Government Standards
Common Core
Math - Grade 11
Assessment Exam - Common Core Math - High School: Number and Quantity| The Real Number System | eTAP Lesson |
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| Extend the properties of exponents to rational exponents. | |
| 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. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
CCSS.Math.Content.HSN.RN.A.1 |
Real Numbers Square Roots |
| Rewrite expressions involving radicals and rational exponents using the properties of exponents.
CCSS.Math.Content.HSN.RN.A.2 |
Simplifying Square Roots |
| Use properties of rational and irrational numbers. | |
| Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
CCSS.Math.Content.HSN.RN.B.3 |
Adding and Subtracting Radical Expressions Radical Equations |
| Quantities | eTAP Lesson |
| Reason quantitatively and use units to solve problems. | |
| Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
CCSS.Math.Content.HSN.Q.A.1 |
Word Problems of Measurements & Four Operations |
| Define appropriate quantities for the purpose of descriptive modeling.
CCSS.Math.Content.HSN.Q.A.2 |
Cubic Units for Volume |
| Interpreting Categorical and Quantitative Data | eTAP Lesson |
| Summarize, represent, and interpret data on two categorical and quantitative variables | |
| Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
CCSS.Math.Content.HSS.ID.B.5 |
Data Classification, Range, and Midrange |
| Quantities | eTAP Lesson |
| Reason quantitatively and use units to solve problems. | |
| Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
CCSS.Math.Content.HSN.Q.A.3 |
Finding Answers to Questions |
| The Complex Number System | eTAP Lesson |
| Perform arithmetic operations with complex numbers. | |
| Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.
CCSS.Math.Content.HSN.CN.A.1 |
Complex Numbers |
| Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
CCSS.Math.Content.HSN.CN.A.2 |
Commutative and Associative Property |
| Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
CCSS.Math.Content.HSN.CN.A.3 |
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| Represent complex numbers and their operations on the complex plane. | |
| Represent 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.
CCSS.Math.Content.HSN.CN.B.4 |
Complex Plane |
| Represent 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°.
CCSS.Math.Content.HSN.CN.B.5 |
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| Calculate 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.
CCSS.Math.Content.HSN.CN.B.6 |
Complex Numbers |
| Use complex numbers in polynomial identities and equations. | |
| Solve quadratic equations with real coefficients that have complex solutions.
CCSS.Math.Content.HSN.CN.C.7 |
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| Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).
CCSS.Math.Content.HSN.CN.C.8 |
Multiplying and Dividing Polynomials |
| Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
CCSS.Math.Content.HSN.CN.C.9 |
De Moivre’s Theorem |
| Vector and Matrix Quantities | eTAP Lesson |
| Represent and model with vector quantities. | |
| Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
CCSS.Math.Content.HSN.VM.A.1 |
Two Dimensional Vectors |
| Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
CCSS.Math.Content.HSN.VM.A.2 |
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| Solve problems involving velocity and other quantities that can be represented by vectors.
CCSS.Math.Content.HSN.VM.A.3 |
One Dimensional Motion Problems (Newton's Second Law) |
| Perform operations on vectors. | |
| Add 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.
CCSS.Math.Content.HSN.VM.B.4.a |
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| Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
CCSS.Math.Content.HSN.VM.B.4.b |
Two Dimensional Trajectory Problems |
| Understand 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 by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
CCSS.Math.Content.HSN.VM.B.4.c |
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| Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
CCSS.Math.Content.HSN.VM.B.5.a |
Two Dimensional Problems Involving Balanced Forces |
| Compute 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).
CCSS.Math.Content.HSN.VM.B.5.b |
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| Perform operations on matrices and use matrices in applications. | |
| Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
CCSS.Math.Content.HSN.VM.C.6 |
What are Matrices |
| Add, subtract, and multiply matrices of appropriate dimensions.
CCSS.Math.Content.HSN.VM.C.7 |
Adding Matrices Subtracting Matrices |
| Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
CCSS.Math.Content.HSN.VM.C.9 |
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| Understand 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.
CCSS.Math.Content.HSN.VM.C.10 |
Solving Linear Systems with Matrices |
| Multiply 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.
CCSS.Math.Content.HSN.VM.C.11 |
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| Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
CCSS.Math.Content.HSN.VM.C.12 |
Determinant |
