PSAT Math Formulas

These are trigger and response flashcards for the formulas needed on the PSAT that are not in the reference sheet.

Word problem asks for a constant rate of change, unit rate, per [item], or hourly fee

slope formula: m = (y₂-y₁) / (x₂-x₁)

Question asks you to identify the starting value/initial amount and the rate of change in a straight-line graph

Slope-intercept form: y=mx+b (where m is the rate/slope and b is the starting value/intercept)

You are given a point (x₁, y₁) and a slope m, and asked to find the equation of the line

Point-slope form: y-y₁ = m(x-x₁)

A linear equation is written with x and y on the same side, and you need the slope quickly without rewriting it

Standard form slope shortcut: for Ax + By = C, slope = -(A/B)

The problem states that two lines have “no solutions” or “never intersect”

Parallel lines: the slopes must be equal (m₁=m₂)

The problem states that two lines meet at a “right angle” or are “perpendicular”

Perpendicular lines: the slopes are negative reciprocals (m₁ * m₂ = -1). Flip the fraction & change the sign.

You need to find the “maximum value,” “minimum height,” or “vertex” of a standard quadratic equation y = ax² + bx + c

Vertex x-coordinate formula: h= -(b/2a). (plug this # back into the equation to find k)

A quadratic equation shows a clear shift, like y=(x-3)² +5 and asks for the vertex

Vertex form: y = a(x-h)² + k (the vertex is exactly (h,k). remember to flip the sign inside the parentheses!)

A question asks you to find the “x-intercepts,” “roots,” “zeros,” or “where the ball hits the ground”

Factored form / quadratic formula: y = a(x-r₁)(x-r₂) or quadratic formula

A system with a quadratic says it has “exactly one solution,” “no real solutions,” or “two distinct solutions”

The discriminant: Look at b²-4ac. >0: 2 solutions, =0: 1 solution, <0: 0 solutions

You are given two coordinate points on a grid and need to find the distance or length of the line segment connecting them

Distance formula: d= √(x₂-x₁)² + (y₂-y₁)²
(Or sketch it on desmos & use the Pythagorean theorem)

A problem asks for the “center point” or “halfway point” between two coordinate points

Midpoint formula: M = average the x’s and average the y’s

An equation has both an x² and y² term, and asks for the center or radius of the shape

Circle equation: (x-h)² + (y-k)² = r² (if it’s expanded with single x and y terms, group them & complete the square).

A word problem asks by what percentage a price or population increased or decreased

Percent change: [(New-Old) / Old]x100 (think % error)

A word problem says a value increases or decreases by a fixed percentage over time (grows by % each year)

Exponential growth/decay: y=a(1±r)^t (where a is initial value, r is percent as a decimal, and t is time. plus is growth and minus is decay)

A word problem says a population “doubles every 5 hours” or “triples every half day”

Exponential growth with time delay: y = a(Base)^t/d (ex. doubling every 5 hours is y=a(2)^t/5)

A question asks for the average of a set of numbers or a frequency table

Mean: sum of all values / total number of items

A problem asks for the middle value

Line the numbers up from least to greatest and find the exact middle

A question asks about the spread or range of a data set

Range: maximum value - minimum value