PSAT/NMSQT, PSAT 10 and PSAT 8/9

• Identifying central ideas, themes, and supporting details

  ≈ 4%1 h 30 min

  This topic covers identifying a text’s central idea or theme and distinguishing the details that develop, refine, or qualify it. On the PSAT, questions typically ask for the best statement of the main idea, theme, or the role of specific details in an informational or literary text.

  • Identify the central idea of an informational text from explicit statements and the overall development of the passage.
  • Determine the theme of a literary text from characters, events, setting, and outcome.
  • Distinguish supporting details from less relevant or merely interesting information.
  • Explain how specific details develop, refine, qualify, or illustrate a central idea or theme.
  • Evaluate whether a proposed summary accurately captures the text’s most important ideas without distortion or unnecessary detail.

• Making logical inferences from what a text states and implies

  ≈ 3%1 h 15 min

  This topic covers drawing logical conclusions from what a text directly states and what it strongly implies. On the PSAT, questions test whether students can make warranted inferences about ideas, relationships, attitudes, motivations, or outcomes without overreaching beyond the evidence in the passage.

  • Draw a logical inference from one or more explicit details in a text.
  • Interpret what a text implies about a character, speaker, event, idea, or situation.
  • Infer relationships such as cause and effect, comparison, contrast, or sequence when they are suggested rather than directly stated.
  • Evaluate which conclusion is most strongly supported by the passage.
  • Differentiate a valid inference from an unsupported assumption or overgeneralization.

• Selecting textual evidence that best supports a claim

  ≈ 3%1 h 15 min

  This topic covers selecting the textual evidence that most directly and sufficiently supports a stated claim, answer, or conclusion. On the PSAT, questions may ask students to choose the quotation, detail, or set of lines that best justifies an interpretation of a passage.

  • Select the quotation or detail that best supports a given claim about a text.
  • Match a conclusion or interpretation to the most relevant and sufficient textual evidence.
  • Evaluate competing pieces of evidence for precision, relevance, and strength of support.
  • Identify which lines in a passage provide the clearest basis for an answer to a reading question.
  • Reject evidence that is related to the topic but does not adequately support the specific claim.

• Interpreting tables, graphs, and quantitative evidence in context

  ≈ 3%1 h 30 min

  This topic covers interpreting quantitative information presented in tables, graphs, or simple data displays and connecting it accurately to the accompanying text. On the PSAT, questions test whether students can read values, trends, and comparisons and judge how numerical evidence supports, weakens, or clarifies a written claim.

  • Interpret values, labels, scales, and categories in a table, graph, or other quantitative display.
  • Compare quantities, trends, or groups shown in quantitative evidence.
  • Connect quantitative information to a claim or description in the accompanying text.
  • Determine whether a statement is supported, contradicted, or not fully supported by the data provided.
  • Use quantitative evidence to clarify the meaning of a passage or to identify the most accurate conclusion consistent with both text and data.

About 5 h 30 min of study, lessons and core practice

• Controlling sentence boundaries and core punctuation

  ≈ 4%1 h 45 min

  This topic covers the conventions that create complete sentences and correctly connect or separate sentence parts. On the PSAT, students edit short passages to fix run-ons, fragments, comma splices, and errors with punctuation marks such as commas, semicolons, colons, dashes, apostrophes, and end punctuation.

  • Identify and correct sentence boundary errors, including fragments, run-on sentences, and comma splices.
  • Distinguish independent clauses from dependent clauses and apply the punctuation needed to join or separate them correctly.
  • Apply standard conventions for commas, semicolons, colons, and dashes in sentences with introductory elements, items in a series, nonrestrictive elements, and clause relationships.
  • Use apostrophes correctly in contractions and in singular and plural possessive nouns.
  • Choose and maintain appropriate end punctuation and internal punctuation to preserve standard written English and intended meaning.

• Using phrases, clauses, and modifiers clearly

  ≈ 2.5%1 h 15 min

  This topic focuses on building clear sentences by placing phrases, clauses, and modifiers so that relationships are precise and unambiguous. On the PSAT, questions ask students to revise awkward or unclear constructions, including misplaced and dangling modifiers and faulty coordination or subordination.

