PSAT Mathematics

Who Should Take This

High‑school juniors and seniors aiming for competitive PSAT/NMSQT scores should enroll. The course fits students with solid foundational math who need targeted practice on algebraic manipulation, geometry reasoning, trigonometric identities, and data‑analysis techniques to boost confidence and accuracy on the test.

What's Included in AccelaStudy® AI

Adaptive Knowledge Graph

Practice Questions

Lesson Modules

Console Simulator Labs

Exam Tips & Strategy

20 Activity Formats

Course Outline

76 learning goals

1 Algebra

5 topics

Linear Equations in One Variable

Define what constitutes a linear equation in one variable and identify its standard forms, including ax + b = c and equations requiring distribution and combining like terms.
Solve linear equations in one variable involving distribution, combining like terms, variables on both sides, and fractional or decimal coefficients, interpreting the solution in context.
Analyze the structure of a simplified linear equation to determine whether it has one solution, no solution, or infinitely many solutions based on the resulting identity or contradiction.

Linear Equations in Two Variables

Identify slope-intercept form (y = mx + b), point-slope form, and standard form (Ax + By = C) of linear equations, and describe what each parameter represents graphically.
Calculate the slope of a line given two points, a graph, or a table, and determine the equation of a line given slope and a point or two points.
Interpret the slope and y-intercept of a linear equation in the context of a real-world situation, explaining what each value means in terms of the problem's variables.
Analyze how changing the slope or y-intercept of a linear equation affects its graph and the real-world scenario it models, predicting the outcome of parameter changes.

Linear Functions

Define a linear function and recognize its key characteristics, including constant rate of change, domain and range over the real numbers, and graphical representation as a straight line.
Use function notation f(x) to evaluate a linear function at a given input, find the input that produces a given output, and interpret f(a) = b in context.
Determine the x-intercept and y-intercept of a linear function from its equation, graph, or table, and explain the meaning of each intercept in a real-world context.
Analyze how changes to the slope or y-intercept of a linear function affect its graph, predicting the graphical result of increasing, decreasing, or negating each parameter.

Systems of Two Linear Equations

Describe the three possible outcomes for a system of two linear equations: one unique solution (intersecting lines), no solution (parallel lines), and infinitely many solutions (coincident lines).
Solve a system of two linear equations using substitution or elimination, selecting the more efficient method based on the structure of the equations.
Interpret the solution of a system of linear equations in a real-world context, explaining what the intersection point represents and evaluating whether the solution is feasible.
Analyze the coefficients of a system of two linear equations to determine without solving whether the system has one solution, no solution, or infinitely many solutions.

Linear Inequalities

State the rules for solving linear inequalities, including the rule that multiplying or dividing by a negative number reverses the inequality sign.
Solve linear inequalities in one variable and represent the solution set on a number line using open and closed circles and appropriate shading.
Interpret a system of linear inequalities in two variables graphically, identifying the solution region as the intersection of half-planes on the coordinate plane.
Analyze a word problem to set up and solve a linear inequality or system of inequalities, interpreting the solution set in terms of the constraints described.

2 Advanced Math

4 topics

Equivalent Expressions

List the exponent rules (product, quotient, power, zero exponent, negative exponent) and the properties used for simplifying polynomial and rational expressions.
Apply the distributive property, FOIL method, and special product patterns to expand polynomial expressions, and factor using GCF, difference of squares, and trinomial factoring.
Apply factoring to simplify rational expressions by canceling common factors in the numerator and denominator, identifying restrictions on the variable.
Apply exponent rules to simplify and rewrite exponential expressions, including expressions with fractional and negative exponents.
Analyze whether two algebraic expressions are equivalent by applying multiple simplification strategies and comparing the resulting forms.

Nonlinear Equations

Recognize the standard form (ax^2 + bx + c = 0), vertex form (a(x - h)^2 + k = 0), and factored form (a(x - r)(x - s) = 0) of quadratic equations and state the quadratic formula.
Solve quadratic equations by factoring, applying the quadratic formula, and completing the square, selecting the most efficient method based on the equation's structure.
Use the discriminant (b^2 - 4ac) to determine the number and nature of solutions of a quadratic equation without solving it.
Solve simple radical equations by isolating the radical and squaring both sides, checking for extraneous solutions in the original equation.
Analyze a nonlinear equation to determine which solution strategy is most appropriate, evaluating the trade-offs between algebraic manipulation and graphical approaches using Desmos.

