MATHEMATICS

• Apply arithmetic properties to operate on and simplify expressions that include radicals and other real numbers.
• Use the complex number system, the notation for complex numbers, and the definition of “i” to solve problems in standard form.
• Add, subtract, multiply, and divide complex numbers.
• Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic problems.
• Use advanced formulas or functions to solve problems.
• Apply the properties of arithmetic and geometric sequences and series to solve problems.
• Use exponential functions to solve problems involving exponential growth and decrease.
• Use the properties of many types of functions including polynomial, absolute value, exponential, and logarithmic, to identify the function’s graph.
• Use the appropriate terminology and notation to define functions and their properties, including domain, range, function composition, inverses, zeros and asymptotes.
• Describe the relationship among relations and functions.
• Solve equations and inequalities involving absolute values.
• Solve systems of linear equations and inequalities in two or three variables using a variety of strategies, such as substitution, graphing or matrices.
• Solve equations containing radicals and exponents.
• Factor polynomials representing perfect squares, the difference in squares, perfect square trinomials, the sum and difference of cubes and general trinomials.
• Apply quadratic equations to solve real-world situations and complex number problems.
• Use the binomial theorem to expand binomial expression.
• Use the fundamental counting principles for combinations and permutations to determine probability.
• Calculate probabilities of events under different relationships such as inclusion, disjoint, complementary, independent, and dependent, with replacement and without replacement.
• Use the right triangle relationships of trigonometric ratio, cosine, sine and tangent to solve problems.

• Use right triangle trigonometric ratios to determine an unknown length of a side or the measure or an angle.
• Solve problems using the formulas for perimeter, circumference, area and volume of two- and three- dimensional figures and solids and determine the effect of dimension changes to perimeter, area and volume.
• Use reasoning to create and defend geometric conjectures.
• Use the concept of corresponding parts to prove that triangles and other polygons are congruent or similar.
• Explain properties and characteristics of angle bisectors, perpendicular bisectors and parallel lines.
• Use the relationship between pairs of angles (complementary, supplementary, vertical, exterior, interior) to determine unknown angle measures or definitions of properties.
• Apply the concepts of special right triangles to real-world situations.
• Use the relationships among properties of circles (chords, secants, tangents, arcs, circumference, radius, diameter, inscribed polygons) to solve problems.
• Use coordinate geometry to produce formulas and prove theorems for the midpoint of a line segment, the distance formula and forms of equations of lines and circles.
• Describe the concept of rigid motion on figures in the coordinate plane, including rotation, translation and reflection.
• Use concrete objects, pictorial representations, computer software or graphing calculators to solve geometric problems.

• Express complex numbers in standard and polar form and convert from one to another.
• Add, subtract, multiply, divide, and find powers of complex numbers in polar form.
• Use vector operations, including dot product and cross product, the law of sines and the law of cosines to solve problems.
• Calculate linear and angular velocity.
• Find the sine, cosine, tangent, cotangent, secant and cosecant of an angle in standard position.
• Use the relationship among the six trigonometric functions to translate among them.
• Recognize the trigonometric functions of benchmark angles.
• Translate between radians and degrees.
• Find the value of any trigonometric function and inverse trigonometric function and solve trigonometric equations
• Use the fundamental trigonometric identities, including the sum and difference formulas, double-angle formulas and half-angle formulas to solve problems
• Verify trigonometric identities.
• Solve trigonometric equations and inverse trigonometric equations that include all solutions or solutions with restricted domains
• Use the trigonometric functions in the form y = ASin (Bx+C) + D to determine various properties of the function including domain, range, period, phase shift and amplitude.
• Identify real-world phenomena that can be represented by a trigonometric function in the form y = ASin (Bx + C) + D.
• Explain the relationship between trigonometric functions and their inverse.

• Recognize limits from graphs and tables.
• Find limits of sums, differences, products, quotients and rational functions.
• Understand continuity in terms of limits and functions.
• Find the derivatives of functions, including polynomial, rational, trigonometric, logarithmic, inverse, composite and exponential functions.
• Find the derivatives of implicitly-defined functions.
• Find points of inflection of functions.
• Use implicit differentiation to find the derivative of an inverse function.
• Use integration by substitution or change of variable to evaluate integrals.
• Use Riemann sums, the trapezoidal rule and technology to approximate definite integrals of functions represented algebraically, geometrically or by tables of values.
• Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions and applications to motion along a line.
• Use definite integrals to find the area between a curve and the x-axis, the average value of a function over a closed interval and the volume of a solid with known cross-sectional area.
• Apply the intermediate value theorem and extreme value theorem on a function over a closed interval.
• Apply the fundamental theorem of calculus, that is, interpret a definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval.
• Describe the concept of a derivative geometrically, numerically, analytically and verbally.
• Find second derivatives and derivatives of higher order.
• Prove the mean value theorem.
• Find average and instantaneous rates of change.
• Use first and second derivatives to describe the behavior of functions.