  • Distinguish phrases from clauses and use each structure appropriately in standard written English.
  • Revise sentences to place modifiers next to the words they modify and eliminate misplaced or dangling modifiers.
  • Use subordinate and coordinate structures to show logical relationships among ideas clearly.
  • Choose among participial, prepositional, appositive, relative, and other modifying structures to make meaning precise.
  • Maintain clarity and sentence sense when adding, deleting, or repositioning modifying words, phrases, and clauses.

• Maintaining verb form, tense, mood, and agreement

  ≈ 3%1 h 30 min

  This topic covers verb tense, form, mood, and agreement so that sentences are grammatically consistent and logically clear. On the PSAT, students must edit verbs to match subjects, maintain appropriate tense sequences, and use standard English forms in finite and nonfinite constructions.

  • Ensure subject-verb agreement in simple and more complex sentences, including sentences with intervening phrases or inverted order.
  • Maintain consistent and appropriate verb tense to reflect timing, sequence, and general truth.
  • Choose correct verb forms, including principal parts and appropriate uses of finite and nonfinite verbs.
  • Apply standard English conventions for mood, including indicative, imperative, and conditional or subjunctive uses where tested.
  • Revise sentences to preserve logical agreement and consistency among verbs across a sentence or passage.

• Using pronouns and possessives precisely

  ≈ 1.5%1 h

  This topic addresses the precise use of pronouns and possessive forms so that references are clear and grammatically correct. On the PSAT, questions test agreement, case, clarity of reference, and the distinction between pronoun forms and possessive determiners or nouns.

  • Ensure pronoun-antecedent agreement in number and, when appropriate, person.
  • Choose the correct pronoun case in subject, object, and possessive positions.
  • Revise sentences to eliminate ambiguous, vague, or missing pronoun references.
  • Distinguish correctly among pronouns, contractions, and possessive forms such as its/it’s, whose/who’s, and their/they’re/there when tested in context.
  • Form and use singular and plural possessives correctly to express ownership or association.

• Maintaining comparison, parallelism, and sentence sense

  ≈ 2%1 h 15 min

  This topic covers sentence constructions that must be logically matched and grammatically balanced, including comparisons, parallel structure, and conventional usage. On the PSAT, students revise sentences to make comparisons clear, coordinate ideas in parallel form, and preserve standard idiomatic patterns and overall sentence sense.

  • Revise faulty comparisons so that items compared are logically and grammatically comparable.
  • Maintain parallel structure in words, phrases, clauses, and items in a series or paired construction.
  • Use comparative and superlative forms appropriately to express degree and comparison.
  • Choose standard idiomatic expressions and conventional preposition patterns in context.
  • Evaluate sentence sense and revise awkward or illogical constructions that disrupt meaning even when wording appears grammatically similar.

About 6 h 45 min of study, lessons and core practice

• Choosing transitions and logical links

  ≈ 3.5%1 h

  This topic covers choosing words, phrases, and clauses that clearly show the logical relationship within and between sentences and ideas. On the PSAT, students revise a sentence or short passage by selecting the transition or linking language that best matches the meaning and flow of the surrounding text.

  • Choose a transition that accurately signals the relationship between ideas, including addition, contrast, concession, cause and effect, condition, sequence, comparison, and example.
  • Apply transitions to connect information within a sentence, across adjacent sentences, and between parts of a short paragraph.
  • Evaluate whether a proposed transition matches the direction of the writer’s reasoning and the context established by surrounding statements.
  • Distinguish between logical links that are similar in tone or category but differ in meaning, such as contrast versus concession or sequence versus result.
  • Revise a sentence or passage to improve coherence by replacing vague, redundant, or illogical transitions with precise connecting language.

• Revising for organization, precision, and concision

  ≈ 2.5%1 h 15 min

  This topic covers revising text so that ideas appear in the most effective order and wording is exact, relevant, and economical. On the PSAT, students improve short passages by choosing the sentence placement, wording, or deletion that best strengthens coherence, precision, and concision.

  • Determine the most logical placement of a sentence or detail to improve the organization and progression of ideas in a paragraph or short passage.
  • Evaluate whether a sentence, phrase, or detail should be added, retained, revised, or deleted to maintain focus and relevance.
  • Revise wording to increase precision by selecting language that more exactly conveys the intended meaning, claim, or description.
  • Revise text for concision by eliminating redundancy, unnecessary repetition, and wordiness without changing the intended meaning.
  • Apply principles of coherence to ensure that supporting details, examples, and explanations appear in a logical sequence and align with the passage’s purpose.