Nonlinear Functions

Identify the key features of quadratic functions including vertex, axis of symmetry, direction of opening, x-intercepts (zeros), y-intercept, and maximum or minimum value.
Identify the key characteristics of exponential functions including growth versus decay, initial value, growth or decay factor, and asymptotic behavior.
Determine the vertex, axis of symmetry, and intercepts of a quadratic function from its equation in standard, vertex, or factored form.
Apply function notation to evaluate quadratic and exponential functions at given inputs, and interpret the output in the context of a real-world growth or projectile scenario.
Interpret the graph of an exponential function to determine its initial value, growth or decay factor, and whether it models increasing or decreasing real-world quantities.
Analyze a real-world scenario to determine whether it is best modeled by a linear, quadratic, or exponential function, justifying the choice based on the pattern of change.
Compare the rates of change of linear, quadratic, and exponential functions over specified intervals, evaluating which function type grows fastest in different contexts.

Function Notation and Concepts

Define what a function is, state the vertical line test, and describe the concepts of domain and range using set notation or interval notation.
Determine the domain and range of a function from its equation, graph, or table, identifying restrictions caused by division by zero or square roots of negative numbers.
Interpret the meaning of f(a), f(a) = 0, and f(a) = f(b) in the context of a graph or real-world scenario, explaining what each statement conveys about the function's behavior.
Analyze how a basic vertical or horizontal shift of a function's graph (f(x) + k or f(x - h)) changes its equation and the real-world interpretation of its parameters.

3 Problem-Solving and Data Analysis

5 topics

Ratios, Rates, and Proportions

Define ratio, rate, and proportion, and describe the relationship between unit rates and the slope of a proportional relationship's graph.
Solve proportion problems using cross-multiplication, and apply unit rate concepts to calculate missing values in tables, graphs, and word problems.
Analyze multi-step ratio and rate problems involving unit conversion, comparing rates across different units to determine the most efficient or cost-effective option.

Percentages and Units

Define percent as a ratio per hundred and state the formulas for percent increase, percent decrease, and finding a percentage of a quantity.
Calculate percent increase, percent decrease, and the result of applying successive percentage changes to a quantity in real-world contexts such as discounts and taxes.
Apply dimensional analysis to convert between units within and across measurement systems, setting up conversion factors to solve multi-step unit conversion problems.
Analyze problems involving compounding percentages or multi-step unit conversions, determining the final result after multiple sequential operations.

One-Variable Data Analysis

Define mean, median, mode, and range, and describe what standard deviation measures about the spread of a data set.
Calculate the mean, median, and range of a data set, and interpret these measures in the context of the data's real-world meaning.
Interpret data distributions displayed in histograms, dot plots, and box plots, identifying shape, center, spread, and the presence of outliers.
Analyze how adding, removing, or changing data values affects the mean, median, and standard deviation of a data set, predicting the direction and magnitude of the change.

Two-Variable Data Analysis

Describe what a scatterplot represents, define positive and negative correlation, and recognize when a line of best fit is appropriate for a data set.
Interpret the slope and y-intercept of a line of best fit in the context of a scatterplot's real-world variables, using the equation to make predictions.
Evaluate the strength and direction of a linear association in a scatterplot, and assess whether a linear model is appropriate or whether the data suggest a nonlinear pattern.

Probability and Inference

Define probability as the ratio of favorable outcomes to total outcomes, and describe the difference between theoretical and experimental probability.
Calculate the probability of simple and compound events using counting principles, addition rules, and multiplication rules for independent events.
Use two-way frequency tables to calculate joint, marginal, and conditional probabilities, interpreting the results in context.
Evaluate whether a sample is representative of a population and assess the validity of conclusions drawn from survey data or experimental results.

4 Geometry and Trigonometry