Common Core

Common Core State Standards for Mathematics (United States). The calculus kingdom uses AP Calculus AB learning objectives, which pick up where the Common Core stops.

297 codes, each linked to the lesson that teaches it. These are tags, not gates — nothing in the game reads them to decide what a student may do.

Grade 1

1.NBT.B.3Compare two two-digit numbers using >, = and <.

Grade 2

2.MD.B.6Represent whole numbers as lengths on a number line and find sums and differences on it.
2.OA.A.1Use addition and subtraction within 100 to solve take-from, compare and unknown-addend problems.
2.OA.B.2Fluently add and subtract within 20; know all sums of two one-digit numbers from memory.

Grade 3

3.MD.B.3Draw a scaled picture graph and a scaled bar graph, and solve one- and two-step problems using the information in them.
3.MD.D.8Solve problems involving the perimeter of polygons, including finding an unknown side length.
3.NBT.A.2Fluently add and subtract within 1000 using strategies based on place value.
3.NF.A.1Understand a fraction 1/b as one part of a whole partitioned into b equal parts.
3.NF.A.3.DCompare two fractions with the same numerator or the same denominator by reasoning about size.
3.OA.A.1Interpret products of whole numbers as a number of equal groups.
3.OA.A.2Interpret whole-number quotients as sharing equally or as repeated subtraction.
3.OA.C.7Fluently multiply and divide within 100; know all products of two one-digit numbers from memory.

Grade 4

4.G.A.2Classify two-dimensional figures by the presence of parallel or perpendicular lines and by angle size.
4.MD.C.5Recognise angles as geometric figures formed by two rays and understand angle measurement.
4.NBT.A.1Recognise that a digit in one place is ten times what it represents in the place to its right.
4.NBT.A.2Read, write and compare multi-digit whole numbers using >, = and <.
4.NBT.A.3Round multi-digit whole numbers to any place.
4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.5Multiply a multi-digit number by a one-digit number, and two two-digit numbers, using place value.
4.NBT.B.6Find whole-number quotients and remainders with up to four-digit dividends.
4.NF.A.1Explain why a fraction is equivalent to another by multiplying or dividing numerator and denominator.
4.NF.A.2Compare fractions with different numerators and denominators, using a common denominator or a benchmark.
4.NF.B.3.AUnderstand adding and subtracting fractions with like denominators as joining and separating parts of the same whole.
4.NF.B.3.BDecompose a fraction, and convert between mixed numbers and improper fractions.
4.NF.C.7Compare two decimals to hundredths by reasoning about their size.
4.OA.A.3Solve multi-step word problems, including interpreting a remainder sensibly.
4.OA.B.4Find all factor pairs of a whole number and decide whether it is prime or composite.

Grade 5

5.G.A.1Use a pair of perpendicular number lines to define a coordinate system, and understand how the two numbers of an ordered pair locate a point.
5.G.A.2Represent real-world and mathematical problems by graphing points in the first quadrant and interpret coordinate values in context.
5.NBT.A.3Read, write and compare decimals to thousandths using place value.
5.NBT.B.7Add, subtract, multiply and divide decimals to hundredths.
5.NF.A.1Add and subtract fractions with unlike denominators, including mixed numbers, using equivalent fractions.
5.NF.A.2Solve word problems with fractions, and check the answer against a benchmark estimate.
5.NF.B.4Multiply a fraction by a whole number or by another fraction.
5.NF.B.5Interpret multiplication as scaling: predict whether a product is larger or smaller than the starting number.
5.OA.A.1Use parentheses, brackets and braces in numerical expressions and evaluate them.

