# Student Question Bank: Math Questions

Because each question on the Math section deals with different numbers and mathematical scenarios, it's not as simple as the Reading and Writing section to identify exactly what each question stem will look like. You can still use the descriptions in this section to determine which math domains and skills you want to focus on in the Student Question Bank.

## Math Questions

Identify, create, work with, and solve linear equations. This skill may include interpreting different parts of an equation like constants, variables, factors, terms, or solutions.

Domain: Algebra

Skill: Linear equations in one variable

Skill: Linear equations in one variable

Work with linear functions to model relationships. This may include interpreting input/output pairs, variables, constants, graphs, tables, and rate of change. This skill may also test your ability to make connections between a function and a matching table or algebraic representation.

Domain: Algebra

Skill: Linear functions in one variable

Skill: Linear functions in one variable

Work with linear equations in the form

*Ax+By=C*, including finding the value of one variable when given the other and making connections between models, graphs, tables, and algebraic representation of these equations. This skill may also test your ability to write the equation of a line, find its slope, or identify a parallel or perpendicular line.
Domain: Algebra

Skill: Linear equations in two variables

Skill: Linear equations in two variables

Work with systems of equations, including determining when the system has no solution, a unique solution, or infinite solutions. This skill may also test your ability to connect a system of equations to a matching graph.

Domain: Algebra

Skill: Systems of two linear equations in two variables

Skill: Systems of two linear equations in two variables

Work with linear inequalities in one or two variables, including interpreting a point in the

*xy*-plane as a possible solution and making connections between tabular, algebraic, and graphical representations of the inequality.
Domain: Algebra

Skill: Linear inequalities in one or two variables

Skill: Linear inequalities in one or two variables

Use algebraic structure and the properties of operations to factor, rewrite, add, subtract, and multiply polynomials. This skill may also test your ability to rewrite an expression with rational exponents in radical form.

Domain: Advanced Math

Skill: Equivalent expressions

Skill: Equivalent expressions

Solve quadratic equations, absolute value equations, rational and radical equations, polynomial equations, and systems of equations. This skill may also test your ability to determine the number of real solutions that exist for a quadratic equation or to match the solutions to a system of equations with a graph.

Domain: Advanced Math

Skill: Nonlinear equations in one variable and systems of equations in two variables

Skill: Nonlinear equations in one variable and systems of equations in two variables

Work with quadratic and exponential functions to model a relationship, including interpreting the meaning of input/output pairs, constants, variables, factors, and terms. This skill may also test your ability to interpret and transform the graph of a quadratic, exponential, polynomial, or rational function.

Domain: Advanced Math

Skill: Nonlinear functions

Skill: Nonlinear functions

Solve problems by using a proportional relationship between quantities, calculating or using a ratio or rate, and/or using units, derived units, and unit conversion. This skill may also test your ability to work with scale drawings and problems in natural and social sciences.

Domain: Problem-Solving and Data Analysis

Skill: Ratios, rates, proportional relationships, and units

Skill: Ratios, rates, proportional relationships, and units

Use percentages to solve problems including, but not limited to, calculating discounts, interest, taxes, and tips. This skill may also test your ability to recognize the relationship between a percent increase or decrease and growth factor.

Domain: Problem-Solving and Data Analysis

Skill: Percentages

Skill: Percentages

Analyze and interpret data distributions represented with frequency tables, histograms, dot plots, and box plots. This skill may test your ability to calculate and interpret mean, median, range, measures of center and spread, outliers, and standard deviation. You may also be asked to compare these factors between multiple data distributions.

Domain: Problem-Solving and Data Analysis

Skill: One-variable data—Distributions and measures of center and spread

Skill: One-variable data—Distributions and measures of center and spread

Use scatterplots to analyze, interpret, and make predictions about data. This skill may also test your ability to fit linear, quadratic, and exponential models to data in a scatterplot or to interpret a graph modeling a relationship between two quantities.

Domain: Problem-Solving and Data Analysis

Skill: Two-variable data—Models and scatterplots

Skill: Two-variable data—Models and scatterplots

Solve problems by calculating probability or conditional probability using tables, area models, or descriptions of situations.

Domain: Problem-Solving and Data Analysis

Skill: Probability and conditional probability

Skill: Probability and conditional probability

Use sample mean and sample proportion to estimate population mean and population proportion. Interpret margin of error, and understand that a larger sample size generally leads to a smaller margin of error.

Domain: Problem-Solving and Data Analysis

Skill: Inference from sample statistics and margin of error

Skill: Inference from sample statistics and margin of error

Given a description of a study, determine whether there is evidence for a causal relationship, and understand why random assignment provides evidence for a causal relationship. You may also be given random samples and asked to identify or describe which population the results can be extended to.

Domain: Problem-Solving and Data Analysis

Skill: Evaluating statistical claims—Observational studies and experiments

Skill: Evaluating statistical claims—Observational studies and experiments

Solve real-world and mathematical problems about area, perimeter, surface area, or volume of a geometric figure, and use scale factors to calculate changes to length and area.

Domain: Geometry and Trigonometry

Skill: Area and volume

Skill: Area and volume

Solve problems using concepts and theorems relating to congruence and similarity of triangles, including the triangle sum theorem, vertical angel theorem, and the relationship of angles formed when a transversal cuts parallel lines. Understand how scale factor changes lengths but doesn't change angles.

Domain: Geometry and Trigonometry

Skill: Lines, angles, and triangles

Skill: Lines, angles, and triangles

Solve problems using the Pythagorean theorem, properties of special right triangles, and right triangle trigonometry. Calculate sine, cosine, and tangent for similar triangles, and solve problems using the relationship between sine and cosine of complementary angles.

Domain: Geometry and Trigonometry

Skill: Right triangles and trigonometry

Skill: Right triangles and trigonometry

Solve problems using definitions, properties, and theorems relating to circles, radii, diameters, tangents, angles, arc lengths, and sector areas. This skill may include working with ordered pairs, converting angle measures between degrees and radians, creating and interpreting graphs of circles, using the distance formula, using the unit circle, or completing the square in an equation representing a circle.

Domain: Geometry and Trigonometry

Skill: Circles

Skill: Circles