SAT Math: Algebra & Advanced Math
The Complete SAT Bible · Digital SATMath: Algebra & Advanced Math
- The Complete SAT Bible
- Digital SAT
- 13 sections
SAT Math: Algebra & Advanced Math is the foundation of the Digital SAT Math section: together these two content domains are about 70% of the scored Math questions (roughly 13 to 15 Algebra and 13 to 15 Advanced Math out of 40), so they are the single biggest lever on your Math score.
- How the Digital SAT Math section assesses this Share of scored Math questions ~70% · Scored Math questions (total) 40 · Multiple choice 4 choices (A to D)
- Key terms Balance principle, Slope (m), Slope-intercept form, System of equations
- How to study for SAT Math: Algebra & Advanced Math Treat this as the foundation domain. It is about 70% of the scored Math questions, so the time you put here moves your score more than anywhere else.
- SAT Math: Algebra & Advanced Math FAQ How much of SAT Math is Algebra and Advanced Math?
What SAT Math: Algebra & Advanced Math covers
The whole domain → one exam-ready map. Nine parts, core Algebra through Advanced Math, then 40 worked practice questions. Each links to its free chapter guide.
Linear equations in one variable
Chapter 1. The balance principle, clearing parentheses and fractions, collecting like terms, expressions vs equations, and the special cases (no solution vs infinitely many solutions).02Linear equations in two variables
Chapter 2. Slope as a constant rate of change, x- and y-intercepts, slope-intercept and point-slope forms, function notation f(x), and reading a line off its graph.03Systems of linear equations
Chapter 3. Substitution and elimination, the three solution cases (one, none, infinitely many), and the SAT shortcut of finding a combination such as x + y without fully solving.04Linear inequalities
Chapter 4. Solving, when to flip the sign (only on multiply or divide by a negative), graphing and shading, translating worded constraints, and greatest- or least-integer answers.05Equivalent expressions
Chapter 5. Rewriting rather than solving: distribution and FOIL, factoring, combining and simplifying rational expressions, and exponent rules.06Nonlinear equations
Chapter 6. Quadratics three ways (factoring with the zero-product rule, the quadratic formula, completing the square), the discriminant, and extraneous-solution checks.07Nonlinear functions
Chapter 7. The three forms of a quadratic (standard, factored, vertex) and what each reveals, the vertex and axis of symmetry, and exponential growth and decay models.08Formulas to memorize
Chapter 8. The algebra toolkit on one page: slope, the line forms, the quadratic formula and discriminant, the exponential model, and the exponent and factoring rules worth knowing cold.09Practice: 40 questions with solutions
Chapter 9. Forty exam-difficulty questions across Algebra and Advanced Math, in multiple-choice and student-produced-response formats, each with a full worked solution and the trap behind every wrong choice.It spans the full arc from core Algebra (linear equations in one and two variables, linear functions, systems, and inequalities) into Advanced Math (equivalent expressions, nonlinear equations such as quadratics, and nonlinear functions). Each skill is taught from the ground up with fully worked, step-by-step examples and labelled graphs.
The Digital SAT presents these questions in two formats: multiple choice (four answer choices, A to D) and student-produced response (you type the answer directly; fractions or decimals are accepted, with no percent sign, dollar sign or commas).
This guide teaches the method behind each question type, then drills it with 40 exam-difficulty questions across Easy, Medium and Hard, each worked in full with the trap behind every wrong choice. The aim is a reliable process for each type: set to zero, factor or formula, then check.
How the Digital SAT Math section assesses this
Only what this guide can support from the question set is stated below. Confirm current section structure, timing and tools on the official College Board test specifications before you rely on them.
| Item | Weight / count | What it means |
|---|---|---|
| Share of scored Math questions | ~70% | Algebra and Advanced Math together make up about 70% of the scored Math questions: roughly 13 to 15 Algebra and 13 to 15 Advanced Math out of 40. They are the single biggest lever on the Math score. |
| Scored Math questions (total) | 40 | This guide drills 40 exam-difficulty questions spanning the two domains, matching the count of scored Math questions. |
| Multiple choice | 4 choices (A to D) | Each multiple-choice question gives four answer choices, A to D, with exactly one correct answer. |
| Student-produced response | Type the answer | You enter the answer directly. Fractions or decimals are accepted; no percent sign, dollar sign or commas. In this question set, 12 of the 40 are this format. |
| Difficulty | Easy / Medium / Hard | Questions are tagged by difficulty across all topics, so you can build from confidence questions up to the hardest Advanced Math. |
Translate a word problem into a linear equation, then solve
- Step 1Translate the words into an equation. Total = fee + rate × months, so 40 + 25m = 215. The joining fee is a one-off constant; the $25 is the per-month rate that multiplies the number of months.
- Step 2Isolate the variable term using the balance principle. Subtract 40 from both sides: 25m = 175.
- Step 3Undo the multiplication. Divide both sides by 25: m = 7.
- Step 4Check by substituting back: 40 + 25(7) = 40 + 175 = 215. It matches, so m = 7 is correct.
Key terms
- Balance principle
- Whatever you do to one side of an equation you must do to the other. It is the basis of solving every equation in this domain.
