Skills to prepare for PSAT
Find the math, reading and writing skills covered by PSAT/NMSQT, PSAT 10 and PSAT 8/9.
PSAT/NMSQT math skills
34 skill groups across 4 topic areasAlgebra
Linear equations, functions, systems and inequalities
Algebra
Linear equations, functions, systems and inequalities
Solve linear equations
Solve a linear equation in one variable, including equations with brackets and fractions. Use its structure to choose an efficient method.
Write equations from a situation
Translate a relationship into a linear equation and explain what its variables, constants and solution mean.
Recognize equations with one, no or many solutions
Determine which coefficient values make a linear equation have one solution, no solution or infinitely many solutions.
Connect linear graphs, tables and rules
Find a linear function from two input-output pairs or a point and a rate of change. Move between its equation, table and graph.
Interpret slope, intercepts and function values
Explain a rate of change, starting amount or input-output pair in context. Evaluate a linear function or find the input for a given output.
Work with equations in two variables
Write and graph a linear relationship or constraint, identify solutions and interpret intercepts. Use slopes to recognize parallel or perpendicular lines.
Solve two linear equations together
Represent two constraints with a system, find their shared solution algebraically or graphically, and interpret the intersection in context.
Determine how many solutions a system has
Use the relationship between two linear equations to decide whether their graphs meet once, never meet or represent the same line.
Represent and solve linear inequalities
Translate constraints into inequalities in one or two variables. Interpret a point or shaded region as satisfying, or not satisfying, the constraints.
Advanced math
Equivalent expressions, quadratic equations and nonlinear functions
Advanced math
Equivalent expressions, quadratic equations and nonlinear functions
Calculate with polynomials
Add, subtract and multiply polynomial expressions, combining like terms and applying the distributive property.
Factor polynomial expressions
Take out a common factor, factor a difference of squares and rewrite a quadratic trinomial as a product of two binomials.
Solve quadratic equations
Choose factoring, square roots, completing the square or the quadratic formula to solve an equation in one variable.
Solve a linear and a nonlinear equation together
Find solutions shared by a line and a nonlinear graph, using algebra or intersections, and connect the solutions to the two equations.
Rearrange an equation or formula
Treat the other quantities as parameters and isolate the variable being asked for.
Read quadratic and exponential functions
Connect tables, equations and graphs of quadratic, exponential, polynomial and simple rational functions, including transformations. Interpret features and parameters in context.
Use nonlinear function notation
Evaluate a nonlinear function at a given input. For a quadratic function, find an input that produces a specified output.
Solve absolute-value, rational and radical equations
Use equation structure and valid algebraic operations to solve linear absolute-value equations and simple rational or radical equations.
Determine the number of real quadratic solutions
Decide which parameter values give a quadratic equation no real solutions, one real solution or two real solutions.
Create quadratic and exponential models
Choose a quadratic or exponential function for a situation and explain how its parameters and graph describe the relationship.
Problem-solving and data analysis
Rates, percentages, data displays and probability
Problem-solving and data analysis
Rates, percentages, data displays and probability
Use ratios, rates and proportions
Solve proportional relationships, including unit rates, and convert quantities between units consistently.
Calculate percentages and percent change
Solve discounts, interest, tax and tip problems. Connect a percent increase or decrease with its multiplier, including percentages greater than 100.
Read one-variable data displays
Interpret frequency tables, histograms, dot plots and box plots. Use their scales and frequencies to describe a distribution.
Compare center, spread and outliers
Calculate and interpret mean, median and range. Compare distributions using center and standard deviation, and explain how outliers affect mean and median.
Read scatterplots and fit a linear model
Interpret a scatterplot, fit linear, quadratic or exponential models, and use a model to make predictions. Distinguish linear from exponential growth.
Calculate probability from a data display
Use one- or two-way tables, area models or a description to find relative frequencies, probabilities and conditional probabilities. Work backward to find a missing frequency when a probability is given.
Estimate a population from a sample
Use a sample mean or sample proportion to estimate the corresponding population mean or proportion.
Geometry and trigonometry
Measurement, similar triangles and right-triangle trigonometry
Geometry and trigonometry
Measurement, similar triangles and right-triangle trigonometry
Calculate perimeter and area
Choose and use a suitable formula to solve a geometric or real-world measurement problem.
Calculate surface area and volume
Use the given dimensions and the appropriate surface-area or volume formula. Find a missing quantity when other measurements are supplied.
Apply scale factors to measurements
Use a length scale factor of k, an area factor of k squared and a volume factor of k cubed.
