#### IM3.1: Algebra and Functions

IM3.1.1: Find the zeros, domain and range of a function.

IM3.1.4: Analyze, describe and sketch graphs of quadratic functions and include the lines of symmetry.

IM3.1.5: Determine how the graph of a parabola changes if a, b and c changes in the equation y = a(x - b)² + c. Find an equation for a parabola when given sufficient information.

IM3.1.7: Analyze, describe and sketch graphs of polynomial functions by examining intercepts, zeros, domain and range, and end behavior.

IM3.1.9: Perform arithmetic operations, including long division and division with remainders, on polynomials by others of equal or lower degree.

IM3.1.10: Factor polynomials completely and solve polynomial equations by factoring.

IM3.1.14: Analyze, describe and sketch graphs of rational functions by examining intercepts, zeros, domain and range, and asymptotic and end behavior.

IM3.1.16: Understand the properties of rational exponents and use the properties to simplify, multiply, divide and find powers of expressions containing negative and fractional exponents. Relate expressions containing rational exponents to the corresponding radical expressions.

IM3.1.17: Analyze, describe and sketch graphs of square root and cube root functions by examining intercepts, zeros, domain and range, and end behavior.

IM3.1.19: Solve problems that can be modeled using equations involving rational and radical functions, including problems of direct and inverse variation. Interpret the solutions and determine whether the solutions are reasonable.

IM3.1.20: Analyze, describe and sketch graphs of exponential functions by examining intercepts, zeros, domain and range, and asymptotic and end behavior.

IM3.1.21: Know that the inverse of an exponential function is a logarithm. Use laws of exponents to derive laws of logarithms. Use the inverse relationship between exponential functions and logarithms and the laws of logarithms to solve problems.

IM3.1.24: Write the recursive formula for arithmetic and geometric sequences and find specified terms of arithmetic and geometric sequences.

IM3.1.25: Write the formula for the general term for arithmetic and geometric sequences and make connections to linear and exponential functions.

IM3.1.27: Solve problems involving applications that can be modeled using sequences and finite arithmetic and geometric series. Interpret the solutions and determine whether the solutions are reasonable using spreadsheets as appropriate.

#### IM3.2: Geometry and Measurement

IM3.2.1: Represent geometric objects and figures algebraically using coordinates, use algebra to solve geometric problems, and develop simple coordinate proofs involving geometric objects in the coordinate plane.

IM3.2.2: Construct triangles congruent to given triangles. Explain and justify the process used.

IM3.2.3: Develop simple geometric proofs involving triangles and provide reasons for each statement of the proof.

IM3.2.4: Find the equation of a circle in the coordinate plane in terms of its center and radius and determine how the graph of a circle changes if a, b and r are changed in the equation (x - a)² + (y - b)² = r².

IM3.2.5: Find and use measures of sides, volumes and surface areas of prisms, regular pyramids, cylinders, right circular cones and spheres. Relate these measures to each other using formulas.

IM3.2.6: Visualize solids and surfaces in three-dimensional space when given two-dimensional representations, and create two-dimensional representations for the surfaces of three-dimensional objects.

#### IM3.3: Data Analysis and Statistics

IM3.3.1: Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions.

IM3.3.4: Compute basic statistics (mean, median, weighted mean, range, variance, standard deviation) and understand the distinction between a statistic and a parameter.

IM3.3.6: Use simulations to construct empirical probability distributions.

IM3.3.9: Compute the probability of compound events.

#### IM3.4: Discrete Mathematics

IM3.4.5: Explain and illustrate the role of definitions, conjectures, theorems, proofs and counterexamples in mathematical reasoning. Construct logical arguments, assess the validity of logical arguments and give counterexamples to disprove statements.

IM3.4.6: Model and solve problems involving patterns using recursion and iteration, growth and decay, and compound interest.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.