Grade 6

6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.
6.EE.A.2Write, read and evaluate expressions in which letters stand for numbers.
6.EE.A.2.BIdentify the parts of an expression, including viewing a product as a single entity.
6.EE.A.2.CEvaluate expressions, performing the operations in the conventional order, including whole-number exponents.
6.EE.A.3Apply the properties of operations to generate equivalent expressions, including the distributive property.
6.EE.A.4Identify when two expressions are equivalent, whatever value the variable takes.
6.EE.B.5Understand solving an equation as finding the values that make it true.
6.EE.B.7Solve real-world problems by writing and solving equations of the form x + p = q and px = q.
6.EE.B.8Write an inequality to represent a constraint and graph its solutions on a number line.
6.G.A.1Find the area of triangles, special quadrilaterals and polygons by composing and decomposing them.
6.G.A.4Represent three-dimensional figures with nets and use them to find surface area.
6.NS.A.1Divide a fraction by a fraction, and explain why multiplying by the reciprocal works.
6.NS.B.3Fluently add, subtract, multiply and divide multi-digit decimals.
6.NS.B.4Find the greatest common factor and the least common multiple of two whole numbers.
6.NS.C.5Understand that positive and negative numbers describe quantities with opposite directions.
6.NS.C.6.CFind and position integers and other rational numbers on a number line and pairs of them on a coordinate plane.
6.NS.C.7Order and compare rational numbers, and interpret them on a number line.
6.NS.C.7.CUnderstand the absolute value of a rational number as its distance from 0 on the number line.
6.NS.C.8Solve problems by graphing points in all four quadrants, and use coordinates and absolute value to find distances between points with the same first or second coordinate.
6.RP.A.1Understand the concept of a ratio and describe a relationship between two quantities with it.
6.RP.A.2Understand a unit rate and use rate language.
6.RP.A.3.CFind a percent of a quantity, and find the whole given a part and the percent.
6.SP.A.2Understand that a set of data has a distribution described by its centre, spread and overall shape.
6.SP.A.3Recognise that a measure of centre summarises all of the values with a single number, while a measure of variation describes how the values vary.
6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms and box plots.
6.SP.B.5Summarise numerical data sets in relation to their context, reporting measures of centre and describing the shape of the distribution.

Grade 7

7.EE.B.3Solve multi-step problems with positive and negative rational numbers in any form.
7.EE.B.4.ASolve equations of the form px + q = r and p(x + q) = r fluently, and compare an algebraic solution with an arithmetic one.
7.EE.B.4.BSolve word problems leading to inequalities of the form px + q > r, and graph and interpret the solution set.
7.G.A.1Solve problems involving scale drawings, including computing lengths from a scale.
7.G.A.2Draw triangles from three given measures and notice when they determine one triangle, many, or none.
7.G.B.4Know and use the formulas for the area and circumference of a circle, and relate them to each other.
7.G.B.5Use supplementary, complementary, vertical and adjacent angles to write and solve equations for an unknown angle.
7.G.B.6Solve problems involving the area of two-dimensional objects composed of triangles, quadrilaterals and polygons.
7.NS.A.1Add and subtract rational numbers, including subtracting a negative as adding its opposite.
7.NS.A.2Multiply and divide rational numbers and know the rules for the sign of the result.
7.NS.A.2.DConvert a rational number to a decimal, and recognise terminating and repeating decimals.
7.RP.A.2Recognise and represent proportional relationships, and find the constant of proportionality.
7.RP.A.3Solve multi-step percent problems: increase, decrease, discount, tax, tip and interest.
7.SP.A.1Understand that statistics can gain information about a population by examining a sample, and that a random sample tends to be representative.
7.SP.A.2Use data from a random sample to draw inferences about a population, and gauge the variation in estimates from repeated samples.
7.SP.B.4Use measures of centre and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
7.SP.C.5Understand that the probability of a chance event is a number between 0 and 1 expressing how likely it is to occur.
7.SP.C.6Approximate the probability of a chance event by collecting data, observing its long-run relative frequency, and predicting the approximate relative frequency given the probability.
7.SP.C.7Develop a probability model and use it to find probabilities of events, comparing probabilities from a model with observed frequencies.
7.SP.C.7.ADevelop a uniform probability model by assigning equal probability to all outcomes, and use it to find probabilities of events.
7.SP.C.8Find probabilities of compound events using organised lists, tables, tree diagrams and simulation.
7.SP.C.8.AUnderstand that the probability of a compound event is the fraction of outcomes in the sample space for which the event occurs.

