What 10th grade math students should know varies depending on where they live. No national mathematics curriculum exists in the United States. Individual states and school districts set up their own curricula and determine the progression, pacing and sequencing of math courses.

### The Facts

Because there is no nationally delineated curriculum, a 10th-grade student in one school may have completed a course in geometry, while a 10th-grade student in another school hasn’t yet begun a geometry course. Moreover, many districts have moved to blended curricula in which components of arithmetic, algebra and geometry are combined. In this type of setup, students may solve algebraic equations, construct geometric proofs and calculate probabilities all within the same week. However, the Common Core State Standards -- a set of suggested guidelines which some states have opted to follow -- describe general mathematical processes that high school students should be developing. For instance, students should be making conjectures, recognizing patterns, evaluating claims and analyzing solutions. And broadly speaking, there are particular skills and concepts most 10th-grade math students should have attained or be in the process of attaining.

### Arithmetic Skills

Tenth-grade math students should be highly proficient in all facets of arithmetic. They should be able to convert between fractions, decimals and percents and solve problems written in these forms. Students must be comfortable using the order of operations to solve problems involving radicals and exponents, including fractional and negative exponents. They should know how to work with absolute value and scientific notation. Students need to be able to classify numbers by type, such as rational, irrational, complex and real, and also must be able to identify number properties, such as the commutative and associative properties.

### Algebraic Topics

By 10th grade, most students already will have completed Algebra 1 or a blended course which focuses heavily on algebraic concepts. Thus, most 10th-grade students should be able to solve multistep linear and quadratic equations, employing methods such as factoring or the quadratic formula when necessary. They should solve systems of two or more equations via substitution or elimination. Students should understand equations as functions and know how to graph them in the coordinate plane. They also must be able to solve and graph inequalities and systems of inequalities. Other important algebraic skills include understanding slope as a rate of change, expanding binomials and simplifying rational expressions.

### Geometry Concepts

Although many 10th-grade students are just beginning a full year geometry, they already should be familiar with certain facets of the subject. They should know how to calculate the area and perimeter of basic two-dimensional shapes including squares, rectangles, triangles and parallelograms. They should understand the Pythagorean Theorem, a^2 + b^2 = c^2, and be able to use it to find the side and hypotenuse lengths of right triangles. Students should know how to calculate the diameter, radius and circumference of circles, and should be comfortable finding volumes of cubes, cylinders and rectangular prisms. Additional geometric topics 10th graders should be familiar with include parallelism, perpendicularity and similar figures.