Free SAT Math Exam Flashcards
Memorize 50 essential terms and definitions for the SAT Math Section (Digital SAT). See the term, recall the definition, then flip to check yourself.
What is the slope formula for a line through two points (x1, y1) and (x2, y2)?
m = (y2 - y1) / (x2 - x1) — the change in y divided by the change in x (rise over run).
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About These SAT Math Flashcards
These 50 flashcards are designed to help you memorize key terms and definitions for the SAT Math Section (Digital SAT). Each card shows a term on the front and its definition on the back—the classic flashcard format for vocabulary memorization. Use these alongside our practice questions to build both recall and comprehension.
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Review every term in this set. Open any term to reveal its definition.
What is the slope formula for a line through two points (x1, y1) and (x2, y2)?
m = (y2 - y1) / (x2 - x1) — the change in y divided by the change in x (rise over run).
In slope-intercept form y = mx + b, what do m and b represent?
m is the slope (rate of change); b is the y-intercept, the value of y when x = 0 (the starting value).
How do you write a line's equation when you know its slope and one point (x1, y1)?
Use point-slope form: y - y1 = m(x - x1). Expand and simplify to convert it to slope-intercept form if needed.
In standard form Ax + By = C, how do you quickly find the x-intercept and y-intercept?
Set y = 0 and solve for x to get the x-intercept (x = C/A). Set x = 0 and solve for y to get the y-intercept (y = C/B).
How can you tell two lines are parallel just from their equations?
Parallel lines have equal slopes but different y-intercepts, so they never intersect even though they never match exactly.
How can you tell two lines are perpendicular from their slopes?
Perpendicular lines have slopes that are negative reciprocals of each other — if one slope is m, the other is -1/m, and their product is -1.
A table shows a constant change in y for every unit increase in x. What kind of relationship is this, and how do you find its rate?
It's a linear relationship. The constant rate of change IS the slope — divide the change in y by the change in x to find m.
When solving a system of two linear equations by substitution, what's the first step?
Solve one equation for one variable (isolate x or y), then substitute that expression into the other equation to solve for the remaining variable.
When is the elimination method most efficient for solving a system of linear equations?
When the coefficients of one variable are the same or opposites (or can easily be made so by multiplying an equation), letting you add or subtract the equations to cancel that variable.
A system of two linear equations has no solution. What does that tell you about the lines?
The lines are parallel — equal slopes but different y-intercepts — so they never intersect and no (x, y) satisfies both equations.
A system of two linear equations has infinitely many solutions. What does that tell you about the equations?
The two equations represent the exact same line (equal slope and equal y-intercept) — one equation is just a scalar multiple of the other.
How many solutions can a system of one linear and one quadratic equation have, and how do you find them?
Up to two solutions, where the line crosses the parabola. Set the expressions equal, move everything to one side, and solve the resulting quadratic equation.
What happens to an inequality sign when you multiply or divide both sides by a negative number?
The inequality sign flips direction. For example, -2x < 6 becomes x > -3 after dividing both sides by -2.
How do you solve a compound inequality like -3 < 2x + 1 < 7?
Perform the same operation on all three parts at once. Subtract 1 from all parts: -4 < 2x < 6; divide by 2: -2 < x < 3.
How do you solve the absolute value equation |x - 4| = 9?
Split into two cases: x - 4 = 9 (giving x = 13) or x - 4 = -9 (giving x = -5). Absolute value equations generally have two solutions.
What does the graph of a linear inequality like y > 2x + 1 look like?
A dashed boundary line y = 2x + 1 (dashed because points on the line itself are not included), with the region above the line shaded since y is greater.
How do you solve an absolute value inequality like |x + 2| < 5?
Rewrite it as a compound inequality: -5 < x + 2 < 5, then solve: -7 < x < 3. A 'less than' absolute value inequality produces a bounded ('and') range.
How do you solve an absolute value inequality like |x - 1| > 3?