Use the triangle angle sum
Find a missing angle by using the fact that the interior angles of a triangle add to 180 degrees.
Apply the Pythagorean theorem
Find an unknown side of a right triangle and use the result in a geometric or practical problem.
Use triangle congruence and similarity
Apply congruence or similarity criteria, proportional side lengths and the fact that angle measures do not change under a dilation.
Use line and angle relationships
Solve problems involving vertical angles and the angles formed when a transversal crosses parallel lines. Identify statements needed to establish a geometric relationship.
Use special triangles and trigonometric ratios
Find missing measurements with special right-triangle relationships and right-triangle trigonometry.
PSAT/NMSQT reading and writing skills
21 skill groups across 4 topic areasInformation and ideas
Main points, evidence and inferences
Information and ideas
Main points, evidence and inferences
Identify the central idea
Determine the main point of a short passage and distinguish it from a detail or a statement that goes beyond the text.
Interpret key supporting details
Explain what a specific detail says and how it supports the main idea or a stated conclusion.
Choose evidence for a claim
Select the fact, quotation, example or finding that most directly supports a specified claim.
Use evidence from a graph or table
Read the values and categories in an informational graphic and select the data that support a specified claim.
Draw a supported inference
Combine stated information with what the passage implies to reach a conclusion that follows from the evidence.
Craft and structure
Word choice, text purpose and connections between passages
Craft and structure
Word choice, text purpose and connections between passages
Determine what a word means in context
Choose the meaning of an academic word or phrase that fits the surrounding passage.
Choose a precise word or phrase
Select wording that expresses the intended meaning logically and precisely in the supplied context.
Explain a text purpose or structure
Identify the main rhetorical purpose of a passage or explain how its information is organized.
Explain the role of a sentence or detail
Determine how a specific part of a passage contributes to the argument, explanation or overall purpose.
Connect two related passages
Determine where two authors agree or differ, or how one author would respond to a claim in the other passage.
Expression of ideas
Using notes and connecting ideas for a writing goal
Expression of ideas
Using notes and connecting ideas for a writing goal
Combine notes for a specific purpose
Select and integrate relevant information from supplied notes to introduce a topic, emphasize a finding, compare ideas or meet another stated writing goal.
Choose a logical transition
Identify the relationship between ideas, such as contrast, example, cause or continuation, and choose the transition that expresses it.
Standard English conventions
Complete sentences, punctuation and grammatical agreement
Standard English conventions
Complete sentences, punctuation and grammatical agreement
Punctuate sentence boundaries
Choose an appropriate sentence ending or clause connection so that the result is complete, not a fragment or run-on.
Punctuate clauses and lists
Use punctuation and, where needed, a conjunction or conjunctive adverb to connect clauses or separate items in a series.
Punctuate added information
Set off an appositive or parenthetical phrase correctly and recognize when a sentence element needs no separating punctuation.
Match subjects and verbs
Identify the grammatical subject and choose a verb that agrees with it in number, even when other words intervene.
Match pronouns with their antecedents
Choose a singular or plural pronoun that agrees with the noun or noun phrase it refers to.
Choose a verb or verbal form
Distinguish a sentence verb from a gerund, participle or infinitive and use the form required by the sentence structure.
Use the right verb tense and aspect
Use the surrounding time relationships to choose the appropriate tense and aspect of a verb.
Place modifiers next to what they describe
Choose a sentence structure in which a descriptive phrase clearly and logically modifies the intended subject.
Distinguish plurals, possessives and contractions
Use singular, plural and possessive nouns or pronouns correctly. Distinguish forms such as its and it is, their and they are, and there.
PSAT 10 math skills
34 skill groups across 4 topic areasAlgebra
Linear equations, functions, systems and inequalities
Algebra
Linear equations, functions, systems and inequalities
Solve linear equations
Solve a linear equation in one variable, including equations with brackets and fractions. Use its structure to choose an efficient method.
Write equations from a situation
Translate a relationship into a linear equation and explain what its variables, constants and solution mean.
Recognize equations with one, no or many solutions
Determine which coefficient values make a linear equation have one solution, no solution or infinitely many solutions.
Connect linear graphs, tables and rules
Find a linear function from two input-output pairs or a point and a rate of change. Move between its equation, table and graph.
Interpret slope, intercepts and function values
Explain a rate of change, starting amount or input-output pair in context. Evaluate a linear function or find the input for a given output.
Work with equations in two variables
Write and graph a linear relationship or constraint, identify solutions and interpret intercepts. Use slopes to recognize parallel or perpendicular lines.
Solve two linear equations together
Represent two constraints with a system, find their shared solution algebraically or graphically, and interpret the intersection in context.
