MML Algebra I Bundle

CCSSHSA-SSE.A.1
Interpret expressions that represent a quantity in terms of its context.

CCSSHSA-SSE.A.1a
Interpret parts of an expression, such as terms, factors, and coefficients.

CCSSHSA-SSE.A.1b
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.

CCSSHSA-SSE.A.2
Use the structure of an expression to identify ways to rewrite it. For example, see 𝘹⁴ – 𝘺⁴ as (𝘹²)² – (𝘺²)², thus recognizing it as a difference of squares that can be factored as (𝘹² – 𝘺²)(𝘹² + 𝘺²).

CCSSHSA-SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

CCSSHSA-SSE.B.3a
Factor a quadratic expression to reveal the zeros of the function it defines.

CCSSHSA-SSE.B.3b
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

CCSSHSA-SSE.B.3c
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 to the 𝘵 power can be rewritten as ((1.15 to the 1/12 power) to the 12𝘵 power) is approximately equal to (1.012 to the 12𝘵 power) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

CCSSHSA-SSE.B.4
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

CCSSHSA-APR.A.1
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.

CCSSHSA-APR.B.2
Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).

CCSSHSA-APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

CCSSHSA-APR.C.4
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (𝘹² + 𝘺²)² = (𝘹² – 𝘺²)² + (2𝘹𝘺)² can be used to generate Pythagorean triples.

CCSSHSA-APR.C.5
Know 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.

CCSSHSA-APR.D.6
Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system.

CCSSHSA-APR.D.7
Understand 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.

CCSSHSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems.

CCSSHSA-CED.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

CCSSHSA-CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

CCSSHSA-CED.A.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law 𝘝 = 𝘭𝘙 to highlight resistance 𝘙.

CCSSHSA-REI.A.1
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.

CCSSHSA-REI.A.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

CCSSHSA-REI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

CCSSHSA-REI.B.4
Solve quadratic equations in one variable.

CCSSHSA-REI.B.4a
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.

CCSSHSA-REI.B.4b
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.

CCSSHSA-REI.C.5
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

CCSSHSA-REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

CCSSHSA-REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line 𝘺 = –3𝘹 and the circle 𝘹² + 𝘺² = 3.

CCSSHSA-REI.C.8
Represent a system of linear equations as a single matrix equation in a vector variable.

CCSSHSA-REI.C.9
Find 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).

CCSSHSA-REI.D.10
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

CCSSHSA-REI.D.11
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) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

CCSSHSA-REI.D.12
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.

CCSSHSF-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹).

CCSSHSF-IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

CCSSHSF-IF.A.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by 𝘧(0) = 𝘧(1) = 1, 𝘧(𝘯+1) = 𝘧(𝘯) + 𝘧(𝘯-1) for 𝘯 greater than or equal to 1.

CCSSHSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

CCSSHSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function 𝘩(𝘯) gives the number of person-hours it takes to assemble 𝘯 engines in a factory, then the positive integers would be an appropriate domain for the function.

CCSSHSF-IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

CCSSHSF-IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

CCSSHSF-IF.C.7a
Graph linear and quadratic functions and show intercepts, maxima, and minima.

CCSSHSF-IF.C.7b
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

CCSSHSF-LE.A.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.

CCSSHSF-LE.A.1a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

CCSSHSF-LE.A.1b
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

CCSSHSF-LE.A.1c
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

CCSSHSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

CCSSHSF-LE.A.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

CCSSHSF-LE.A.4
For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology.

CCSSHSF-LE.B.5
Interpret the parameters in a linear or exponential function in terms of a context.