Split into two separate inequalities joined by 'or': x - 1 > 3 or x - 1 < -3, giving x > 4 or x < -2. A 'greater than' absolute value inequality produces two unbounded rays.
What is the quadratic formula, and when should you use it?
x = (-b ± √(b² - 4ac)) / 2a. Use it to solve any quadratic equation ax² + bx + c = 0, especially one that doesn't factor cleanly.
What is the discriminant of a quadratic, and what does its value tell you?
The discriminant is b² - 4ac. If positive, the equation has two distinct real roots; if zero, one repeated real root; if negative, no real roots.
How do you find the x-coordinate of a parabola's vertex from ax² + bx + c?
x = -b / (2a). Substitute this x-value back into the equation to find the y-coordinate of the vertex.
In vertex form y = a(x - h)² + k, what do h and k represent, and what's a common sign trap?
(h, k) is the vertex. The trap: in (x + 3)², h = -3, not +3 — you must flip the sign inside the parentheses to correctly read off h.
What does the sign of 'a' tell you about a parabola y = ax² + bx + c?
If a > 0, the parabola opens upward and has a minimum at its vertex. If a < 0, it opens downward and has a maximum at its vertex.
How do you factor a difference of squares like x² - 25?
a² - b² = (a + b)(a - b), so x² - 25 = (x + 5)(x - 5). Recognize this pattern whenever two perfect squares are subtracted.
What's the relationship between a quadratic's factored form and its roots?
If a quadratic factors as a(x - p)(x - q), then p and q are its roots (x-intercepts) — the values that make each factor equal zero.
How do you complete the square to convert x² + 6x + 5 to vertex form?
Take half the coefficient of x (6/2 = 3), square it (9), and add/subtract to preserve equality: x² + 6x + 9 - 9 + 5 = (x + 3)² - 4.
What is the general formula for exponential growth, and what does each variable mean?
y = a(1 + r)^t, where a is the initial amount, r is the growth rate as a decimal, and t is time. Swap in (1 - r) instead of (1 + r) for decay.
What's the rule for multiplying powers with the same base, like x^a · x^b?
Add the exponents: x^a · x^b = x^(a+b). This rule only applies when the bases are identical.
What's the rule for raising a power to a power, like (x^a)^b?
Multiply the exponents: (x^a)^b = x^(a·b).
What does a negative exponent like x^-a mean?
x^-a = 1/x^a — a negative exponent creates a reciprocal; it does not make the resulting value negative.
What does the fractional exponent x^(1/n) mean?
It represents the nth root of x. For example, x^(1/2) = √x, and x^(1/3) is the cube root of x.
How do you determine the end behavior of a polynomial function's graph?
Look at the leading term (the highest-degree term). Its degree (even or odd) and sign determine whether both ends rise, both fall, or the ends go in opposite directions.
Why must you check your solutions after solving a radical (square root) equation?
Squaring both sides can introduce extraneous roots — solutions that satisfy the squared equation but not the original. Always substitute back to verify each answer.
What does √(x²) simplify to, and why is this a common trap?
√(x²) = |x|, not x. Students forget the absolute value, which matters because x could be negative while √(x²) is always non-negative.
How does adding a constant k outside a function, as in f(x) + k, transform its graph?
It shifts the entire graph vertically: up by k if k is positive, down if k is negative. The shape of the graph itself doesn't change.
How does f(x - h) transform the graph of f(x), and what's the common sign mistake?
It shifts the graph horizontally right by h (for positive h). The trap: f(x + 3) shifts the graph LEFT 3, not right — the shift is opposite the sign inside the parentheses.
How do you calculate percent increase or decrease?
Percent change = (New Value - Original Value) / Original Value × 100. Always divide by the ORIGINAL value, not the new one — a common trap.
What's the difference between direct variation and inverse variation?
Direct variation: y = kx, so y increases as x increases with a constant ratio. Inverse variation: y = k/x, so y decreases as x increases with a constant product.