Determine how many solutions a system has
Use the relationship between two linear equations to decide whether their graphs meet once, never meet or represent the same line.
Represent and solve linear inequalities
Translate constraints into inequalities in one or two variables. Interpret a point or shaded region as satisfying, or not satisfying, the constraints.
Advanced math
Equivalent expressions, quadratic equations and nonlinear functions
Advanced math
Equivalent expressions, quadratic equations and nonlinear functions
Calculate with polynomials
Add, subtract and multiply polynomial expressions, combining like terms and applying the distributive property.
Factor polynomial expressions
Take out a common factor, factor a difference of squares and rewrite a quadratic trinomial as a product of two binomials.
Solve quadratic equations
Choose factoring, square roots, completing the square or the quadratic formula to solve an equation in one variable.
Solve a linear and a nonlinear equation together
Find solutions shared by a line and a nonlinear graph, using algebra or intersections, and connect the solutions to the two equations.
Rearrange an equation or formula
Treat the other quantities as parameters and isolate the variable being asked for.
Read quadratic and exponential functions
Connect tables, equations and graphs of quadratic, exponential, polynomial and simple rational functions, including transformations. Interpret features and parameters in context.
Use nonlinear function notation
Evaluate a nonlinear function at a given input. For a quadratic function, find an input that produces a specified output.
Solve absolute-value, rational and radical equations
Use equation structure and valid algebraic operations to solve linear absolute-value equations and simple rational or radical equations.
Determine the number of real quadratic solutions
Decide which parameter values give a quadratic equation no real solutions, one real solution or two real solutions.
Create quadratic and exponential models
Choose a quadratic or exponential function for a situation and explain how its parameters and graph describe the relationship.
Problem-solving and data analysis
Rates, percentages, data displays and probability
Problem-solving and data analysis
Rates, percentages, data displays and probability
Use ratios, rates and proportions
Solve proportional relationships, including unit rates, and convert quantities between units consistently.
Calculate percentages and percent change
Solve discounts, interest, tax and tip problems. Connect a percent increase or decrease with its multiplier, including percentages greater than 100.
Read one-variable data displays
Interpret frequency tables, histograms, dot plots and box plots. Use their scales and frequencies to describe a distribution.
Compare center, spread and outliers
Calculate and interpret mean, median and range. Compare distributions using center and standard deviation, and explain how outliers affect mean and median.
Read scatterplots and fit a linear model
Interpret a scatterplot, fit linear, quadratic or exponential models, and use a model to make predictions. Distinguish linear from exponential growth.
Calculate probability from a data display
Use one- or two-way tables, area models or a description to find relative frequencies, probabilities and conditional probabilities. Work backward to find a missing frequency when a probability is given.
Estimate a population from a sample
Use a sample mean or sample proportion to estimate the corresponding population mean or proportion.
Geometry and trigonometry
Measurement, similar triangles and right-triangle trigonometry
Geometry and trigonometry
Measurement, similar triangles and right-triangle trigonometry
Calculate perimeter and area
Choose and use a suitable formula to solve a geometric or real-world measurement problem.
Calculate surface area and volume
Use the given dimensions and the appropriate surface-area or volume formula. Find a missing quantity when other measurements are supplied.
Apply scale factors to measurements
Use a length scale factor of k, an area factor of k squared and a volume factor of k cubed.
Use the triangle angle sum
Find a missing angle by using the fact that the interior angles of a triangle add to 180 degrees.
Apply the Pythagorean theorem
Find an unknown side of a right triangle and use the result in a geometric or practical problem.
Use triangle congruence and similarity
Apply congruence or similarity criteria, proportional side lengths and the fact that angle measures do not change under a dilation.
Use line and angle relationships
Solve problems involving vertical angles and the angles formed when a transversal crosses parallel lines. Identify statements needed to establish a geometric relationship.
Use special triangles and trigonometric ratios
Find missing measurements with special right-triangle relationships and right-triangle trigonometry.
PSAT 10 reading and writing skills
21 skill groups across 4 topic areasInformation and ideas
Main points, evidence and inferences
Information and ideas
Main points, evidence and inferences
Identify the central idea
Determine the main point of a short passage and distinguish it from a detail or a statement that goes beyond the text.
Interpret key supporting details
Explain what a specific detail says and how it supports the main idea or a stated conclusion.
Choose evidence for a claim
Select the fact, quotation, example or finding that most directly supports a specified claim.
Use evidence from a graph or table
Read the values and categories in an informational graphic and select the data that support a specified claim.
