Grade 9 Math Practice

Understand the definition of exponential functions and graph them, identifying key features like growth/decay rates and asymptotes.

Factor polynomials, including common binomial factors and trinomials, to simplify expressions and solve equations.

Understand the definition of a function and use function notation, evaluating functions for given inputs and interpreting the meaning of the output.

Solve linear equations and inequalities in one variable, including those with absolute value, and interpret their solutions in context.

Graph linear functions, identifying and interpreting slope, y-intercept, and domain/range in real-world contexts.

Construct exponential functions to model situations involving exponential growth or decay, interpreting the parameters.

Construct linear functions to model relationships between quantities, interpreting the parameters in terms of the context.

Add, subtract, and multiply polynomials, understanding the properties of exponents.

Identify and graph quadratic functions, understanding the shape of a parabola and key features like the vertex and axis of symmetry.

Simplify radical expressions and expressions with rational exponents, applying properties of exponents.

Understand the concept of rational expressions as fractions with polynomial numerators and denominators, and identify values for which they are undefined.

Understand arithmetic sequences and series, identifying the common difference and calculating terms and sums.

Understand geometric sequences and series, identifying the common ratio and calculating terms and sums.

Simplify rational expressions by factoring and canceling common factors, understanding the restrictions on the variable.

Solve quadratic equations by completing the square, understanding the process and its connection to the quadratic formula.

Solve quadratic equations by factoring, understanding the zero product property.

Solve rational equations, identifying extraneous solutions that arise from the process.

Solve systems of linear equations and inequalities in two variables, including by graphing, substitution, and elimination, and interpret the solutions graphically.

Apply the quadratic formula to solve quadratic equations, including those with no real solutions.

Explore the concept of imaginary numbers and their extension to complex numbers, including basic operations like addition, subtraction, and multiplication.

Develop foundational skills in logical reasoning, including understanding conditional statements, converses, inverses, and contrapositives, and applying these to construct basic geometric proofs.

Calculate the area and perimeter of various polygons, including triangles, quadrilaterals, and regular polygons, using appropriate formulas.

Study the properties of circles, including tangents, secants, chords, and inscribed angles, and apply theorems related to them.

Explore the properties of rigid transformations (translations, rotations, reflections) and their impact on geometric figures, establishing criteria for congruence.

Utilize the coordinate plane to analyze geometric figures, including calculating distances between points and finding midpoints of segments.

Perform compass and straightedge constructions to create geometric figures and demonstrate understanding of their properties.

Investigate and prove properties of parallelograms, rectangles, rhombuses, squares, trapezoids, and kites, using deductive reasoning.

Understand the concept of similarity, focusing on dilations and establishing similarity criteria for triangles (AA, SAS, SSS).

Introduce and apply trigonometric ratios (sine, cosine, tangent) to solve problems involving right triangles, including finding unknown side lengths and angles.

Determine the volume and surface area of three-dimensional figures such as prisms, pyramids, cylinders, cones, and spheres.

Compare and contrast two or more univariate datasets by examining their distributions, including measures of center, spread, and shape, using appropriate graphical displays and statistical measures.

Create scatterplots to visualize the relationship between two quantitative variables and interpret patterns, trends, and associations, including identifying outliers.

Analyze and interpret the characteristics of a single variable dataset, including measures of center, spread, and shape, using graphical representations like histograms and box plots.

Understand the concept of correlation and use linear regression to model the relationship between two quantitative variables, including interpreting the slope and intercept of the regression line.

Introduce fundamental trigonometric identities and use them to solve basic trigonometric equations.

Explore the unit circle to understand trigonometric functions for any angle and learn to measure angles in radians.