vectors.
- Word problems relating guy wire in trigonometry
- Word problems on vectors
CC.HSN.VM.B.4Add and subtract vectors.
- Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- Adding and subtracting vectors in component form
- Operations on vectors in magnitude and direction form
CC.HSN.VM.B.5Multiply a vector by a scalar.
- Slope intercept form: y = mx + b
- Unit vector
CC.HSN.VM.C.6Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- Notation of matrices
- Adding and subtracting matrices
CC.HSN.VM.C.7Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- Scalar multiplication of matrices
CC.HSN.VM.C.8Add, subtract, and multiply matrices of appropriate dimensions.
- Matrix multiplication
- The three types of matrix row operations
CC.HSN.VM.C.9Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
- Properties of matrix multiplication
CC.HSN.VM.C.10Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
- Zero matrix
- Identity matrix
- The determinant of a 2 x 2 matrix
- The determinant of a 3 x 3 matrix (General & Shortcut Method)
- The Inverse of a 2 x 2 matrix
CC.HSN.VM.C.11Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
- Transforming vectors with matrices
- Transforming shapes with matrices
CC.HSN.VM.C.12Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
- Finding the transformation matrix
CC.HSA.REI.C.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- System of linear-quadratic equations
- Nature of roots of quadratic equations: The discriminant
- Applications of quadratic equations
- Solving quadratic inequalities
CC.HSA.REI.C.8Represent a system of linear equations as a single matrix equation in a vector variable.
- Representing a linear system as a matrix
- Notation of matrices
- Adding and subtracting matrices
- Scalar multiplication of matrices
CC.HSA.REI.C.9Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
- The Inverse of a 2 x 2 matrix
- Solving linear systems using 2 x 2 inverse matrices
- Matrix multiplication
- The three types of matrix row operations
CC.HSG.C.A.4Construct a tangent line from a point outside a given circle to the circle.
- Tangent properties
CC.HSG.GPE.A.2Derive the equation of a parabola given a focus and directrix.
- Conics - Parabola
CC.HSG.GPE.A.3Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
- Conics - Ellipse
- Conics - Hyperbola
CC.HSN.RN.B.3Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
- Rational vs. Irrational numbers
- Solving radical equations
- Converting repeating decimals to fractions
CC.HSN.Q.A.1Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
- Metric systems
- Imperial systems
- Scale diagrams
- Conversions involving squares and cubic
CC.HSN.Q.A.2Define appropriate quantities for the purpose of descriptive modeling.
- Conversions between metric and imperial systems
- Squares and square roots
- Pythagorean theorem
- Estimating square roots
- Using the pythagorean relationship
- Applications of pythagorean theorem
CC.HSN.Q.A.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Upper and lower bound
- Cubic and cube roots
- Ratios
- Rates
- Proportions
- Percents, fractions, and decimals
CC.HSS.IC.A.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
- Sampling methods
CC.HSS.IC.A.2Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
- Sampling distributions
- Rare event rule
CC.HSS.IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
- Census and bias
CC.HSS.IC.B.4Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
- Margin of error
- Confidence intervals to estimate population mean
- Making a confidence interval
CC.HSS.IC.B.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
- Traditional hypothesis testing
- P-value hypothesis testing
- Analysis of variance (ANOVA)
CC.HSS.IC.B.6Evaluate reports based on data.
- Influencing factors in data collection
CC.HSS.CP.A.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
- Comparing experimental and theoretical probability
CC.HSS.CP.B.7Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
- Addition rule for
CC.HSS.MD.A.1Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
- Probability distribution - histogram, mean, variance & standard deviation
CC.HSS.MD.A.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
- Properties of expectation
CC.HSS.MD.A.3Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
- Binomial distribution
- Mean and standard deviation of binomial distribution
CC.HSS.MD.B.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
- Type 1 and type 2 errors
CC.HSG.GMD.A.2Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
- Surface area and volume of spheres

Precalculus

About High School Alabama Precalculus

Alabama Precalculus follows the Alabama Course of Study Math, organized around a wide range of advanced topics. This course covers complex numbers and the complex plane, trigonometric functions and identities, vectors and matrices, conic sections, polynomial and rational expressions, probability and statistics, and geometric measurement. StudyPug provides video lessons and practice problems aligned to every strand so students stay on track with their Alabama coursework.

Core strands: complex numbers, trigonometry, vectors, matrices, conic sections, polynomial and rational expressions, probability, and statistics
Video lessons covering every Alabama Course of Study Precalculus topic
Practice problems and step-by-step explanations for each strand
Content aligned to the Alabama Course of Study Math standards

Curriculum topics by strand

Find lessons and practice for every Precalculus topic, aligned to the Alabama Course of Study Math.

Topic includes:

Practice

Video

Quiz

Standard

StudyPug Topic

Alabama High School Precalculus Topics

Complex Numbers and the Complex Plane: Representing complex numbers in rectangular and polar form, performing operations geometrically, and calculating distances and midpoints in the complex plane.
Trigonometric Functions and Identities: Radian measure, the unit circle, special triangles, inverse trig functions, the Pythagorean identity, and addition and subtraction formulas for sine, cosine, and tangent.
Laws of Sines and Cosines: Proving and applying the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles, including area using the sine formula.
Vectors: Representing vector quantities with directed line segments, finding components, adding and subtracting vectors, multiplying by a scalar, and solving problems involving velocity.
Matrices: Using matrices to represent data, performing addition, subtraction, and multiplication, working with identity and zero matrices, finding inverses, and applying matrix transformations to vectors and the plane.
Polynomial, Rational Expressions, and the Binomial Theorem: Proving polynomial identities, operating with rational expressions, and applying the Binomial Theorem with Pascal's Triangle.
Conic Sections: Deriving equations of parabolas, ellipses, and hyperbolas from their geometric definitions, and constructing tangent lines to circles.
Probability and Statistics: Conditional probability, independence, random variables, expected value, probability distributions, simulation, and evaluating data-based reports.
Reasoning with Quantities and Number Properties: Using units for modeling, defining appropriate quantities, understanding rational and irrational number properties, and choosing appropriate levels of accuracy.

How StudyPug Helps Alabama High School Precalculus Students

When a student gets stuck on a topic like matrix inverses or the unit circle, StudyPug lets them go back to a focused video lesson, work through guided practice problems, and review step-by-step explanations at their own pace. This makes it easier to fill gaps before a test rather than waiting for the next class.

Parents can also follow along with the Alabama Course of Study Math strands to see exactly where their child needs more support, whether that is trigonometric identities, vectors, or probability concepts.

Aligned to Alabama High School Precalculus Curriculum

Every lesson and practice problem on StudyPug is matched to the Alabama Course of Study Math for Precalculus, covering the same complex numbers, trigonometry, vectors, matrices, conic sections, and statistics strands that Alabama high school teachers use in the classroom.

Ready to put your High School Precalculus skills to the test?

Jump into practice questions for every AL Precalculus topic - with instant feedback and step-by-step video solutions when you get stuck.

Start Practicing

Written by the StudyPug Math Team

Last updated June 5, 2026

3 M+

students

★★★★★

4.8 average

92%

improve grades