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Heart of Algebra on the SAT Test

Heart of Algebra Subscore on the SAT Test

Included topics: linear equations, linear systems of equations, linear functions and linear inequalities.

  • Heart of algebra subscore is one of the three SAT math test subscores.
  • Heart of algebra subscore includes four core algebra topics: linear functions, linear equations, systems of linear equations and linear inequalities.
  • Heart of algebra subscore questions include multiple choice questions and student produced response questions. 
  • The use of a calculator is permitted for part of the questions.
  • The grade of heart of algebra subscore is reported on a scale of 1 to 15.
  • The skills tested in heart of algebra subscore include creating, analyzing and solving equations and inequalities.
  • Some questions test your ability to represent a word problem algebraically. This will require defining variables, writing expressions, solving equations and interpreting the solution in terms of the question.
  • Other questions focus on interpreting the relationship between graphic and algebraic presentations. 

Linear equations SAT topic

linear equation is an algebraic equation in which each term has an exponent of one. It is called linear because it can be graphed as a straight line in the xy-plane. Since this is a fundamental topic it appears in many SAT questions. 

Linear equations formula sheet and types of questions are listed below.

Click here to learn the required skills and solve questions about linear equations.

Linear equations formula sheet

Calculating an output of an expression SAT questions

In these questions you need to calculate the value of an expression. In some questions you are given a word problem and in other questions you are given an equation that you have to use it order to solve the expression.

Solving a linear equation SAT questions

 In these questions you are given an equation and you are asked to solve it. Some questions may include fractions or absolute values. 

Linear equations that don't have one solution SAT questions

 In these questions you are asked to solve an equation that has no solution or an infinite number of solutions.

Creating and solving an equation from a word problem SAT questions

In these questions you are given a word problem from which you need to write an equation and solve it.

Click here to learn the required skills and solve questions about linear equations.

Linear functions SAT topic

linear function is an equation that represents the relationship between two variables, most commonly called x and y. It is called linear because it can be graphed as a straight line in the xy-plane. Since this is a fundamental topic it appears in many SAT questions.

Linear functions formula sheet and types of questions are listed below.

Click here to learn the required skills and solve questions about linear functions.

Creating a linear function SAT questions

In these questions you are given a word problem and you are asked to write the function that describes the problem without solving it.

Finding the value of an output of a given function SAT questions

In these questions you are given the equation of the function and you are asked to solve this function given the values of the variables.

Finding the input that corresponds to a given output of a function SAT questions

In these questions you know the equation of the function and you are asked to calculate the input of this function given the value of the output.

Interpretation of a linear function SAT questions

In these questions you need to analyze the linear function in its slope-intercept form: y=mx+b.

Finding the equation of a linear function SAT questions

In these questions you need to write the equation of the linear function y=mx+b given values of its points or its slope b.

Graphic presentation of a linear function SAT questions

In these questions you need to identify a graph of a given linear function or to find the equation of a linear function y=mx+b given the graph of the function.

Relationships between two linear functions SAT questions

In these questions you need to find the slope of a linear function given the slope of another function or to find the equation of a linear function given an equation of another function.

Click here to learn the required skills and solve questions about linear functions.

Systems of linear equations SAT topic

System of linear equations is a set of two or more linear equations. In SAT questions we usually see systems of equations containing 2 equations with 2 variables x and y. If we are given a word problem, we first need to define the variables and then write 2 equations with these variables.

The types of questions about linear equations are listed below.

Click here to learn the required skills and solve questions about system of linear equations.

Creating a system of linear equations SAT questions

In these questions you need to create a system of linear equations from a word problem.

Solving a system of linear equations SAT questions

In these questions you need to solve a system of linear equations. In order to solve the equations, we need to reduce 2 equations with 2 variables to 1 equation with 1 variable. This should be done with either substitution or elimination. 

Determining the number of solutions for a system of linear equations SAT questions

In these questions you will be asked to determine if the  system of equations has one solution, no solution and an infinite number of solutions. 

Graphic presentation of a system of linear equations SAT questions

In these questions you need to identify a graph of a given system of equations.

Click here to learn the required skills and solve questions about system of linear equations.

Linear inequalities SAT topic

Linear inequality is linear equation in which the equal sign is replaced by one of the symbols of inequality. The solution of a linear equation is a range of values, rather than one specific value.

A system of linear inequalities is similar to a system of linear equations, the difference is in the sign. We use the system of inequalities when we a have a word problem with number of constrains instead of one (we write an inequality for each constrain). 

The types of questions about linear inequalities are listed below.

Click here to learn the required skills and solve questions about linear inequalities.

Creating and solving a linear inequality SAT questions

In these questions you need to create a linear inequality from a word problem and solve it. Solving a linear inequality may require changing the direction of the inequality sign.

Finding values that don't satisfy an inequality SAT questions

In these questions you need to find values that are not a solution for a linear inequality.

Graphic presentation of a linear inequality SAT questions

In these questions you need to identify a graphic presentation of an inequality. The answers to the inequality are represented by the area below or above the line of its equation. 

Creating a system of linear inequalities SAT questions

In these questions you need to create a system of linear inequalities from a word problem.

Finding possible solutions for a system of linear inequalities SAT questions

In these questions you need to decide which values satisfy a given system of linear inequalities. Sometimes you will need to translate a word problem into a system of inequalities as explained before.

Solving a system of linear inequalities SAT questions

In these questions you need to turn a system of linear inequalities to one inequality that can be solved easily. This can be achieved using additional data or by turning one of the inequalities to an equation. You may also need to translate a word problem to a system of inequalities.

Graphic presentation of a system of linear inequalities SAT questions

In these questions you need to identify a graphic presentation of a system of inequalities given its formulas or to write the formulas of the system that correspond to a given graphic presentation. 

Click here to learn the required skills and solve questions about linear inequalities.