Looking for free content that’s aligned to your standards? You’ve come to the right place!

## Get Free 2nd Grade Math Content

Khan Academy is a nonprofit with thousands of free videos, articles, and practice questions for just about every standard.

No ads, no subscriptions – just 100% free, forever.

### HSN Number and Quantity

- HSN.RN The Real Number System
- HSN.RN.A Extend the properties of exponents to rational exponents.
- HSN.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
- HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

- HSN.RN.A Extend the properties of exponents to rational exponents.
- HSN.Q Quantities
- HSN.Q.A Reason quantitatively and use units to solve problems.
- HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.

- HSN.Q.A Reason quantitatively and use units to solve problems.
- HSN.CN The Complex Number System
- HSN.CN.A Perform arithmetic operations with complex numbers.
- HSN.CN.A.1 Know there is a complex number
*i*such that*i*= −1, and every complex number has the form^{2}*a + bi*with*a*and*b*real. - HSN.CN.A.2 Use the relation
*i*= −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.^{2}

- HSN.CN.A.1 Know there is a complex number
- HSN.CN.C Use complex numbers in polynomial identities and equations.
- HSN.CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

- HSN.CN.A Perform arithmetic operations with complex numbers.

### HSA Algebra

- HSA.SSE Seeing Structure in Expressions
- HSA.SSE.A Interpret the structure of expressions.
- HSA.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

- HSA.SSE.B Write expressions in equivalent forms to solve problems.
- HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- HSA.SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
- HSA.SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- HSA.SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions.

- HSA.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.

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

- HSA.SSE.A Interpret the structure of expressions.
- HSA.APR Arithmetic with Polynomials and Rational Expressions
- HSA.APR.B Understand the relationship between zeros and factors of polynomials.
- HSA.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*p(a)*= 0 is a factor of*p(x)*. - HSA.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.

- HSA.APR.B.2 Know and apply the Remainder Theorem: For a polynomial
- HSA.APR.C Use polynomial identities to solve problems.
- HSA.APR.C.4 Prove polynomial identities and use them to describe numerical relationships.

- HSA.APR.D Rewrite rational expressions.
- HSA.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.

- HSA.APR.D.6 Rewrite simple rational expressions in different forms; write

- HSA.APR.B Understand the relationship between zeros and factors of polynomials.
- HSA.CED Creating Equations
- HSA.CED.A Create equations that describe numbers or relationships.
- HSA.CED.A.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.

- HSA.CED.A Create equations that describe numbers or relationships.
- HSA.REI Reasoning with Equations and Inequalities
- HSA.REI.A Understand solving equations as a process of reasoning and explain the reasoning.
- HSA.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.
- HSA.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

- HSA.REI.B Solve equations and inequalities in one variable.
- HSA.REI.B.4 Solve quadratic equations in one variable.
- HSA.REI.B.4.b Solve quadratic equations by inspection (e.g., for
*x*^{2}= 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*.

- HSA.REI.B.4.b Solve quadratic equations by inspection (e.g., for

- HSA.REI.B.4 Solve quadratic equations in one variable.
- HSA.REI.C Solve systems of equations.
- HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- HSA.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

- HSA.REI.D Represent and solve equations and inequalities graphically.
- HSA.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.

- HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations

- HSA.REI.A Understand solving equations as a process of reasoning and explain the reasoning.

### HSF Functions

- HSF.IF Interpreting Functions
- HSF.IF.A Understand the concept of a function and use function notation.
- HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

- HSF.IF.B Interpret functions that arise in applications in terms of the context.
- HSF.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.
*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.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.

- HSF.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.
- HSF.IF.C Analyze functions using different representations.
- HSF.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.
- HSF.IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
- HSF.IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- HSF.IF.C.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- HSF.IF.C.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

- HSF.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- HSF.IF.C.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.C.8.b Use the properties of exponents to interpret expressions for exponential functions.

- HSF.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

- HSF.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.

- HSF.IF.A Understand the concept of a function and use function notation.
- HSF.BF Building Functions
- HSF.BF.A Build a function that models a relationship between two quantities.
- HSF.BF.A.1 Write a function that describes a relationship between two quantities.
- HSF.BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
- HSF.BF.A.1.b Combine standard function types using arithmetic operations.

- HSF.BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

- HSF.BF.A.1 Write a function that describes a relationship between two quantities.
- HSF.BF.B Build new functions from existing functions.
- HSF.BF.B.3 Identify the effect on the graph of replacing
*f(x)*by*f(x) + k*,*kf(x)*,*f(kx)*, and*f(x + k)*for specific values of*k*(both positive and negative); find the value of*k*given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. - HSF.BF.B.4 Find inverse functions.
- HSF.BF.B.4.a Solve an equation of the form
*f(x) = c*for a simple function*f*that has an inverse and write an expression for the inverse.

- HSF.BF.B.4.a Solve an equation of the form

- HSF.BF.B.3 Identify the effect on the graph of replacing

- HSF.BF.A Build a function that models a relationship between two quantities.
- HSF.LE Linear, Quadratic, and Exponential Models
- HSF.LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
- HSF.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).
- HSF.LE.A.4 For exponential models, express as a logarithm the solution to
*ab*=^{ct}*d*where*a*,*c*, and*d*are numbers and the base*b*is 2, 10, or*e*; evaluate the logarithm using technology.

- HSF.LE.B Interpret expressions for functions in terms of the situation they model.
- HSF.LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.

- HSF.LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
- HSF.TF Trigonometric Functions
- HSF.TF.A Extend the domain of trigonometric functions using the unit circle.
- HSF.TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- HSF.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

- HSF.TF.B Model periodic phenomena with trigonometric functions.
- HSF.TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

- HSF.TF.C Prove and apply trigonometric identities.
- HSF.TF.C.8 Prove the Pythagorean identity sin
^{2}(*θ*) + cos^{2}(*θ*) = 1 and use it to find sin(*θ*), cos(*θ*), or tan (*θ*) given sin(*θ*), cos(*θ*), or tan(*θ*) and the quadrant of the angle.

- HSF.TF.C.8 Prove the Pythagorean identity sin

- HSF.TF.A Extend the domain of trigonometric functions using the unit circle.

### HSS Statistics and Probability

- HSS.ID Interpreting Categorical and Quantitative Data
- HSS.ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.
- HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- HSS.ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

- HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

- HSS.ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.