Standards: Math
CCSS.MATH.CONTENT.HSG.SRT.4
(0)
Education Level: 9-12
Prove theorems involving similarity.
Description:
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
CCSS.MATH.CONTENT.HSG.SRT.5
(1)
Education Level: 9-12
Prove theorems involving similarity.
Description:
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
CCSS.MATH.CONTENT.HSG.SRT.6
(2)
Education Level: 9-12
Define trigonometric ratios and solve problems involving right triangles.
Description:
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
CCSS.MATH.CONTENT.HSG.SRT.7
(0)
Education Level: 9-12
Define trigonometric ratios and solve problems involving right triangles.
Description:
Explain and use the relationship between the sine and cosine of complementary angles.
CCSS.MATH.CONTENT.HSG.SRT.8
(1)
Education Level: 9-12
Define trigonometric ratios and solve problems involving right triangles.
Description:
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
CCSS.MATH.CONTENT.HSG.SRT.9
(0)
Education Level: 9-12
Apply trigonometry to general triangles.
Description:
Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
CCSS.MATH.CONTENT.HSN.CN.1
(1)
Education Level: 9-12
Perform arithmetic operations with complex numbers.
Description:
Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real.
CCSS.MATH.CONTENT.HSN.CN.2
(1)
Education Level: 9-12
Perform arithmetic operations with complex numbers.
Description:
Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
CCSS.MATH.CONTENT.HSN.CN.3
(1)
Education Level: 9-12
Perform arithmetic operations with complex numbers.
Description:
Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
CCSS.MATH.CONTENT.HSN.CN.4
(0)
Education Level: 9-12
Represent complex numbers and their operations on the complex plane.
Description:
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.5
(0)
Education Level: 9-12
Represent complex numbers and their operations on the complex plane.
Description:
Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3i)^3 = 8 because (-1 + √3i) has modulus 2 and argument 120°.
CCSS.MATH.CONTENT.HSN.CN.6
(0)
Education Level: 9-12
Represent complex numbers and their operations on the complex plane.
Description:
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.7
(0)
Education Level: 9-12
Use complex numbers in polynomial identities and equations.
Description:
Solve quadratic equations with real coefficients that have complex solutions.
CCSS.MATH.CONTENT.HSN.CN.8
(0)
Education Level: 9-12
Use complex numbers in polynomial identities and equations.
Description:
Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
CCSS.MATH.CONTENT.HSN.CN.9
(0)
Education Level: 9-12
Use complex numbers in polynomial identities and equations.
Description:
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.