Draw a supported inference
Combine stated information with what the passage implies to reach a conclusion that follows from the evidence.
Craft and structure
Word choice, text purpose and connections between passages
Craft and structure
Word choice, text purpose and connections between passages
Determine what a word means in context
Choose the meaning of an academic word or phrase that fits the surrounding passage.
Choose a precise word or phrase
Select wording that expresses the intended meaning logically and precisely in the supplied context.
Explain a text purpose or structure
Identify the main rhetorical purpose of a passage or explain how its information is organized.
Explain the role of a sentence or detail
Determine how a specific part of a passage contributes to the argument, explanation or overall purpose.
Connect two related passages
Determine where two authors agree or differ, or how one author would respond to a claim in the other passage.
Expression of ideas
Using notes and connecting ideas for a writing goal
Expression of ideas
Using notes and connecting ideas for a writing goal
Combine notes for a specific purpose
Select and integrate relevant information from supplied notes to introduce a topic, emphasize a finding, compare ideas or meet another stated writing goal.
Choose a logical transition
Identify the relationship between ideas, such as contrast, example, cause or continuation, and choose the transition that expresses it.
Standard English conventions
Complete sentences, punctuation and grammatical agreement
Standard English conventions
Complete sentences, punctuation and grammatical agreement
Punctuate sentence boundaries
Choose an appropriate sentence ending or clause connection so that the result is complete, not a fragment or run-on.
Punctuate clauses and lists
Use punctuation and, where needed, a conjunction or conjunctive adverb to connect clauses or separate items in a series.
Punctuate added information
Set off an appositive or parenthetical phrase correctly and recognize when a sentence element needs no separating punctuation.
Match subjects and verbs
Identify the grammatical subject and choose a verb that agrees with it in number, even when other words intervene.
Match pronouns with their antecedents
Choose a singular or plural pronoun that agrees with the noun or noun phrase it refers to.
Choose a verb or verbal form
Distinguish a sentence verb from a gerund, participle or infinitive and use the form required by the sentence structure.
Use the right verb tense and aspect
Use the surrounding time relationships to choose the appropriate tense and aspect of a verb.
Place modifiers next to what they describe
Choose a sentence structure in which a descriptive phrase clearly and logically modifies the intended subject.
Distinguish plurals, possessives and contractions
Use singular, plural and possessive nouns or pronouns correctly. Distinguish forms such as its and it is, their and they are, and there.
PSAT 8/9 math skills
25 skill groups across 4 topic areasAlgebra
Linear equations, functions, systems and inequalities
Algebra
Linear equations, functions, systems and inequalities
Solve linear equations
Solve a linear equation in one variable, including equations with brackets and fractions. Use its structure to choose an efficient method.
Write equations from a situation
Translate a relationship into a linear equation and explain what its variables, constants and solution mean.
Connect linear graphs, tables and rules
Find a linear function from two input-output pairs or a point and a rate of change. Move between its equation, table and graph.
Interpret slope, intercepts and function values
Explain a rate of change, starting amount or input-output pair in context. Evaluate a linear function or find the input for a given output.
Work with equations in two variables
Write and graph a linear relationship or constraint, identify solutions and interpret intercepts. Use slopes to recognize parallel or perpendicular lines.
Solve two linear equations together
Represent two constraints with a system, find their shared solution algebraically or graphically, and interpret the intersection in context.
Represent and solve linear inequalities
Translate constraints into inequalities in one or two variables. Interpret a point or shaded region as satisfying, or not satisfying, the constraints.
Advanced math
Equivalent expressions, quadratic equations and nonlinear functions
Advanced math
Equivalent expressions, quadratic equations and nonlinear functions
Calculate with polynomials
Add, subtract and multiply polynomial expressions, combining like terms and applying the distributive property.
Factor polynomial expressions
Take out a common factor, factor a difference of squares and rewrite a quadratic trinomial as a product of two binomials.
Solve quadratic equations
Choose factoring, square roots, completing the square or the quadratic formula to solve an equation in one variable.
Solve a linear and a nonlinear equation together
Find solutions shared by a line and a nonlinear graph, using algebra or intersections, and connect the solutions to the two equations.
Rearrange an equation or formula
Treat the other quantities as parameters and isolate the variable being asked for.
Read quadratic and exponential functions
Connect a table, equation and graph of a quadratic or exponential function without transformations. Interpret an intercept, initial value or other input-output pair.
Use nonlinear function notation
Evaluate a nonlinear function at a given input. For a quadratic function, find an input that produces a specified output.
