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Questions
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Answers
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SAT Math
Strategy Guide
Master Every Question Type and Score 750+
The SAT Math section tests four major domains. This guide breaks each one down, shows you what to expect, and gives you concrete strategies to earn every point available. Whether you're targeting 600 or 800, the approach is the same: know the content, master the strategy, and practice under time pressure.
Section Overview
The Math section has 44 questions spread across two modules, totaling 70 minutes. All question types fall into four domains:
Domain | What It Tests |
Algebra | Linear equations, systems of equations, inequalities, linear functions |
Advanced Math | Quadratics, polynomials, exponentials, nonlinear functions |
Problem-Solving & Data Analysis | Ratios, percentages, statistics, probability, data interpretation |
Geometry & Trigonometry | Area, volume, angles, triangles, circles, basic trig |
About 35% of questions are Algebra, 35% Advanced Math, 15% Problem-Solving & Data Analysis, and 15% Geometry & Trigonometry. Focus your energy accordingly.
Key Format Facts 44 questions total | 70 minutes across two modules Module 1 is fixed difficulty. Module 2 adapts based on your Module 1 performance. Score higher on Module 1 = harder (and higher-scoring) Module 2. Roughly 75% multiple choice, 25% student-produced response (grid-in). No guessing penalty. Always fill in an answer. |
Domain 1: Algebra
Algebra is the largest domain on the SAT. If you can master linear equations and systems, you've secured a major chunk of the test.
Linear Equations and Inequalities
These questions ask you to solve for a variable, interpret what a solution means, or set up an equation from a word problem.
Core Skills
• Solve one-variable equations: isolate x using inverse operations.
• Solve inequalities: flip the sign when multiplying or dividing by a negative.
• Interpret solutions: understand what x = 5 means in context.
• Translate word problems: identify the unknown, write the equation, solve.
Strategy: Word Problems Step 1: Identify the unknown. What is x? Step 2: Write one equation using the given information. Step 3: Solve and check your answer against the original problem. Tip: Plug your answer back in. If it doesn't work, re-read the problem. |
Systems of Linear Equations
You'll be given two equations and asked to find where they intersect, or how many solutions exist.
Three Methods
• Substitution: solve one equation for a variable, plug into the other. Best when one variable is isolated.
• Elimination: add or subtract equations to cancel a variable. Best when coefficients are easy to match.
• Graphing (mental): think about slope and y-intercept to reason about solutions visually.
How Many Solutions?
• One solution: lines intersect at one point. Different slopes.
• No solution: lines are parallel. Same slope, different intercepts.
• Infinite solutions: lines are identical. Same slope, same intercept.
Watch Out: No-Solution Questions These appear frequently. If two equations have the same slope, ask: same or different y-intercept? Same intercept = infinite solutions. Different intercept = no solution. Quick test: Put both in y = mx + b form and compare. |
Linear Functions
Linear functions appear as equations, tables, and graphs. You need to move fluently between all three.
• Slope formula: m = (y2 - y1) / (x2 - x1)
• Slope-intercept form: y = mx + b, where m is slope and b is y-intercept.
• Point-slope form: y - y1 = m(x - x1). Useful when you have a point and a slope.
• Interpret slope in context: 'for every 1 unit increase in x, y increases by m.'
• Interpret y-intercept in context: 'the value of y when x = 0.'
Domain 2: Advanced Math
Advanced Math covers nonlinear relationships. Quadratics are the most tested topic in this domain. Master them first.
Quadratic Equations
Quadratics appear in equation, graph (parabola), and word problem form. You need to solve them, factor them, and interpret them.
Solving Quadratics: Four Methods
• Factoring: works when the quadratic factors cleanly. Fastest when it applies.
• Quadratic formula: x = (-b ± √(b²-4ac)) / 2a. Always works. Use when factoring is messy.
• Completing the square: useful for identifying vertex form.
• Square root method: use when the equation is in the form (x - h)² = k.
