Integrated Math 2–3 Honors
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28 minQuadratic formula · Exact roots · Discriminant
Derive the quadratic formula by completing the square, solve quadratics with exact roots, and use the discriminant to predict two, one, or no real solutions.
37 minSquared binomials · Exact roots · Fractional coefficients
Turn a quadratic into a squared binomial, keep both sides balanced, and use the square root principle to find exact solutions, including fractional coefficients and equations with no real solutions.
33 minZero product property · Two roots · Exact radicals
Set an equation equal to zero, factor it, and use the zero product property. Connect difference-of-squares factoring to the square root principle, keep both roots, and simplify exact radical answers.
13 minPerfect squares · Conjugates · Factor completely
Recognize differences of squares, use conjugate binomials, factor higher powers repeatedly, and remove a GCF first.
27 minFactor pairs · Product and sum · Split the middle term
Factor monic and non-monic quadratic trinomials, use sign patterns, split the middle term, and factor completely.
39 minFactors · Greatest common factor · Factoring by grouping
Find numerical and variable GCFs, factor the GCF from a polynomial, and factor four-term polynomials completely by grouping.
56 minMonomials · Degree and terms · Polynomial operations
Identify polynomial structure, classify by degree and number of terms, and add, subtract, and multiply polynomial expressions.
11 minRadical denominators · Fractional exponents · Negative exponents
Fill a denominator’s exponent to the next whole power, then simplify numerical and variable expressions.
29 minLike radicals · Conjugates · Rationalizing denominators
Combine and multiply radicals, use conjugates, and remove radicals from one-term and binomial denominators.
25 minRational exponents · Perfect powers · Radicals
Connect fractional powers to roots, find perfect-power factors, and simplify numeric and variable radicals.
30 minProduct rule · Quotient rule · Negative exponents
Use the exponent rules to combine powers, simplify rational monomials, and rewrite expressions with positive exponents.
6 minV-shaped boundaries · Test points · Shading
Transform the boundary, choose solid or dashed, test an ordered pair, and shade the full two-variable solution region.
16 minAbsolute value · AND · OR · Interval notation
Distance meaning, inward and outward shortcuts, multi-step inequalities, negative coefficients, graphs, and interval notation.
13 minAND · OR · Graphs · Interval notation
Intersections and unions, chained inequalities, interval notation, all-real solution sets, and the empty set.
37 minPiecewise functions · Vertices · Transformations
Piecewise definitions, the parent V-graph, vertex form, translations, stretches, compressions, reflections, and equations from graphs.
25 minFunctions · Domain and range · Absolute value
Ordered-pair and graph tests for functions; domain and range; the piecewise definition of absolute value; and solving absolute-value equations.
22 minIntervals · One- and two-variable inequalities
Open and closed endpoints; intervals with infinity; solving a one-variable inequality; boundary lines; test points; and shaded half-planes.
37 minFoundations · Equations and relations
Expressions versus equations; true, false, and open equations; solution sets; two-variable equations; relations; and inequalities.
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