SAT Math Exam Flashcards

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Question 1

What is the slope formula for a line through two points (x1, y1) and (x2, y2)?

Accepted Answer

m = (y2 - y1) / (x2 - x1) — the change in y divided by the change in x (rise over run).

Question 2

In slope-intercept form y = mx + b, what do m and b represent?

Accepted Answer

m is the slope (rate of change); b is the y-intercept, the value of y when x = 0 (the starting value).

Question 3

How do you write a line's equation when you know its slope and one point (x1, y1)?

Accepted Answer

Use point-slope form: y - y1 = m(x - x1). Expand and simplify to convert it to slope-intercept form if needed.

Question 4

In standard form Ax + By = C, how do you quickly find the x-intercept and y-intercept?

Accepted Answer

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).

Question 5

How can you tell two lines are parallel just from their equations?

Accepted Answer

Parallel lines have equal slopes but different y-intercepts, so they never intersect even though they never match exactly.

Question 6

How can you tell two lines are perpendicular from their slopes?

Accepted Answer

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.

Question 7

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?

Accepted Answer

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.

Question 8

When solving a system of two linear equations by substitution, what's the first step?

Accepted Answer

Solve one equation for one variable (isolate x or y), then substitute that expression into the other equation to solve for the remaining variable.

Question 9

When is the elimination method most efficient for solving a system of linear equations?

Accepted Answer

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.

Question 10

A system of two linear equations has no solution. What does that tell you about the lines?

Accepted Answer

The lines are parallel — equal slopes but different y-intercepts — so they never intersect and no (x, y) satisfies both equations.

Question 11

A system of two linear equations has infinitely many solutions. What does that tell you about the equations?

Accepted Answer

The two equations represent the exact same line (equal slope and equal y-intercept) — one equation is just a scalar multiple of the other.

Question 12

How many solutions can a system of one linear and one quadratic equation have, and how do you find them?

Accepted Answer

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.

Question 13

What happens to an inequality sign when you multiply or divide both sides by a negative number?

Accepted Answer

The inequality sign flips direction. For example, -2x < 6 becomes x > -3 after dividing both sides by -2.

Question 14

How do you solve a compound inequality like -3 < 2x + 1 < 7?

Accepted Answer

Perform the same operation on all three parts at once. Subtract 1 from all parts: -4 < 2x < 6; divide by 2: -2 < x < 3.

Question 15

How do you solve the absolute value equation |x - 4| = 9?

Accepted Answer

Split into two cases: x - 4 = 9 (giving x = 13) or x - 4 = -9 (giving x = -5). Absolute value equations generally have two solutions.

Question 16

What does the graph of a linear inequality like y > 2x + 1 look like?

Accepted Answer

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.

Question 17

How do you solve an absolute value inequality like |x + 2| < 5?

Accepted Answer

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.

Question 18

How do you solve an absolute value inequality like |x - 1| > 3?

Accepted Answer

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.

Question 19

What is the quadratic formula, and when should you use it?

Accepted Answer

x = (-b ± √(b² - 4ac)) / 2a. Use it to solve any quadratic equation ax² + bx + c = 0, especially one that doesn't factor cleanly.

Question 20

What is the discriminant of a quadratic, and what does its value tell you?

Accepted Answer

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.

Question 21

How do you find the x-coordinate of a parabola's vertex from ax² + bx + c?

Accepted Answer

x = -b / (2a). Substitute this x-value back into the equation to find the y-coordinate of the vertex.

Question 22

In vertex form y = a(x - h)² + k, what do h and k represent, and what's a common sign trap?

Accepted Answer

(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.

Question 23

What does the sign of 'a' tell you about a parabola y = ax² + bx + c?

Accepted Answer

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.

Question 24

How do you factor a difference of squares like x² - 25?

Accepted Answer

a² - b² = (a + b)(a - b), so x² - 25 = (x + 5)(x - 5). Recognize this pattern whenever two perfect squares are subtracted.

Question 25

What's the relationship between a quadratic's factored form and its roots?

Accepted Answer

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.

Question 26

How do you complete the square to convert x² + 6x + 5 to vertex form?

Accepted Answer

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.