The Discriminant Shortcut b² - 4ac tells you how many real solutions exist. > 0: two real solutions (parabola crosses x-axis twice) = 0: one real solution (parabola touches x-axis once) < 0: no real solutions (parabola doesn't cross x-axis) SAT loves to test this concept without asking you to solve. |
Parabola Key Features
• Vertex: the maximum or minimum point. x-coordinate = -b/2a in standard form.
• Axis of symmetry: vertical line x = -b/2a that divides the parabola in half.
• x-intercepts (roots/zeros): where y = 0. Set the equation equal to zero and solve.
• y-intercept: where x = 0. Substitute x = 0 into the equation.
Exponential Functions
Exponential functions model growth and decay. The key formula: f(x) = a · b^x
• a: the initial value (when x = 0).
• b > 1: exponential growth.
• 0 < b < 1: exponential decay.
• Percent growth/decay: b = 1 + r for growth, b = 1 - r for decay, where r is the rate.
Growth vs. Decay: Quick Check If a population grows by 3% per year: b = 1.03 If a substance decays by 5% per hour: b = 0.95 The SAT often gives you a table or graph and asks you to write the equation. Find b by dividing any y-value by the previous y-value. |
Polynomials
• Add/subtract: combine like terms.
• Multiply: distribute carefully, especially (a + b)(c + d) = ac + ad + bc + bd.
• Factor: look for GCF first, then difference of squares or trinomial factoring.
• Remainder theorem: if p(a) = 0, then (x - a) is a factor of p(x).
Domain 3: Problem-Solving and Data Analysis
This domain tests your ability to apply math to real-world contexts. Many questions involve reading data from tables or graphs. Precision matters.
Ratios, Rates, and Proportions
• Ratio: a comparison of two quantities. Can be written as a:b or a/b.
• Rate: a ratio with different units (e.g., miles per hour).
• Proportion: two equal ratios. Set up as a/b = c/d and cross-multiply.
• Unit conversion: multiply by conversion fractions until units cancel correctly.
Percentages
• Percent of a number: multiply by the decimal form. 30% of 80 = 0.30 × 80 = 24.
• Percent increase: (new - old) / old × 100.
• Percent decrease: (old - new) / old × 100.
• Percent change combined: apply each change sequentially. Don't add percentages directly.
Common Percentage Trap A 20% increase followed by a 20% decrease does NOT return to the original. Example: 100 → +20% = 120 → -20% = 96. Net result: -4%. Always calculate step by step using the actual values. |
Statistics
Term | Definition |
Mean | Sum of all values divided by the count. Affected by outliers. |
Median | Middle value when sorted. Not affected by outliers. |
Mode | Most frequently occurring value. |
Range | Maximum minus minimum. |
Standard Deviation | Measures spread. Higher = more spread out from the mean. |
IQR | Interquartile range = Q3 - Q1. Measures middle 50% spread. |
The SAT often asks which measure is most appropriate for a given context. When outliers are present, median is more representative than mean.
Data Interpretation
You'll encounter bar charts, scatterplots, histograms, and two-way tables. The strategy is always the same:
• Step 1: read the title, axes, and units before anything else.
• Step 2: identify exactly what the question is asking.
• Step 3: find the relevant data point or calculate the value.
• Scatterplots: identify the line of best fit, the correlation direction, and whether the relationship is linear or nonlinear.
• Two-way tables: pay attention to whether the question asks for a row total, column total, or grand total as the denominator.
Probability
• Basic probability: P(event) = favorable outcomes / total outcomes.
• Conditional probability: P(A | B) = P(A and B) / P(B). Restrict your sample space to the given condition.
• Two-way table probability: use the appropriate row or column total as your denominator.
Domain 4: Geometry and Trigonometry
Geometry questions test area, volume, angle relationships, and coordinate geometry. You're given a formula sheet on test day — know how to use it efficiently.