Problem-solving and data analysis
Rates, percentages, data displays and probability
Problem-solving and data analysis
Rates, percentages, data displays and probability
Use ratios, rates and proportions
Solve proportional relationships, including unit rates, and convert quantities between units consistently.
Calculate percentages and percent change
Solve discounts, interest, tax and tip problems. Connect a percent increase or decrease with its multiplier, including percentages greater than 100.
Read one-variable data displays
Interpret frequency tables, histograms, dot plots and box plots. Use their scales and frequencies to describe a distribution.
Compare center, spread and outliers
Calculate and interpret mean, median and range. Compare distributions with different means and the same standard deviation, and explain how outliers affect mean and median.
Read scatterplots and fit a linear model
Describe a relationship shown in a scatterplot, fit a linear model to the data, and interpret a graph representing two quantities.
Calculate probability from a data display
Use one- or two-way tables, area models or a description to find relative frequencies, probabilities and conditional probabilities. Work backward to find a missing frequency when a probability is given.
Geometry
Area, volume, scale factors and right triangles
Geometry
Area, volume, scale factors and right triangles
Calculate perimeter and area
Choose and use a suitable formula to solve a geometric or real-world measurement problem.
Calculate surface area and volume
Use the given dimensions and the appropriate surface-area or volume formula. Find a missing quantity when other measurements are supplied.
Apply scale factors to measurements
Use a length scale factor of k, an area factor of k squared and a volume factor of k cubed.
Use the triangle angle sum
Find a missing angle by using the fact that the interior angles of a triangle add to 180 degrees.
Apply the Pythagorean theorem
Find an unknown side of a right triangle and use the result in a geometric or practical problem.
PSAT 8/9 reading and writing skills
21 skill groups across 4 topic areasInformation and ideas
Main points, evidence and inferences
Information and ideas
Main points, evidence and inferences
Identify the central idea
Determine the main point of a short passage and distinguish it from a detail or a statement that goes beyond the text.
Interpret key supporting details
Explain what a specific detail says and how it supports the main idea or a stated conclusion.
Choose evidence for a claim
Select the fact, quotation, example or finding that most directly supports a specified claim.
Use evidence from a graph or table
Read the values and categories in an informational graphic and select the data that support a specified claim.
Draw a supported inference
Combine stated information with what the passage implies to reach a conclusion that follows from the evidence.
Craft and structure
Word choice, text purpose and connections between passages
Craft and structure
Word choice, text purpose and connections between passages
Determine what a word means in context
Choose the meaning of an academic word or phrase that fits the surrounding passage.
Choose a precise word or phrase
Select wording that expresses the intended meaning logically and precisely in the supplied context.
Explain a text purpose or structure
Identify the main rhetorical purpose of a passage or explain how its information is organized.
Explain the role of a sentence or detail
Determine how a specific part of a passage contributes to the argument, explanation or overall purpose.
Connect two related passages
Determine where two authors agree or differ, or how one author would respond to a claim in the other passage.
Expression of ideas
Using notes and connecting ideas for a writing goal
Expression of ideas
Using notes and connecting ideas for a writing goal
Combine notes for a specific purpose
Select and integrate relevant information from supplied notes to introduce a topic, emphasize a finding, compare ideas or meet another stated writing goal.
Choose a logical transition
Identify the relationship between ideas, such as contrast, example, cause or continuation, and choose the transition that expresses it.
Standard English conventions
Complete sentences, punctuation and grammatical agreement
Standard English conventions
Complete sentences, punctuation and grammatical agreement
Punctuate sentence boundaries
Choose an appropriate sentence ending or clause connection so that the result is complete, not a fragment or run-on.
Punctuate clauses and lists
Use punctuation and, where needed, a conjunction or conjunctive adverb to connect clauses or separate items in a series.
Punctuate added information
Set off an appositive or parenthetical phrase correctly and recognize when a sentence element needs no separating punctuation.
Match subjects and verbs
Identify the grammatical subject and choose a verb that agrees with it in number, even when other words intervene.
Match pronouns with their antecedents
Choose a singular or plural pronoun that agrees with the noun or noun phrase it refers to.
Choose a verb or verbal form
Distinguish a sentence verb from a gerund, participle or infinitive and use the form required by the sentence structure.
Use the right verb tense and aspect
Use the surrounding time relationships to choose the appropriate tense and aspect of a verb.
Place modifiers next to what they describe
Choose a sentence structure in which a descriptive phrase clearly and logically modifies the intended subject.
Distinguish plurals, possessives and contractions
Use singular, plural and possessive nouns or pronouns correctly. Distinguish forms such as its and it is, their and they are, and there.