Grade 8

8.EE.A.1Know and apply the properties of integer exponents, including zero and negative exponents.
8.EE.A.2Use square root and cube root symbols to represent solutions to x^2 = p and x^3 = p, and evaluate roots of small perfect squares and cubes.
8.EE.A.3Use numbers expressed as a single digit times an integer power of 10 to estimate very large or very small quantities and compare their sizes.
8.EE.A.4Perform operations with numbers expressed in scientific notation, including problems that mix decimal and scientific notation.
8.EE.B.5Graph proportional relationships, interpreting the unit rate as the slope, and compare two proportional relationships represented in different ways.
8.EE.B.6Use similar triangles to explain slope, and derive y = mx + b for a line through the origin and elsewhere.
8.EE.C.7.AGive examples of linear equations with one solution, no solution or infinitely many solutions.
8.EE.C.7.BSolve linear equations with rational coefficients, expanding with the distributive property and collecting like terms.
8.EE.C.8.BSolve systems of two linear equations algebraically, and solve simple cases by inspection.
8.F.A.1Understand that a function assigns to each input exactly one output.
8.F.A.2Compare properties of two functions represented differently — algebraically, graphically, numerically or in words.
8.F.A.3Interpret y = mx + b as a linear function and give examples of functions that are not linear.
8.F.B.4Construct a function to model a linear relationship and interpret its rate of change and initial value.
8.F.B.5Describe qualitatively the relationship a graph shows, and sketch a graph from a verbal description.
8.G.A.1Verify experimentally that rotations, reflections and translations preserve lengths, angle measures and parallel lines.
8.G.A.2Understand that two figures are congruent if one can be obtained from the other by a sequence of rotations, reflections and translations, and describe such a sequence.
8.G.A.3Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
8.G.A.4Understand similarity through dilations, and describe a sequence that shows two figures are similar.
8.G.A.5Use informal arguments about the angles created when a transversal crosses parallel lines.
8.G.B.6Explain a proof of the Pythagorean theorem and its converse.
8.G.B.7Apply the Pythagorean theorem to find unknown side lengths in right triangles in two and three dimensions.
8.G.B.8Apply the Pythagorean theorem to find the distance between two points in the coordinate plane.
8.G.C.9Know and use the formulas for the volume of cones, cylinders and spheres.
8.NS.A.1Know that numbers that are not rational are irrational, and convert a decimal expansion that repeats eventually into a rational number.
8.NS.A.2Use rational approximations of irrational numbers to compare them and locate them approximately on a number line.
8.SP.A.1Construct and interpret scatter plots for bivariate measurement data, and describe patterns such as clustering, outliers and linear association.
8.SP.A.2Know that straight lines are used to model relationships between two quantitative variables, and informally fit a straight line to data.
8.SP.A.3Use the equation of a linear model to solve problems, interpreting the slope and the intercept.
8.SP.A.4Construct and interpret a two-way table of frequencies for two categorical variables, and use relative frequencies to describe association.

