SAT Mathematics Practice

Strengthen the algebra foundations that drive a large share of SAT Mathematics questions, especially linear relationships and equation-based modeling.

• Combining like terms, using the distributive property, factoring linear expressions, and rewriting expressions in equivalent forms
• Solving one-step, multi-step, and variable-on-both-sides linear equations, including equations with fractions and decimals
• Working with literal equations and solving for a specified variable correctly
• Solving linear inequalities, compound inequalities, and graphing solutions on the number line
• Solving systems of linear equations by substitution, elimination, or graphing, including no-solution and infinitely-many-solutions cases
• Modeling real situations with linear equations such as rate, distance, time, age, and consecutive-integer problems

Build fluency with function notation, slope, intercepts, and graph interpretation so linear models become easier to analyse quickly.

• Understanding function notation, evaluating functions, and interpreting domain and range in context
• Reading and graphing linear functions using slope-intercept and point-slope forms
• Interpreting slope as rate of change and y-intercept as an initial value in applied contexts
• Finding slope between two points and distinguishing positive, negative, zero, and undefined slopes
• Identifying and writing equations of parallel and perpendicular lines
• Comparing linear models from graphs, tables, and equations in growth or decay settings

Improve quantitative reasoning through ratios, percentages, data displays, statistical interpretation, and probability.

• Unit rates, proportional relationships, and scale-based reasoning such as maps and scale drawings
• Percent increase, percent decrease, reverse percentage, and percent error problems
• Interpreting tables, line graphs, bar graphs, and scatterplots accurately
• Using mean, median, mode, range, and interquartile range to describe data
• Recognising correlation, line of best fit, residuals, and overall trends in scatterplots
• Solving basic, compound, independent, dependent, and conditional probability questions

Tackle more advanced algebraic structures involving quadratics, parabolas, and polynomial operations.

• Expanding and factoring quadratic expressions, including perfect square trinomials and difference of squares
• Solving quadratic equations by factoring, completing the square, and the quadratic formula
• Graphing quadratic functions and interpreting vertex form, standard form, and turning points
• Finding maximum and minimum values from quadratic graphs and equations
• Adding, subtracting, and multiplying polynomials accurately
• Solving polynomial equations and reasoning about the possible number of solutions

Develop confidence with algebraic fractions, restrictions, and rational equations that require careful simplification.

• Factoring numerators and denominators in rational expressions
• Cancelling common factors correctly while respecting algebraic structure
• Solving equations that involve rational expressions
• Identifying extraneous solutions after solving
• Understanding restrictions on variables and excluded values
• Interpreting rational functions conceptually, including asymptotic behaviour at an introductory SAT level

Work accurately with roots, powers, exponent rules, and exponential models used in algebraic and applied questions.

• Simplifying square roots and performing basic operations with radicals
• Solving radical equations carefully and checking for extraneous solutions
• Applying the laws of exponents, including rational exponents
• Rewriting expressions using exponent rules in cleaner equivalent forms
• Interpreting exponential growth and decay in word problems
• Comparing exponential models with linear patterns in realistic contexts

Sharpen geometry reasoning with angle relationships, triangle properties, and polygon rules commonly examined on the SAT.

• Complementary, supplementary, and vertical angles
• Angles formed by parallel lines and transversals
• Triangle angle sum and angle-based reasoning
• Properties of right, isosceles, and equilateral triangles
• Triangle inequality theorem and perimeter reasoning
• Interior and exterior angles of polygons, including regular polygons

Link geometry to the coordinate plane through circle properties, formulas, and graphical interpretation.

• Radius, diameter, circumference, and area of circles
• Arc length and sector area calculations
• Distance between two points and midpoint formula on the coordinate plane
• Equation of a circle in standard form at an introductory level
• Interpreting geometric figures drawn on the coordinate plane
• Combining algebra and geometry in diagram-based coordinate problems

Handle measurement-based SAT questions involving plane figures, 3D solids, and unit conversion with confidence.

• Area of rectangles, triangles, trapezoids, and composite figures
• Surface area of prisms, cylinders, and pyramids
• Volume of rectangular solids, cylinders, cones, and spheres
• Selecting and applying the correct formula efficiently
• Converting between units in geometry and measurement contexts
• Understanding how scaling affects perimeter, area, and volume

Complete SAT Mathematics coverage with right-triangle trigonometry, the Pythagorean theorem, applications, and introductory complex numbers.

• Sine, cosine, and tangent as trigonometric ratios in right triangles
• Using right-triangle trigonometry to find missing sides or angles
• Applying the Pythagorean theorem in geometry and distance problems
• Angle of elevation and angle of depression in real-world settings
• Introductory work with the imaginary unit and basic operations with complex numbers
• Solving quadratics that do not have real solutions using complex-number ideas at an introductory level