Algebra 2 & Trigonometry: A Complete High School Curriculum

Learn how matrices organize data as rows and columns, including constants or variables, explore dimensions like two by three, and practice adding and subtracting matrices with consistent dimensions.

Apply scalar multiplication to matrices by multiplying every element by the scalar, including fractions like one third and one fifth; learn to add and subtract matrices of the same dimensions.

Explore real-world matrices by reading and solving problems with shirt sizes and colors, school sports wins, workers' hours, student subject popularity, and furniture sales by wood type.

Learn to solve matrix equations by equating corresponding elements, deriving separate scalar equations to find variables like x, y, z, a, C, g, and H.

Explore reflection matrices for the x axis, y axis, and line y equals x, using coordinate matrices and matrix multiplication to find reflected images of points and shapes.

explore second order determinants of 2x2 matrices using the ad minus bc formula, with examples calculating determinants, exploring signs, fractions, and solving for missing elements.

Explore identity and inverse matrices, learn how multiplying by the identity yields the original matrix, and compute inverses of 2×2 matrices using determinant, swapping, sign changes, and 1/det.

Master solving inequalities with symbols >, <, ≥, ≤, graph solutions on a number line using open or closed circles, and apply sign-flip rules for negative multipliers or divisors.

Solve absolute value inequalities by splitting into two inequalities, plotting intersections or unions on the number line, and solving examples like |A|<3, |x|>1, and |5K+3|<12.

Define relations as sets of ordered pairs, explain set notation for domain and range, and show how functions map each domain value to one range value, including one-to-one cases.

Explore operations on functions by adding, subtracting, multiplying, and dividing f(x) and g(x), including distributing negatives, combining like terms, and evaluating at a numerical input.

Explore the composition of functions using the f∘g notation, apply g to x, then f to the result, and evaluate examples like f(x)=x+3 and g(x)=x^2-6.

Explore inverse functions and relations by swapping domain and range, solving for y, and testing inverses with compositions; includes examples of linear and quadratic functions.

Explore the slope of a line as the rate of change, using delta y over delta x, and identify positive, negative, zero, and undefined slopes through two-point examples.

Learn how to graph lines using slope-intercept form, identify slope m and y-intercept b, plot points like (0,b), and draw lines for positive and negative slopes.

Explore zero and undefined slopes using horizontal and vertical lines, where y equals a constant and x equals a constant, and distinguish functions from non-functions.

Discover how to find x and y intercepts for linear equations, including those not in slope-intercept form, by plugging zero for x or y and solving to identify intercept coordinates.

practice writing linear equations from graphs and points using slope-intercept form, slope, and y-intercept; convert between y = mx + b, point-slope form, and two-point form.

Explore graphing systems of equations by identifying when lines intersect, yielding one, none, or infinitely many solutions; distinguish between consistent, inconsistent, independent, and dependent systems, and recognize parallel lines.

Graph linear inequalities in two variables on a coordinate plane by plotting the line and shading the side. Use solid lines for inclusive cases and dashed lines for strict ones.

Learn to graph systems of inequalities by drawing dashed and solid lines, using a test point to shade the correct region, and identifying the solution as the overlapping shaded area.

Solve systems of equations using the substitution method, equating expressions for y, solving for x, and then finding the intersection point coordinates on the plane.

Use the elimination method to cancel a variable by adding or subtracting equations, then solve for the remaining variable and back-substitute; identify unique, no, or infinite solutions.

Learn to solve two-variable systems by forming a coefficient matrix and its inverse, using determinants, and multiplying to find x and y; see intersection points of the lines.

Explore the five properties of monomials—product of powers, quotient of powers, power of a power, power of a product, and power of a quotient—and apply exponent rules to simplify.

Master simplifying monomials by flipping fractions to convert negative exponents to positive, and by distributing powers across numerators and denominators to rewrite expressions without negatives.

Explore polynomials, including monomials, binomials, and trinomials, determine polynomial degree by summing exponents, and practice adding, subtracting, and distributing polynomials with like terms.

Master dividing polynomials by monomials and by other polynomials using long division. Simplify terms, handle negative exponents, and interpret remainders through divide, multiply, subtract, and bring down steps.

Discover how to find and factor the greatest common factor of monomials and polynomials by inspecting coefficients and lowest exponents, and practice with multiple examples.

Master factoring binomials through the three cases: difference of squares, sum of cubes, and difference of cubes, with greatest common factor steps and practical examples.

Factor trinomials in the form x^2 + bx + c into binomials by finding two numbers that multiply to c and add to b; if not factorable, prime.