High school

HSA-APR.A.1Understand that polynomials are closed under addition, subtraction and multiplication (multiplying the factors back).
HSA-APR.B.2Know 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).
HSA-APR.B.3Identify zeros of polynomials when suitable factorisations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
HSA-APR.D.6Rewrite simple rational expressions in different forms: write a(x)/b(x) in the form q(x) + r(x)/b(x), where the degree of r(x) is less than the degree of b(x), using inspection or long division.
HSA-APR.D.7Understand 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.
HSA-CED.A.1Create equations in one variable, including quadratics, and use them to solve problems.
HSA-CED.A.2Create equations in two or more variables to represent relationships between quantities, and graph them on coordinate axes with labels and scales.
HSA-CED.A.3Represent constraints by systems of equations and interpret solutions as viable options in a modelling context.
HSA-CED.A.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
HSA-REI.A.1Explain each step in solving an equation as following from the equality of the previous step.
HSA-REI.A.2Solve simple rational equations, and show how extraneous solutions can arise.
HSA-REI.B.3Solve linear equations and inequalities in one variable, including with letters for coefficients.
HSA-REI.B.4.AUse the method of completing the square to transform any quadratic equation in x into the form (x - p)^2 = q.
HSA-REI.B.4.BSolve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring.
HSA-REI.C.6Solve systems of linear equations exactly and approximately, focusing on pairs in two variables.
HSA-REI.C.8Represent a system of linear equations as a single matrix equation in a vector variable.
HSA-REI.C.9Find 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).
HSA-REI.D.11Explain why the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect are the solutions of f(x) = g(x); find the solutions approximately, including cases where f(x) and/or g(x) are exponential or logarithmic functions.
HSA-REI.D.12Graph the solutions to a linear inequality in two variables as a half-plane, and the solution set of a system of linear inequalities as the intersection of half-planes.
HSA-SSE.A.1.AInterpret parts of an expression, such as terms, factors and coefficients.
HSA-SSE.A.2Use the structure of an expression to rewrite it, such as seeing a difference of two squares.
HSA-SSE.B.3.AFactor a quadratic expression to reveal the zeros of the function it defines.
HSA-SSE.B.3.BComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
HSA-SSE.B.3.CUse the properties of exponents to transform expressions for exponential functions, for example 1.15^t = (1.15^(1/12))^(12t) to reveal the equivalent monthly rate.
HSA-SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
HSF-BF.A.1Write a function that describes a relationship between two quantities.
HSF-BF.A.1.ADetermine an explicit expression, a recursive process, or steps for calculation from a context.
HSF-BF.A.1.BCombine standard function types using arithmetic operations; for example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential.
HSF-BF.A.1.CCompose functions; for example, if T(y) is the temperature in the atmosphere as a function of height and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the balloon as a function of time.
HSF-BF.A.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
HSF-BF.B.3Identify the effect on a graph of replacing f(x) by f(x) + k, k·f(x), f(kx) and f(x + k).
HSF-BF.B.4Find inverse functions.
HSF-BF.B.4.ASolve 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.BVerify by composition that one function is the inverse of another.
HSF-BF.B.4.CRead values of an inverse function from a graph or a table, given that the function has an inverse.
HSF-BF.B.4.DProduce an invertible function from a non-invertible function by restricting the domain.
HSF-BF.B.5Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
HSF-IF.A.1Understand the definition of a function and use domain and range correctly.
HSF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use it.
HSF-IF.A.3Recognise that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
HSF-IF.B.4Interpret the key features of a graph or a table in terms of the quantities they describe.
HSF-IF.B.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
HSF-IF.B.6Calculate 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.C.7Graph functions expressed symbolically and show key features of the graph.
HSF-IF.C.7.AGraph linear and quadratic functions and show intercepts, maxima and minima.
HSF-IF.C.7.BGraph square root, cube root and piecewise-defined functions, including step functions and absolute value functions.
HSF-IF.C.7.CGraph polynomial functions, identifying zeros when suitable factorisations are available, and showing end behaviour.
HSF-IF.C.7.DGraph rational functions, identifying zeros and asymptotes when suitable factorisations are available, and showing end behaviour.