How do you solve a proportion like a/b = c/d?
Cross-multiply: a·d = b·c, then solve for the unknown variable. This works because equal ratios always have equal cross products.
If a recipe makes 4 servings and you need 10, how do you scale every ingredient using a unit rate?
Find the scale factor by dividing desired servings by original servings (10/4 = 2.5), then multiply every ingredient amount by that factor.
Why does the mean shift more than the median when a data set has an extreme outlier?
The mean uses every value in its calculation, so one extreme value pulls it up or down. The median only depends on the middle value's position, so it resists outliers.
What does the interquartile range (IQR) measure, and how is it calculated?
IQR measures the spread of the middle 50% of a data set: IQR = Q3 - Q1 (third quartile minus first quartile). It's resistant to outliers, unlike the full range.
On a scatterplot, what does a negative slope in the line of best fit indicate?
A negative association: as the x-variable increases, the y-variable tends to decrease. A positive slope means both variables tend to increase together.
What are the formulas for the area and circumference of a circle?
Area = πr². Circumference = 2πr (equivalently, πd using the diameter). Both depend only on the radius or diameter.
What is the volume formula for a cylinder, and how does it relate to a cone with the same base and height?
Cylinder volume = πr²h. A cone with the same radius and height has exactly one-third that volume: πr²h/3.
What is the formula for the volume of a sphere?
V = (4/3)πr³ — the volume depends only on the radius, cubed.
What are the side ratios of a 45-45-90 right triangle?
The two legs are equal length x, and the hypotenuse is x√2. This follows directly from the Pythagorean theorem applied to an isosceles right triangle.
What are the side ratios of a 30-60-90 right triangle?
The short leg (opposite 30°) is x, the long leg (opposite 60°) is x√3, and the hypotenuse (opposite 90°) is 2x.
What does the mnemonic SOH-CAH-TOA tell you about right-triangle trigonometry?
SOH: sin θ = Opposite/Hypotenuse. CAH: cos θ = Adjacent/Hypotenuse. TOA: tan θ = Opposite/Adjacent — the three basic trig ratios relative to angle θ.
Name two common Pythagorean triples (whole-number right-triangle side lengths) useful for fast geometry work.
3-4-5 and 5-12-13 (and their multiples, like 6-8-10). Recognizing these lets you skip the Pythagorean theorem calculation entirely.
Frequently Asked Questions
Does the SAT Math section have a pass or fail score?
No. The SAT Math section is scored on a scale of 200-800; there is no pass/fail cutoff. College Board's college-readiness benchmark is 530, meaning a student scoring at or above 530 has roughly a 75% chance of earning a C or better in an entry-level college course, but individual colleges set their own score expectations.
How soon can I retake the SAT Math section, and how many times can I take it?
College Board imposes no mandatory waiting period and no limit on attempts — you can register for any upcoming national test date, offered about 7-8 times per year in the US. Because Math and Reading & Writing are taken together in one sitting, retaking means sitting the full exam again, not just the Math portion.
How does the adaptive Module 1 / Module 2 structure affect the Math section?
All students take the same 22-question Module 1. Based on Module 1 performance, the adaptive engine routes each student to either a harder or easier 22-question Module 2. Scoring above roughly 650-700 on Math requires being routed into the harder Module 2, so performing well early in the section matters more than pacing evenly across it.
Is a calculator allowed on every SAT Math question?
Yes. Unlike the old paper SAT, the Digital SAT allows an approved calculator — including the built-in Bluebook Desmos graphing calculator — on all 44 Math questions in both modules.
How are the four SAT Math domains weighted?
Algebra and Advanced Math each make up about 35% of the section (roughly 13-15 questions each), while Problem-Solving & Data Analysis and Geometry & Trigonometry each make up about 15% (roughly 5-7 questions each). Algebra and Advanced Math together account for about 70% of all Math questions.
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