Secondary Mathematics II (Utah Core Standards)

Number and Quantity

• SII.N.RN.1 Explain how rational exponents are defined by extending the rules for integer exponents (e.g. 5^(1/3) as the cube root of 5).
• SII.N.RN.2 Rewrite expressions with radicals and rational exponents using exponent properties.
• SII.N.RN.3 Explain why sums and products of rationals are rational and why mixing a rational and an irrational (nonzero) gives an irrational.
• SII.N.CN.1 Know the number i with i² = −1 and that every complex number is a + bi with real a and b.
• SII.N.CN.2 Add, subtract and multiply complex numbers using i² = −1 (powers of i limited to i²).
• SII.N.CN.7 Solve quadratics with real coefficients whose solutions are complex.
• SII.N.CN.8 Extend polynomial identities to complex numbers for quadratics with real coefficients.
• SII.N.CN.9 Know the Fundamental Theorem of Algebra and show it holds for quadratic polynomials.

Algebra

• SII.A.SSE.1 Interpret quadratic and exponential expressions in terms of their context.
  • a. Interpret terms, factors and coefficients in an expression.
  • b. Interpret complex expressions by treating parts as single quantities, e.g. P(1 + r)ⁿ.
• SII.A.SSE.2 Use an expression's structure to find ways to rewrite it (e.g. x⁴ − y⁴ as a difference of squares).
• SII.A.SSE.3 Choose an equivalent form of an expression that reveals properties of the quantity.
  • a. Factor a quadratic to show the zeros of its function.
  • b. Complete the square to show a quadratic function's maximum or minimum.
  • c. Use exponent properties to rewrite exponential expressions (e.g. annual to monthly rates).
• SII.A.APR.1 Know polynomials are closed under addition, subtraction and multiplication like the integers; add, subtract and multiply them.
• SII.A.CED.1 Create one-variable equations and inequalities from linear, quadratic and exponential situations.
• SII.A.CED.2 Create equations in two or more variables for relationships and graph them with labeled axes and scales.
• SII.A.CED.4 Rearrange formulas to isolate a quantity, including formulas with squared variables.
• SII.A.REI.4 Solve quadratic equations in one variable.
  • a. Complete the square to rewrite a quadratic as (x − p)² = q and derive the quadratic formula.
  • b. Solve quadratic equations by inspection, square roots, completing the square, the formula and factoring.
• SII.A.REI.7 Solve a system of one linear and one quadratic equation algebraically and graphically.

Functions

• SII.F.IF.4 Interpret key graph and table features in context (intercepts, increase/decrease, maxima, symmetry, end behavior) and sketch graphs.
• SII.F.IF.5 Link a function's domain to its graph and to the situation it models.
• SII.F.IF.6 Calculate and interpret average rate of change over an interval and estimate it from a graph.
• SII.F.IF.7 Graph functions from their equations and show key features, by hand or with technology.
  • a. Graph linear and quadratic functions showing intercepts, maxima and minima.
  • b. Graph piecewise functions, including step and absolute value functions, noting domain restrictions.
• SII.F.IF.8 Rewrite a function in equivalent forms to reveal different properties.
  • a. Factor or complete the square in a quadratic to show zeros, extreme values and symmetry, and interpret them.
  • b. Use exponent properties to interpret exponential functions, e.g. as percent growth or decay.
• SII.F.IF.9 Compare properties of two functions shown in different ways, relating coefficients to roots where useful.
• SII.F.BF.1 Write a function for a relationship between two quantities.
  • a. Find an explicit expression or recursive steps for quadratic and exponential contexts.
  • b. Combine standard function types with arithmetic operations to model a situation.
• SII.F.BF.3 Describe how adding k, multiplying by k or replacing x by kx or x + k changes a graph; find k; recognize even and odd functions.
• SII.F.LE.3 Use graphs and tables to see that exponential growth eventually exceeds linear, quadratic or any polynomial growth.
• SII.F.TF.8 Prove that sine squared plus cosine squared equals 1, then use it to find other trig values from one value and the quadrant.

Geometry

• SII.G.CO.9 Prove theorems about lines and angles (vertical angles, angles with parallel lines, perpendicular bisector points).
• SII.G.CO.10 Prove theorems about triangles (angle sum, isosceles base angles, midsegment, medians meeting at a point).
• SII.G.CO.11 Prove theorems about parallelograms (opposite sides and angles, bisecting diagonals, rectangles' diagonals).
• SII.G.SRT.1 Check by experiment the properties of dilations with a center and scale factor.
  • a. A dilation maps a line not through the center to a parallel line and leaves lines through the center unchanged.
  • b. A dilated segment is longer or shorter by the scale factor.
• SII.G.SRT.2 Use similarity transformations to decide if figures are similar and explain similarity of triangles through matching angles and proportional sides.
• SII.G.SRT.3 Use similarity transformations to establish the AA similarity criterion.
• SII.G.SRT.4 Prove triangle theorems such as the side-splitter theorem and the Pythagorean Theorem using similarity.
• SII.G.SRT.5 Use congruence and similarity criteria to solve problems and prove relationships in figures.
• SII.G.SRT.6 Understand that side ratios in right triangles depend on the angles, leading to the trigonometric ratios.
• SII.G.SRT.7 Explain and use how sine and cosine of complementary angles are related.
• SII.G.SRT.8 Solve right triangles in applied problems with trig ratios and the Pythagorean Theorem.
• SII.G.C.1 Prove that all circles are similar.
• SII.G.C.2 Describe relationships among inscribed, central and circumscribed angles, radii and chords, including tangent and radius.
• SII.G.C.3 Construct a triangle's inscribed and circumscribed circles and prove angle facts for cyclic quadrilaterals.
• SII.G.C.4 (+) Construct a tangent from an outside point to a circle.
• SII.G.C.5 Use similarity to show arc length is proportional to radius, define radians and derive the sector area formula.
• SII.G.GPE.1 Derive the equation of a circle from the Pythagorean Theorem and complete the square to find center and radius.
• SII.G.GPE.4 Prove simple geometry theorems algebraically with coordinates.
• SII.G.GPE.6 Find the point that divides a directed segment in a given ratio.
• SII.G.GMD.1 Give informal arguments for circle circumference and area and for cylinder, pyramid and cone volume formulas.
• SII.G.GMD.3 Solve problems using the formulas for the volume of a cylinder, pyramid, cone or sphere.

Statistics and Probability

• SII.S.ID.5 Summarize two categorical variables in two-way tables and interpret joint, marginal and conditional relative frequencies.
• SII.S.CP.1 Describe events as subsets of the set of outcomes and with unions, intersections and complements ("or", "and", "not").
• SII.S.CP.4 Build and read two-way tables to decide independence and find conditional probabilities.
• SII.S.CP.5 Explain conditional probability and independence in plain language with everyday examples.
• SII.S.CP.6 Find P(A|B) as the share of B's outcomes that are also in A and interpret it.