HSF-IF.C.7.EGraph exponential and logarithmic functions, showing intercepts and end behaviour, and trigonometric functions, showing period, midline and amplitude.
HSF-IF.C.8.AUse factoring and completing the square in a quadratic function to show zeros, extreme values and symmetry of the graph, and interpret these in context.
HSF-IF.C.8.BUse the properties of exponents to interpret expressions for exponential functions, identifying the percent rate of change and classifying them as representing exponential growth or decay.
HSF-LE.A.1.AProve that linear functions grow by equal differences and exponential functions by equal factors over equal intervals.
HSF-LE.A.1.BRecognise situations in which one quantity changes at a constant rate per unit interval relative to another.
HSF-LE.A.1.CRecognise situations in which a quantity grows or decays by a constant percent rate per unit interval.
HSF-LE.A.2Construct an exponential function given a graph, a description of a relationship, or a table of values.
HSF-LE.A.4For 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.5Interpret the parameters in a linear or exponential function in terms of a context.
HSF-TF.A.1Understand radian measure of an angle as the length of the arc on the unit circle it subtends.
HSF-TF.A.2Explain how the unit circle extends sine and cosine to all real numbers, traced counterclockwise.
HSF-TF.A.3Use special triangles to find sine, cosine and tangent for π/3, π/4 and π/6, and use the unit circle for π − x, π + x and 2π − x.
HSF-TF.A.4Use the unit circle to explain the symmetry and periodicity of the trigonometric functions.
HSF-TF.B.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency and midline.
HSF-TF.B.6Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
HSF-TF.B.7Use inverse functions to solve trigonometric equations that arise in modelling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
HSF-TF.C.8Prove the Pythagorean identity sin²θ + cos²θ = 1 and use it to find sine, cosine or tangent given one of them and the quadrant.
HSF-TF.C.9Prove the addition and subtraction formulas for sine, cosine and tangent and use them to solve problems.
HSG-C.A.2Identify and describe relationships among inscribed angles, radii and chords, including the relationship between central, inscribed and circumscribed angles and that a tangent is perpendicular to the radius at the point of tangency.
HSG-C.A.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
HSG-C.A.4Construct a tangent line from a point outside a given circle to the circle.
HSG-C.B.5Derive the fact that arc length and sector area are proportional to the radius, and define radian measure.
HSG-CO.A.1Know precise definitions of angle, circle, perpendicular line, parallel line and line segment.
HSG-CO.A.3Given a rectangle, parallelogram, trapezoid or regular polygon, describe the rotations and reflections that carry it onto itself.
HSG-CO.A.5Given a figure and a rotation, reflection or translation, draw the transformed figure, and specify a sequence of transformations that will carry one figure onto another.
HSG-CO.B.7Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and angles are congruent.
HSG-CO.B.8Explain how the criteria for triangle congruence (ASA, SAS and SSS) follow from the definition of congruence in terms of rigid motions.
HSG-CO.C.10Prove theorems about triangles.
HSG-CO.C.11Prove theorems about parallelograms: opposite sides are congruent, opposite angles are congruent, the diagonals bisect each other, and rectangles are parallelograms with congruent diagonals.
HSG-CO.C.9Prove theorems about lines and angles.
HSG-GMD.A.3Use volume formulas for cylinders, pyramids, cones and spheres to solve problems.
HSG-GMD.B.4Identify the shapes of two-dimensional cross-sections of three-dimensional objects.
HSG-GPE.A.1Derive the equation of a circle of given centre and radius using the Pythagorean theorem; complete the square to find the centre and radius of a circle given by an equation.
HSG-GPE.B.4Use coordinates to prove simple geometric theorems algebraically.
HSG-GPE.B.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
HSG-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
HSG-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, for example using the distance formula.
HSG-MG.A.1Use geometric shapes, their measures and their properties to describe objects.
HSG-MG.A.2Apply concepts of density based on area and volume in modelling situations.
HSG-SRT.B.4Prove theorems about triangles, including that a line parallel to one side divides the other two proportionally, and prove the Pythagorean theorem using triangle similarity.
HSG-SRT.B.5Use congruence and similarity criteria for triangles to solve problems and prove relationships.
HSG-SRT.C.6Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle.
HSG-SRT.C.7Explain and use the relationship between the sine and cosine of complementary angles.
