Grade 10 Math Practice

Understand the properties of exponential functions, including growth and decay, and analyze their graphs, including asymptotes and transformations.

Explore logarithmic functions as the inverse of exponential functions, understanding their properties, including change of base and solving logarithmic equations.

Perform operations of addition, subtraction, and multiplication on polynomials, including combining like terms and applying the distributive property.

Explore the characteristics of polynomial functions, including their degree, identifying roots (zeros), and predicting end behavior based on the leading term.

Analyze and graph quadratic functions by understanding the vertex form and how transformations (translations, stretches, reflections) affect the parent function y=x^2.

Simplify rational expressions by factoring and performing operations (addition, subtraction, multiplication, division), including finding common denominators.

Analyze arithmetic and geometric sequences and series, including finding explicit and recursive formulas, and calculating sums.

Master techniques for solving quadratic equations, including factoring, using the square root property, and completing the square to find real and complex solutions.

Solve equations containing rational expressions by clearing denominators and checking for extraneous solutions.

Solve systems of non-linear equations and inequalities graphically and algebraically, including systems involving quadratic and absolute value functions.

Apply the quadratic formula to solve quadratic equations and use the discriminant to determine the nature and number of solutions (real, complex, distinct, repeated).

Extend the number system to include complex numbers, performing operations (addition, subtraction, multiplication, division) and exploring their geometric interpretation on the complex plane.

Explore the fundamental concept of limits of functions as input approaches a certain value, and understand the definition and properties of continuity for functions.

Students will calculate the arc length and area of sectors of circles, understanding the relationship between the central angle, radius, and these measures.

Students will use coordinate geometry to calculate the area and perimeter of various polygons, employing distance formula and other relevant techniques.

Students will explore theorems related to circles, including inscribed angles, central angles, tangents, secants, and chords, and apply these to solve problems and prove geometric relationships.

Students will write and analyze formal proofs to establish congruence and similarity of triangles and other polygons, utilizing theorems such as SSS, SAS, ASA, AAS, and AA similarity.

Students will visualize and describe the shapes of two-dimensional cross sections resulting from slicing three-dimensional figures with planes.

Students will derive and use the standard equation of a circle given the center and radius, and vice versa, and graph circles in the coordinate plane.

Students will perform and justify fundamental geometric constructions, such as bisecting angles and segments, constructing perpendicular lines, and creating equilateral triangles, using only a compass and straightedge.

Students will understand the geometric interpretations of algebraic equations, such as the relationship between the equation of a line and its graph, and the geometric meaning of solutions to systems of equations.

Students will learn and apply the Law of Sines and the Law of Cosines to find unknown side lengths and angle measures in any triangle, not just right triangles.

Students will investigate and prove properties of parallelograms, rectangles, rhombuses, squares, trapezoids, and kites, including their diagonals, angles, and side lengths.

Students will calculate the surface area and volume of three-dimensional figures, including prisms, pyramids, cylinders, cones, and spheres, using appropriate formulas.

Students will explore and apply translations, reflections, rotations, and dilations to geometric figures in the coordinate plane, understanding how these transformations affect coordinates and properties of shapes.

Students will define and apply sine, cosine, and tangent ratios to solve problems involving right triangles, including finding unknown side lengths and angle measures.

Students will learn to represent and perform operations on vectors, including addition, subtraction, and scalar multiplication, and apply these concepts to solve geometric problems.

Understand the concept of conditional probability and use it to determine if events are independent or dependent, applying these concepts to real-world scenarios.

Understand and apply concepts of correlation to describe the relationship between two quantitative variables, and use linear regression to model and predict.

Analyze and interpret univariate and bivariate data distributions, including measures of center, spread, and shape, and identify patterns and outliers.

Understand the concept of a sampling distribution and its role in making inferences about population parameters from sample data.

Use probability to evaluate outcomes of decisions, including situations involving random events and uncertain outcomes.

Analyze and graph sinusoidal functions, including amplitude, period, phase shifts, and vertical shifts.

Solve trigonometric equations for angles within a specified interval, utilizing identities and inverse trigonometric functions.

Prove and apply fundamental trigonometric identities, including Pythagorean, reciprocal, and quotient identities.

Explore the unit circle to understand trigonometric functions for any angle and convert between degrees and radians.