• Synthesizing notes to meet a rhetorical goal

  ≈ 4%1 h 30 min

  This topic covers using a set of notes to complete a specific writing task while following stated rhetorical goals. On the PSAT, students select the option that most effectively synthesizes relevant information from bullet-point notes for a purpose such as informing, introducing, comparing, or emphasizing.

  • Interpret a set of notes and identify the information relevant to a stated rhetorical goal.
  • Select the sentence that accurately synthesizes source notes without adding unsupported claims or omitting needed information.
  • Apply a specified rhetorical aim, such as introducing a topic, summarizing findings, making a comparison, defining a term, or emphasizing a key point, when choosing among response options.
  • Distinguish relevant from irrelevant details in source notes based on audience, purpose, and task.
  • Evaluate whether a proposed synthesis is clear, concise, and faithful to the information provided in the notes.

About 3 h 45 min of study, lessons and core practice

• Solving linear equations in one variable

  ≈ 4.5%1 h 30 min

  This topic covers solving and interpreting linear equations in one variable, including equations with variables on both sides and equations built from contextual information. On the PSAT, students are tested through direct equation solving, equivalent transformations, and real-world situations that require setting up and solving a linear equation.

  • Solve linear equations in one variable, including equations with rational number coefficients and variables on one or both sides of the equation.
  • Apply properties of equality to rewrite equations into equivalent forms and isolate the variable efficiently.
  • Interpret solutions to linear equations in context, including identifying whether a solution is reasonable for the situation described.
  • Create and solve a linear equation in one variable from a verbal description, table, graph, or applied context.
  • Determine whether a linear equation has one solution, no solution, or infinitely many solutions by comparing equivalent forms.
  • Use structure to simplify expressions within a linear equation before solving, including distributing and combining like terms.

• Interpreting and building linear functions

  ≈ 4.5%1 h 45 min

  This topic covers interpreting, representing, and constructing linear functions in equations, tables, graphs, and verbal contexts. On the PSAT, students must connect slope and intercepts to meaning, compare linear relationships across representations, and write equations that model data or situations.

  • Interpret the rate of change and initial value of a linear function from an equation, graph, table, or context.
  • Write a linear equation or function rule from given information such as two points, a graph, a table, or a verbal description.
  • Convert among representations of a linear relationship, including verbal descriptions, tables, graphs, and equations.
  • Calculate slope from coordinates, tables, graphs, or contextual change, and interpret its meaning using appropriate units.
  • Determine whether a relationship is linear by checking for a constant rate of change or by analyzing its representation.
  • Compare two linear relationships represented in different forms and evaluate which has the greater rate of change or initial value.

• Solving systems of linear equations

  ≈ 3.5%1 h 30 min

  This topic covers solving and interpreting systems of two linear equations, both algebraically and graphically. On the PSAT, students are tested on finding the solution to a system, recognizing the meaning of intersection, and modeling paired constraints or relationships with two equations.

  • Solve a system of two linear equations in two variables algebraically using substitution, elimination, or equivalent transformations.
  • Interpret the solution to a system of linear equations as the point that satisfies both equations or as the intersection of their graphs.
  • Solve a system of linear equations by analyzing a graph or a table when the representation provides sufficient information.
  • Create a system of two linear equations from a verbal description or real-world context and solve it.
  • Determine whether a system has one solution, no solution, or infinitely many solutions by comparing equations or representations.
  • Evaluate whether an ordered pair is a solution to a given system of linear equations.

• Solving linear inequalities and modeling constraints

  ≈ 3.5%1 h 30 min

  This topic covers solving linear inequalities and interpreting linear constraints in one or two variables. On the PSAT, students may solve inequalities symbolically, interpret solution sets, and model feasible values in real-world situations, including constraints represented by graphs or systems of inequalities.

  • Solve linear inequalities in one variable and express the solution set using number-line reasoning, inequality notation, or contextual interpretation.
  • Apply properties of inequality correctly, including reversing the inequality sign when multiplying or dividing by a negative number.
  • Interpret solutions to linear inequalities in context, including recognizing whole-number or nonnegative restrictions when appropriate.
  • Write a linear inequality from a verbal description, graph, or applied situation.
  • Interpret linear constraints in two variables from equations, graphs, or word problems, including identifying whether a point satisfies a constraint.
  • Model a real-world situation with one or more linear inequalities and identify feasible values or regions that satisfy the stated conditions.

