All Lessons

(B) Write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points

(Y11-12) Interpret relationships in terms of the variables (ACMEM143)

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

(A) Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

(E) Solve mathematic and scientific formulas, and other literal equations, for a specified variable.

(Y10) Solve problems involving linear equations, including those derived from formulas (ACMNA235)

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

(A) Add and subtract polynomials of degree one and degree two

(B) Multiply polynomials of degree one and degree two

(D) Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

(Y10A) Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266)

HSA.APR.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.

(B) Solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

(Y10) Solve linear inequalities and graph their solutions on a number line (ACMNA236)

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

(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

(Y10) Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

HSA.SSE.3.A Factor a quadratic expression to reveal the zeros of the function it defines.

(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

HSA.SSE.3.A Factor a quadratic expression to reveal the zeros of the function it defines.

(C) Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

(D) Solve exponential equations of the form y = abx where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions

(I) Generate and solve exponential equations in mathematical and real-world problems

(Y10A) Solve simple exponential equations (ACMNA270)

HSA.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

(Y7) Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

HSN.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

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

(7) Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.

(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions

(C) Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.

(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

(B) Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

(9) Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

(A) Determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities

(B) Interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems

(C) Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

(D) Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems

(E) Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

HSF.IF.8.B Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay.

(10) Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

(A) Add and subtract polynomials of degree one and degree two

(B) Multiply polynomials of degree one and degree two

(C) Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend

(D) Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

(E) Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two

(F) Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

(11) Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.

(A) Simplify numerical radical expressions involving square roots

(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

HSF.IF.8.B Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay.

(A) Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

(Y8) Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)

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

(C) Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation

(C) Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems

(Y8) Plot linear relationships on the Cartesian plane with and without the use of digital technologies (ACMNA193)

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

HSA.REI.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).

HSF.IF.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.

(7) Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.

(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions

(C) Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.

HSF.IF.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

HSF.IF.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.*

HSF.IF.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).

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

HSF.IF.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

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

HSF.IF.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF.IF.7.C Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

HSF.IF.7.E Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

HSF.IF.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).