Essential Formulas (Provided on Test Day)
Shape / Concept | Formula |
Circle area | A = Ï€r² |
Circle circumference | C = 2Ï€r |
Rectangle area | A = lw |
Triangle area | A = ½bh |
Pythagorean theorem | a² + b² = c² |
Rectangular prism volume | V = lwh |
Cylinder volume | V = Ï€r²h |
Sphere volume | V = (4/3)Ï€r³ |
Cone volume | V = (1/3)Ï€r²h |
Triangles
• Interior angles sum to 180°.
• Special right triangles: 30-60-90 (sides 1 : √3 : 2) and 45-45-90 (sides 1 : 1 : √2).
• Similar triangles: corresponding sides are proportional. Set up ratios to find missing lengths.
• The Pythagorean theorem: for any right triangle, a² + b² = c².
Circles
• Arc length: (central angle / 360) × 2Ï€r.
• Sector area: (central angle / 360) × Ï€r².
• Inscribed angle: equals half the central angle that subtends the same arc.
• Tangent line: always perpendicular to the radius at the point of tangency.
Basic Trigonometry
SAT trig is limited to right triangles and the unit circle at a basic level. Know SOH-CAH-TOA cold.
• sin(θ): opposite / hypotenuse
• cos(θ): adjacent / hypotenuse
• tan(θ): opposite / adjacent
• Complementary angles: sin(θ) = cos(90° - θ). This appears frequently.
Universal Math Strategies
Pacing and Time Management
• Module 2 = 35 minutes for ~22 questions. That's about 95 seconds per question.
• Easy and hard questions are worth the same. Do not spend 4 minutes on one hard problem.
• If stuck after 90 seconds: mark it, move on, return at the end.
• Grid-in answers last: they have no answer choices to fall back on, so allocate time accordingly.
Backsolving
When a question has numerical answer choices and you can't see an algebraic path, plug the answers in. Start with the middle value.
• Start with choice B or C (middle values).
• If the result is too small, try a larger choice.
• If the result is too large, try a smaller choice.
• This works especially well on percent problems and number theory questions.
Pick Numbers (Substitution Strategy)
When a question uses variables in both the problem and answer choices, substitute simple numbers for the variables.
• Pick easy numbers: 2, 3, or 10. Avoid 0 and 1 (they cause ambiguity).
• Calculate the target answer using your chosen numbers.
• Test each answer choice with the same numbers. The one that matches is correct.
• If two choices match, try different numbers to break the tie.
Drawing and Labeling
• Always draw a diagram if one isn't provided for geometry problems.
• Label every value from the problem directly on your diagram.
• Write equations next to figures so you don't lose track of your setup.
Checking Your Work
• For equations: plug your answer back in to verify it satisfies the original equation.
• For word problems: re-read the question and confirm your answer makes sense in context.
• For grid-ins: double-check that you're answering what was asked, not an intermediate step.
The #1 Grid-In Mistake Students often solve for x when the question asks for 2x, or find the radius when the question asks for the diameter. Before bubbling your grid-in answer, re-read the last sentence of the question one more time. This single habit can recover 2-4 points per test. |
Math Study Plan by Score Target
Target Score | Focus Areas |
Below 500 | Master linear equations, basic algebra, and word problem translation. Do 20 problems per session on these topics only. |
500 – 600 | Add systems of equations, percentages, and data interpretation. Start timed section practice. |
600 – 700 | Add quadratics, exponential functions, and statistics. Review every missed problem in detail. |
700 – 750 | Add geometry, trig, and advanced polynomial topics. Take full timed sections weekly. |
750+ | Focus on the hardest 5 questions per module. Eliminate all careless errors on easy and medium questions. |
Final Reminders
• The formula sheet is your friend, but don't waste time hunting for formulas you should know cold.
• Algebra is 35% of the test. If you're short on time, prioritize it.
• Adaptive scoring rewards Module 1 performance. Don't rush Module 1. A strong first module unlocks a higher-scoring second module.
• Official practice only. Use College Board's Bluebook app for realistic adaptive practice.
• Every missed problem is a lesson. Write down why you missed it and review before your next session.
Math is learnable. Strategy is learnable. Show up, do the work, and the score will follow.
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