• Using Desmos and numeric entry strategically

  ≈ 1.5%1 h

  This topic covers strategic use of the embedded Desmos graphing calculator and accurate entry of student-produced responses in Math. On the PSAT, students are tested not on Desmos features themselves but on choosing efficient calculator-based methods, reading graphs and tables correctly, and entering valid numeric answers in the required form.

  • Use the Desmos graphing calculator strategically to graph linear equations, inequalities, and systems and to identify key values such as intersections and intercepts.
  • Use Desmos tables, sliders, and equation entry efficiently when exploring or verifying linear relationships.
  • Decide when calculator use is helpful and when mental math or algebraic methods are more efficient for a linear problem.
  • Enter student-produced responses correctly, including integers, decimals, fractions, and equivalent forms that satisfy the prompt.
  • Interpret calculator output carefully, including graph scale, window, labeled coordinates, and numerical approximations.
  • Check the reasonableness of a calculator-based result against the problem context and the underlying algebra.

About 7 h 15 min of study, lessons and core practice

• Rewriting equivalent expressions in polynomials, radicals, and rational forms

  ≈ 4.5%1 h 45 min

  This topic covers rewriting algebraic expressions into equivalent forms, especially polynomial, radical, and rational expressions, to reveal structure or make solving and interpreting easier. On the PSAT, students are tested on factoring, expanding, simplifying, and strategically transforming expressions without changing their value.

  • Rewrite polynomial expressions by applying the distributive property, combining like terms, and using identities such as the difference of squares and perfect-square trinomials.
  • Factor polynomial expressions, including greatest common factor, quadratic trinomials, and special products, to reveal zeros, intercepts, or other useful structure.
  • Simplify radical expressions and expressions with rational exponents by applying the laws of exponents and properties of radicals.
  • Rewrite rational expressions by factoring numerators and denominators, identifying restrictions on the variable, and simplifying equivalent forms when factors cancel.
  • Interpret how an equivalent form of an expression highlights a feature such as a zero, vertex-related structure, or rate of change in context.
  • Choose and apply an efficient algebraic manipulation to create an equivalent expression that supports solving, graphing, or modeling.

• Solving quadratic and other nonlinear equations

  ≈ 4.5%2 h

  This topic covers solving quadratic equations and other nonlinear equations in one variable, including equations involving powers, radicals, and rational expressions. On the PSAT, students solve symbolically or strategically use structure, checking for extraneous solutions when needed.

  • Solve quadratic equations in one variable by factoring, completing the square, applying the square root property, or using the quadratic formula.
  • Determine the number and nature of solutions to a quadratic equation from its structure, equivalent form, or discriminant when appropriate.
  • Solve equations that can be rewritten as quadratics, such as polynomial equations in higher powers with substitution or structure-based factoring.
  • Solve radical equations and verify solutions in the original equation, identifying and excluding extraneous solutions.
  • Solve rational equations in one variable, stating restrictions on the variable and excluding values that make a denominator zero.
  • Interpret solutions to nonlinear equations in context, including selecting only solutions that are reasonable for the situation.

• Interpreting and building nonlinear functions

  ≈ 4%1 h 45 min

  This topic covers interpreting, representing, and building nonlinear functions, especially quadratic and other common nonlinear relationships, from equations, tables, graphs, and verbal descriptions. On the PSAT, students analyze key features and connect multiple representations of a function.

  • Interpret key features of a nonlinear function from a graph, table, or equation, including zeros, intercepts, relative maximum or minimum, intervals of increase or decrease, and end behavior when relevant.
  • Convert a quadratic function among standard, factored, and vertex forms and explain which form best reveals a requested feature.
  • Determine the vertex, axis of symmetry, and zeros of a quadratic function and relate these features across algebraic and graphical representations.
  • Build a nonlinear function to model a relationship from given conditions, data, or context, including determining parameters in quadratic or other nonlinear forms.
  • Evaluate a nonlinear function for a given input and interpret the meaning of the output in context.
  • Compare representations of nonlinear functions to identify equivalent models or to decide which model best fits stated conditions.

• Modeling exponential growth and decay

  ≈ 2.5%1 h 15 min

  This topic covers exponential functions and situations modeled by repeated multiplicative change, including growth and decay. On the PSAT, students interpret parameters, write equations, and compare exponential relationships shown in different forms.