HSG-SRT.C.8Use trigonometric ratios and the Pythagorean theorem to solve right triangles in applied problems.
HSG-SRT.D.10Prove the Laws of Sines and Cosines. (+)
HSG-SRT.D.11Understand and apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles. (+)
HSG-SRT.D.9Derive the formula A = ½ab·sin(C) for the area of a triangle. (+)
HSN-CN.A.1Know there is a complex number i such that i² = −1, and every complex number has the form a + bi with a and b real.
HSN-CN.A.2Use the relation i² = −1 and the commutative, associative and distributive properties to add, subtract and multiply complex numbers.
HSN-CN.A.3Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
HSN-CN.B.4Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
HSN-CN.B.5Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (−1 + √3 i)³ = 8 because (−1 + √3 i) has modulus 2 and argument 120°.
HSN-CN.B.6Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
HSN-CN.C.7Solve quadratic equations with real coefficients that have complex solutions.
HSN-RN.A.1Explain 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.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.
HSN-VM.A.1Recognise vector quantities as having both magnitude and direction; represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
HSN-VM.A.2Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
HSN-VM.A.3Solve problems involving velocity and other quantities that can be represented by vectors.
HSN-VM.B.4Add and subtract vectors.
HSN-VM.B.4.AAdd vectors end-to-end, component-wise, and by the parallelogram rule; understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
HSN-VM.B.4.BGiven two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
HSN-VM.B.4.CUnderstand vector subtraction v − w as v + (−w), where −w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction; represent vector subtraction graphically and perform it component-wise.
HSN-VM.B.5Multiply a vector by a scalar.
HSN-VM.B.5.ARepresent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise.
HSN-VM.B.5.BCompute the magnitude of a scalar multiple cv using ||cv|| = |c| v; compute the direction of cv knowing that when |c| v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
HSN-VM.C.10Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
HSN-VM.C.11Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector; work with matrices as transformations of vectors.
HSN-VM.C.12Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
HSN-VM.C.6Use matrices to represent and manipulate data, for example to represent payoffs or incidence relationships in a network.
HSN-VM.C.7Multiply matrices by scalars to produce new matrices, as when all the payoffs in a game are doubled.
HSN-VM.C.8Add, subtract and multiply matrices of appropriate dimensions.
HSN-VM.C.9Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not commutative, but that it is still associative and distributive.
HSS-CP.A.1Describe events as subsets of a sample space, using characteristics of the outcomes or unions, intersections and complements of other events.
HSS-CP.A.2Understand that two events are independent when the probability of both occurring together is the product of their probabilities.
HSS-CP.B.7Apply the addition rule P(A or B) = P(A) + P(B) - P(A and B), and interpret it in context.
HSS-CP.B.9Use permutations and combinations to compute probabilities of compound events and solve problems.
HSS-IC.A.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
HSS-IC.B.3Recognise the purposes of and differences among sample surveys, experiments and observational studies; explain how randomisation relates to each.
HSS-IC.B.4Use data from a sample survey to estimate a population mean or proportion, and develop a margin of error through the use of simulation models.
HSS-ID.A.1Represent data with plots on the real number line, including dot plots, histograms and box plots.
HSS-ID.A.2Use statistics appropriate to the shape of the data to compare centre (median, mean) and spread (interquartile range, standard deviation) of two or more data sets.
HSS-ID.A.3Interpret differences in shape, centre and spread in the context of the data sets, accounting for possible effects of outliers.
HSS-ID.A.4Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages.
HSS-ID.B.5Summarise categorical data for two categories in two-way frequency tables, and interpret joint, marginal and conditional relative frequencies.
HSS-ID.B.6.AFit a function to the data, and use functions fitted to data to solve problems in the context of the data.
HSS-ID.B.6.BInformally assess the fit of a function by plotting and analysing residuals.
HSS-ID.C.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
HSS-ID.C.8Compute and interpret the correlation coefficient of a linear fit.
HSS-ID.C.9Distinguish between correlation and causation.
HSS-MD.A.2Calculate the expected value of a random variable and interpret it as the mean of the probability distribution.

