High School: Algebra
HSA.REI.D11
Explain 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) … Read More “HSA.REI.D11”
October 1, 2018HSA.REI.D12
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
October 1, 2018HSA.SSE.A1
Interpret expressions that represent a quantity in terms of its context.*
October 1, 2018HSA.SSE.A1a
Interpret parts of an expression, such as terms, factors, and coefficients.
October 1, 2018HSA.SSE.A1b
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
October 1, 2018HSA.REI.A1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
October 1, 2018HSA.REI.A2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
October 1, 2018HSA.REI.B3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
October 1, 2018HSA.REI.B4a
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.
October 1, 2018HSA.APR.A1
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
October 1, 2018HSA.REI.B4b
Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
October 1, 2018