  • Recognize when a relationship is exponential by identifying a constant multiplicative rate of change in a table, graph, equation, or context.
  • Write an exponential function from a verbal description, table, or graph using an initial value and a growth or decay factor.
  • Interpret the parameters of an exponential expression or function in context, including the meaning of the initial value and the multiplicative factor.
  • Evaluate an exponential function for a given input and interpret the result in context.
  • Compare exponential relationships represented in different forms to determine which grows faster, decays faster, or better fits stated conditions.
  • Distinguish exponential change from linear change by analyzing additive versus multiplicative patterns.

• Solving systems with linear and nonlinear equations

  ≈ 2%1 h 15 min

  This topic covers systems consisting of one linear equation and one nonlinear equation, and interpreting their intersection points. On the PSAT, students solve such systems algebraically or graphically and connect solutions to the context or graph.

  • Solve a system consisting of a linear equation and a nonlinear equation by substitution, elimination when appropriate, or graphing.
  • Determine the number of solutions to a linear-and-nonlinear system from equations or from the intersection points on a graph.
  • Interpret each solution of a system as a point that satisfies both equations and explain its meaning in context.
  • Use equivalent transformations to rewrite one or both equations of a system into forms that make solving more efficient.
  • Identify and exclude extraneous solutions that arise during algebraic solution of a system involving radicals or rational expressions.
  • Match a system of equations to its graph or use a graph to estimate solution coordinates when an exact solution is not required.

About 8 h of study, lessons and core practice

• Working with ratios, rates, proportions, and units

  ≈ 2.5%1 h 15 min

  This topic covers proportional relationships, ratios, rates, scale factors, and unit conversions in real-world and mathematical contexts. On the PSAT, students must interpret and set up proportional reasoning correctly, often across tables, graphs, equations, verbal descriptions, and multistep contexts involving units.

  • Calculate and interpret ratios and rates, including unit rates, from verbal, tabular, graphical, and algebraic information.
  • Apply proportional relationships to solve single-step and multistep problems, including finding unknown values in equivalent ratios and proportions.
  • Convert measurements within and across systems of units using conversion factors, and track units through calculations to determine whether results are reasonable.
  • Interpret scale drawings, maps, and similar real-world proportional situations, including scale factors and derived measurements.
  • Compare quantities using ratios, rates, and unit rates, and determine which representation best answers a question in context.

• Solving percent problems and real-world applications

  ≈ 1.5%1 h

  This topic covers percent as a rate per 100 and its use in solving applied problems involving discounts, markups, tax, tips, error, and percent increase or decrease. On the PSAT, questions test whether students can translate among percents, decimals, fractions, and equations and choose the correct base quantity in context.

  • Convert among percents, decimals, and fractions, and interpret percent language in context.
  • Calculate a part, whole, or percent given the other two quantities using equations, proportional reasoning, or equivalent methods.
  • Solve real-world problems involving percent increase, percent decrease, discount, markup, tax, gratuity, commission, and simple percent change.
  • Interpret percent error or other percentage-based comparisons when a measured or estimated value is compared with an actual value.
  • Apply percentages in multistep contexts and distinguish correctly between additive change and multiplicative percent change.

• Analyzing one-variable data and summary statistics

  ≈ 1.5%1 h

  This topic covers the interpretation and computation of summary statistics for a single quantitative data set, including center, spread, and distribution shape. On the PSAT, students analyze tables, dot plots, histograms, box plots, and short scenarios to compare distributions and select appropriate statistics.

  • Calculate and interpret measures of center, including mean and median, for one-variable data.
  • Calculate and interpret measures of spread, including range and interquartile range, and relate them to variability in a distribution.
  • Interpret one-variable data displayed in tables and graphs, including dot plots, histograms, and box plots.
  • Compare distributions using center, spread, and shape, including attention to symmetry, skew, clusters, gaps, and possible outliers.
  • Determine the effect of adding, removing, or changing data values on summary statistics when that effect is directly inferable.

• Interpreting two-variable data, probability, and statistical inference

  ≈ 2%1 h 15 min

  This topic covers relationships in two-variable data, basic probability, and informal statistical inference from samples and studies. On the PSAT, students interpret scatterplots and tables, estimate association, compute probabilities, and evaluate whether conclusions from data are supported by the design and results.