AP Calculus AB

CHA-2.AAP Calculus AB, Unit 2 — Determine average rates of change using difference quotients.
CHA-2.BAP Calculus AB, Unit 2 — Represent the derivative of a function as the limit of a difference quotient.
CHA-2.CAP Calculus AB, Unit 2 — Determine the equation of a line tangent to a curve at a given point.
CHA-2.DAP Calculus AB, Unit 2 — Estimate derivatives of a function at a point, from a table or a graph.
CHA-3.AAP Calculus AB, Unit 4 — Interpret the meaning of a derivative in context.
CHA-3.BAP Calculus AB, Unit 4 — Calculate rates of change in applied contexts, including position, velocity and acceleration.
CHA-3.DAP Calculus AB, Unit 4 — Calculate related rates in applied contexts.
CHA-3.EAP Calculus AB, Unit 4 — Interpret related rates in applied contexts.
CHA-3.FAP Calculus AB, Unit 4 — Approximate a value of a function using local linearity and linearization.
CHA-4.AAP Calculus AB, Unit 6 — Interpret the meaning of areas associated with the graph of a rate of change in context.
CHA-4.BAP Calculus AB, Unit 8 — Determine the average value of a function using definite integrals.
CHA-4.CAP Calculus AB, Unit 8 — Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
CHA-4.EAP Calculus AB, Unit 8 — Determine net change using definite integrals in applied contexts.
CHA-5.AAP Calculus AB, Unit 8 — Calculate areas in the plane using the definite integral.
CHA-5.BAP Calculus AB, Unit 8 — Calculate volumes of solids with known cross sections using definite integrals.
CHA-5.CAP Calculus AB, Unit 8 — Calculate volumes of solids of revolution using definite integrals: the disc and washer methods.
FUN-1.AAP Calculus AB, Unit 1 — Explain the behaviour of a function on an interval using the Intermediate Value Theorem.
FUN-1.BAP Calculus AB, Unit 5 — Justify conclusions about functions by applying the Mean Value Theorem over an interval.
FUN-1.CAP Calculus AB, Unit 5 — Justify conclusions about functions by applying the Extreme Value Theorem.
FUN-2.AAP Calculus AB, Unit 2 — Explain the relationship between differentiability and continuity.
FUN-3.AAP Calculus AB, Unit 2 — Calculate derivatives of familiar functions (the power rule, sums, polynomials).
FUN-3.BAP Calculus AB, Unit 2 — Calculate derivatives of products and quotients of differentiable functions.
FUN-3.CAP Calculus AB, Unit 3 — Calculate derivatives of compositions of differentiable functions (the chain rule).
FUN-3.DAP Calculus AB, Unit 3 — Calculate derivatives of implicitly defined functions.
FUN-3.EAP Calculus AB, Unit 3 — Calculate derivatives of inverse and inverse trigonometric functions.
FUN-3.FAP Calculus AB, Unit 3 — Determine higher-order derivatives of a function.
FUN-4.AAP Calculus AB, Unit 5 — Justify conclusions about the behaviour of a function based on the behaviour of its derivatives.
FUN-4.BAP Calculus AB, Unit 5 — Calculate minimum and maximum values in applied contexts or analysis of functions.
FUN-4.CAP Calculus AB, Unit 5 — Determine critical points of implicit relations.
FUN-5.AAP Calculus AB, Unit 6 — Represent accumulation functions using definite integrals, and differentiate them.
FUN-6.AAP Calculus AB, Unit 6 — Calculate a definite integral using areas and properties of definite integrals.
FUN-6.BAP Calculus AB, Unit 6 — Evaluate definite integrals analytically using the Fundamental Theorem of Calculus.
FUN-6.CAP Calculus AB, Unit 6 — Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives (with the constant of integration).
FUN-6.DAP Calculus AB, Unit 6 — For integrands requiring substitution or rearrangement into equivalent forms, determine indefinite integrals and evaluate definite integrals.
LIM-1.AAP Calculus AB, Unit 1 — Represent limits analytically using correct notation, and interpret limits expressed in analytic notation.
LIM-1.CAP Calculus AB, Unit 1 — Estimate limits of functions (from graphs and from tables).
LIM-1.DAP Calculus AB, Unit 1 — Determine the limits of functions using limit theorems.
LIM-1.EAP Calculus AB, Unit 1 — Determine limits using equivalent expressions for the function, or the squeeze theorem — the 0/0 case.
LIM-2.AAP Calculus AB, Unit 1 — Justify conclusions about continuity at a point using the definition.
LIM-2.BAP Calculus AB, Unit 1 — Determine intervals over which a function is continuous.
LIM-2.CAP Calculus AB, Unit 1 — Determine values of x or solve for parameters that make discontinuous functions continuous, if possible.
LIM-2.DAP Calculus AB, Unit 1 — Interpret the behaviour of functions using limits involving infinity.
LIM-5.AAP Calculus AB, Unit 6 — Approximate a definite integral using geometric and numerical methods.
LIM-5.BAP Calculus AB, Unit 6 — Interpret the limiting case of the Riemann sum as a definite integral.
LIM-5.CAP Calculus AB, Unit 6 — Represent the limiting case of the Riemann sum as a definite integral.