- Slope (m)
- The constant rate of change of a line: rise over run, equal to (y2 minus y1) over (x2 minus x1). Parallel lines have equal slopes; perpendicular lines have negative-reciprocal slopes.
- Slope-intercept form
- y = mx + b, the most graph-ready form of a line. Here m is the slope and b is the y-intercept (the value when x = 0, often the starting amount).
- System of equations
- Two or more equations in the same unknowns; the solution is the point or points satisfying all of them, which graphically is the intersection. It can have one solution, none (parallel lines), or infinitely many (the same line).
- Equivalent expressions
- Expressions that are equal for every value of the variable (a rewrite), as opposed to an equation you solve. Distribution, FOIL and factoring all produce equivalent expressions.
- Discriminant
- The quantity b squared minus 4ac inside the quadratic formula. Its sign gives the number of real solutions: two if positive, one if zero, none if negative.
- Quadratic formula
- x = (negative b plus or minus the square root of (b squared minus 4ac)) over 2a. It solves any quadratic ax squared plus bx plus c = 0.
- Vertex
- The turning point (h, k) of a parabola: its maximum if the parabola opens down, or its minimum if it opens up. The axis of symmetry is the vertical line x = negative b over 2a, which passes through the vertex.
- Exponential model
- A quantity of the form a times b to the power t, or a(1 plus or minus r) to the power t. Here a is the initial amount (the y-intercept); a base greater than 1 grows and a base between 0 and 1 decays.
SAT Math: Algebra & Advanced Math FAQ
How much of SAT Math is Algebra and Advanced Math?
Together they are about 70% of the scored Math questions, roughly 13 to 15 Algebra and 13 to 15 Advanced Math out of 40. They are the single biggest lever on your Math score, which is why they share this foundation guide.
How do I solve a linear equation?
Use the balance principle: do the same inverse operation to both sides. Clear parentheses and fractions first, collect the variable on one side and numbers on the other, then divide. Watch for special cases: an identity has infinitely many solutions and a contradiction has none.
What is slope-intercept form and how do I read it?
It is y = mx + b, where m is the slope (rise over run, the constant rate of change) and b is the y-intercept (the value when x = 0, often the starting amount). Parallel lines have equal slopes; perpendicular lines have negative-reciprocal slopes.
When do I flip the inequality sign?
Only when you multiply or divide both sides by a negative number. Adding, subtracting, or multiplying or dividing by a positive keeps the sign the same.
What are the three ways to solve a quadratic?
Factoring with the zero-product rule, the quadratic formula x = (negative b plus or minus the square root of (b squared minus 4ac)) over 2a, and completing the square. The discriminant b squared minus 4ac tells you how many real solutions there are: two if positive, one if zero, none if negative.
What do the three forms of a quadratic reveal?
Standard form ax squared plus bx plus c shows the y-intercept (c). Factored form a(x minus r1)(x minus r2) shows the roots. Vertex form a(x minus h) squared plus k shows the vertex (h, k), the maximum or minimum.
How do exponential models work on the SAT?
Growth is a(1 + r) to the power t and decay is a(1 - r) to the power t, where a is the initial amount (the y-intercept) and r is the rate. A base greater than 1 grows; a base between 0 and 1 decays.
Related SAT sections
This is one of the three SAT Math content domains. Work across all three, then use the exam total page to plan your full Math section.
SAT Math: Algebra & Advanced Math
This guide. Linear equations, lines, systems, inequalities, equivalent expressions, quadratics and nonlinear functions — about 70% of the scored Math questions.02SAT Math: Problem-Solving & Data Analysis
Ratios, rates and proportions, percentages, units, and reading data from tables and graphs.03SAT Math: Geometry & Trigonometry
Lines and angles, triangles, circles, area and volume, and right-triangle trigonometry.→SAT exam overviewThe full Digital SAT: how the Math and Reading and Writing sections fit together, scoring, and timing.How to study for SAT Math: Algebra & Advanced Math
Treat this as the foundation domain. It is about 70% of the scored Math questions, so the time you put here moves your score more than anywhere else. (1) Work it in three passes: learn the method from each worked example (cover the solution and try the steps yourself first), drill the practice questions cold, then re-do the examples until the process is reflex.
(2) Build a reliable process for each question type rather than memorising answers: for an equation, set to zero, factor or use the formula, then check; for a line, read slope and intercept off y = mx + b; for a system, choose substitution or elimination, and look for a combination such as x + y you can reach without fully solving.
(3) Name the traps before they catch you: distributing to only the first term, sign errors when moving a term across the equals sign, dividing only part of a side, flipping the inequality only when you multiply or divide by a negative, and answering x when the question asked for an expression.
(4) Master the term-vs-term distinctions the test rewards: expression vs equation, slope-intercept vs point-slope form, the three solution cases of a system, the three forms of a quadratic, and growth vs decay. (5) Practise both formats: multiple choice (four choices) and student-produced response (type the answer; fractions or decimals, no percent sign, dollar sign or commas).
(6) Confirm the current section structure, timing and on-screen tools on the official College Board specifications, since this guide states only what its question set supports.