  • Interpret two-variable data in tables, scatterplots, and graphs by describing association, trend, and possible fit.
  • Use linear models or lines of best fit, when appropriate, to estimate values and interpret slope and intercept in context.
  • Calculate probabilities of single events and compound events from tables, lists, or given information, including probabilities expressed as fractions, decimals, or percents.
  • Interpret data from samples, surveys, and experiments, and distinguish reasonable conclusions about a population from unsupported generalizations.
  • Evaluate informal statistical inferences by considering sample size, representativeness, and whether an observed difference is likely meaningful in context.

About 4 h 30 min of study, lessons and core practice

• Finding area, perimeter, and volume

  ≈ 2%1 h 15 min

  This topic covers finding and comparing perimeter, area, surface area, and volume for standard plane figures and solids using formulas, decomposition, and unit reasoning. On the PSAT, questions typically ask students to calculate a measure, interpret a geometric quantity in context, or decide how a change in dimensions affects area or volume.

  • Calculate the perimeter and area of rectangles, triangles, parallelograms, trapezoids, and other composite plane figures using appropriate formulas and decomposition.
  • Calculate the circumference and area of circles, using $\pi$ as given or as an approximation when appropriate.
  • Determine the surface area and volume of right prisms, rectangular solids, cylinders, and related composite solids from dimensions, nets, diagrams, or verbal descriptions.
  • Apply geometric formulas in real-world contexts, including finding missing dimensions from area, perimeter, surface area, or volume.
  • Interpret and convert units correctly for linear, square, and cubic measurement when solving measurement problems.
  • Evaluate how scaling one or more dimensions affects perimeter, area, surface area, and volume in straightforward cases.

• Reasoning with angles, triangles, similarity, and coordinate geometry

  ≈ 2%1 h 30 min

  This topic covers angle relationships, triangle properties, similarity, and coordinate-geometry reasoning with lines and polygons on the coordinate plane. On the PSAT, students must justify or compute unknown measures, use similarity and congruence relationships, and interpret geometric relationships from coordinates, equations, and diagrams.

  • Apply angle relationships involving vertical angles, supplementary angles, complementary angles, and angles formed by parallel lines and transversals to find unknown angle measures.
  • Use properties of triangles, including the angle sum theorem, exterior angle theorem, and isosceles triangle properties, to determine unknown side lengths or angle measures.
  • Apply triangle similarity criteria to solve for missing lengths, compare corresponding parts, and reason about scale factors.
  • Use the distance formula and the midpoint formula to analyze segments on the coordinate plane.
  • Determine slopes of line segments and use slope to identify parallel and perpendicular lines in coordinate-geometry contexts.

• Using right triangles, the Pythagorean theorem, and trigonometry

  ≈ 2%1 h 30 min

  This topic covers right-triangle relationships, the Pythagorean theorem, special right triangles, and basic trigonometric ratios. On the PSAT, questions ask students to find side lengths or angle measures, interpret trigonometric relationships in diagrams or contexts, and connect exact or approximate values to right-triangle geometry.

  • Apply the Pythagorean theorem to find a missing side length in a right triangle and to solve related problems in the coordinate plane or real-world contexts.
  • Use the converse of the Pythagorean theorem to determine whether a triangle is a right triangle when appropriate.
  • Recognize and apply side-length relationships in $45^\circ$-$45^\circ$-$90^\circ$ and $30^\circ$-$60^\circ$-$90^\circ$ triangles.
  • Use the trigonometric ratios sine, cosine, and tangent to find missing side lengths or angle measures in right triangles.
  • Interpret and select appropriate trigonometric relationships from diagrams, tables, or contextual descriptions.
  • Estimate or evaluate trigonometric quantities using a calculator when needed and interpret the result in context.

• Solving problems involving circles, arcs, and sectors

  ≈ 1.5%1 h 15 min

  This topic covers circle measures and relationships involving radii, diameters, chords, arcs, sectors, and angles in circles. On the PSAT, students may need to compute arc length, sector area, or angle measures, or use standard circle relationships to connect central angles, inscribed angles, and intercepted arcs.

  • Use the relationships among radius, diameter, circumference, and area to solve problems involving circles.
  • Determine arc measures from central angles and use arc measures to find central or inscribed angle measures.
  • Calculate arc length and sector area from a radius and a central angle.
  • Apply relationships involving inscribed angles, central angles, chords, and intercepted arcs to find unknown measures.
  • Solve problems involving circles in context, including interpreting diagrams with tangents, secants, or composite figures when only standard circle relationships are required.

About 5 h 30 min of study, lessons and core practice