XMocks · SAT Math

Study SAT Math by understanding the structure

These lessons focus on three recurring algebra decisions: using the relationships between two equations, reading a quadratic from vertex form, and preserving domain restrictions while simplifying a rational expression. Each page explains why a method works, shows a complete example, and gives you a problem to solve.

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Solve a system by elimination

Define quantities, scale an equation to cancel a variable, and check the resulting pair in both original statements.

Start here when a problem gives two totals involving the same unknowns.

Use symmetry in a pair of linear equations

When coefficients switch places, adding and subtracting can reveal the sum and difference of the variables directly.

Start here when the coefficient pattern is balanced across two equations.

Interpret a quadratic in vertex form

Read the vertex, axis of symmetry, and maximum or minimum from the equation, then connect them to values and solutions.

Start here when the quadratic is written as a(x − h)² + k.

Track restrictions in rational expressions

Factor and simplify while keeping every value that made the original denominator zero out of the domain.

Start here when an algebraic fraction contains factorable polynomials.

A useful way to study an algebra problem

  1. Name what the symbols represent. If the variables have units or refer to quantities in a story, write those meanings down before calculating.
  2. Look for a form or relationship. Matching coefficients, a squared binomial, or a factor in both numerator and denominator suggests a method.
  3. Keep the original conditions visible. An answer must fit both equations, the stated interval, and any restrictions in the original expression.
  4. Check a result with a second route. Substitute values, estimate a graph feature, or test an input that exposes a possible sign or domain error.

Read a lesson, cover its worked answer, and attempt the practice question on paper. Then compare your steps with the explanation. If your answer differs, locate the first line where the assumptions or arithmetic stop matching.

Continue with official practice

The College Board provides current SAT practice materials and a searchable student question bank. Use the official material to see current question formats, then use these lessons to review the algebra behind a problem.

These independently prepared XMocks lessons are not affiliated with or endorsed by the College Board. Check College Board resources for current SAT format and policies.