Question 27

What is the general formula for exponential growth, and what does each variable mean?

Accepted Answer

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.

Question 28

What's the rule for multiplying powers with the same base, like x^a · x^b?

Accepted Answer

Add the exponents: x^a · x^b = x^(a+b). This rule only applies when the bases are identical.

Question 29

What's the rule for raising a power to a power, like (x^a)^b?

Accepted Answer

Multiply the exponents: (x^a)^b = x^(a·b).

Question 30

What does a negative exponent like x^-a mean?

Accepted Answer

x^-a = 1/x^a — a negative exponent creates a reciprocal; it does not make the resulting value negative.

Question 31

What does the fractional exponent x^(1/n) mean?

Accepted Answer

It represents the nth root of x. For example, x^(1/2) = √x, and x^(1/3) is the cube root of x.

Question 32

How do you determine the end behavior of a polynomial function's graph?

Accepted Answer

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.

Question 33

Why must you check your solutions after solving a radical (square root) equation?

Accepted Answer

Squaring both sides can introduce extraneous roots — solutions that satisfy the squared equation but not the original. Always substitute back to verify each answer.

Question 34

What does √(x²) simplify to, and why is this a common trap?

Accepted Answer

√(x²) = |x|, not x. Students forget the absolute value, which matters because x could be negative while √(x²) is always non-negative.

Question 35

How does adding a constant k outside a function, as in f(x) + k, transform its graph?

Accepted Answer

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.

Question 36

How does f(x - h) transform the graph of f(x), and what's the common sign mistake?

Accepted Answer

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.

Question 37

How do you calculate percent increase or decrease?

Accepted Answer

Percent change = (New Value - Original Value) / Original Value × 100. Always divide by the ORIGINAL value, not the new one — a common trap.

Question 38

What's the difference between direct variation and inverse variation?

Accepted Answer

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.

Question 39

How do you solve a proportion like a/b = c/d?

Accepted Answer

Cross-multiply: a·d = b·c, then solve for the unknown variable. This works because equal ratios always have equal cross products.

Question 40

If a recipe makes 4 servings and you need 10, how do you scale every ingredient using a unit rate?

Accepted Answer

Find the scale factor by dividing desired servings by original servings (10/4 = 2.5), then multiply every ingredient amount by that factor.

Question 41

Why does the mean shift more than the median when a data set has an extreme outlier?

Accepted Answer

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.

Question 42

What does the interquartile range (IQR) measure, and how is it calculated?

Accepted Answer

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.

Question 43

On a scatterplot, what does a negative slope in the line of best fit indicate?

Accepted Answer

A negative association: as the x-variable increases, the y-variable tends to decrease. A positive slope means both variables tend to increase together.

Question 44

What are the formulas for the area and circumference of a circle?

Accepted Answer

Area = πr². Circumference = 2πr (equivalently, πd using the diameter). Both depend only on the radius or diameter.

Question 45

What is the volume formula for a cylinder, and how does it relate to a cone with the same base and height?

Accepted Answer

Cylinder volume = πr²h. A cone with the same radius and height has exactly one-third that volume: πr²h/3.

Question 46

What is the formula for the volume of a sphere?

Accepted Answer

V = (4/3)πr³ — the volume depends only on the radius, cubed.

Question 47

What are the side ratios of a 45-45-90 right triangle?

Accepted Answer

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.

Question 48

What are the side ratios of a 30-60-90 right triangle?

Accepted Answer

The short leg (opposite 30°) is x, the long leg (opposite 60°) is x√3, and the hypotenuse (opposite 90°) is 2x.

Question 49

What does the mnemonic SOH-CAH-TOA tell you about right-triangle trigonometry?

Accepted Answer

SOH: sin θ = Opposite/Hypotenuse. CAH: cos θ = Adjacent/Hypotenuse. TOA: tan θ = Opposite/Adjacent — the three basic trig ratios relative to angle θ.

Question 50

Name two common Pythagorean triples (whole-number right-triangle side lengths) useful for fast geometry work.

Accepted Answer

3-4-5 and 5-12-13 (and their multiples, like 6-8-10). Recognizing these lets you skip the Pythagorean theorem calculation entirely.

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