You do not need to memorize every geometry formula before the SAT.

Bluebook gives you a Math reference sheet during the test.

But there is an important catch:

The reference sheet gives formulas. It does not tell you which formula to use, how to rearrange it, or how to model the problem.

A better goal is to know the small set of relationships that appear repeatedly across SAT Math and to recognize when each one applies.

The SAT Math domains

College Board organizes SAT Math into four domains:

1. Algebra
2. Advanced Math
3. Problem-Solving and Data Analysis
4. Geometry and Trigonometry

This guide groups formulas the same way.

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Part 1: Formulas Bluebook gives you

Bluebook includes a reference sheet on tests with Math questions.

The SAT reference information includes common geometry formulas and facts such as the following.

Circle

Area

[ A=\pi r^2 ]

Circumference

[ C=2\pi r ]

where (r) is the radius.

Rectangle

[ A=lw ]

Triangle

[ A=\frac12 bh ]

Pythagorean theorem

[ c^2=a^2+b^2 ]

for a right triangle where (c) is the hypotenuse.

Rectangular prism

[ V=lwh ]

Cylinder

[ V=\pi r^2h ]

Sphere

[ V=\frac43\pi r^3 ]

Cone

[ V=\frac13\pi r^2h ]

Pyramid

[ V=\frac13 lwh ]

for the rectangular-base version shown on the reference sheet.

Special right triangles

The reference sheet also shows the side relationships for:

45-45-90

[ x:x:x\sqrt2 ]

30-60-90

[ x:x\sqrt3:2x ]

It also reminds you that:

• a circle has (360^\circ);
• a full circle has (2\pi) radians;
• the angles of a triangle sum to (180^\circ).

So why study formulas at all?

Because most SAT Math questions are not:

“What is the formula for the area of a circle?”

They are more like:

“A circle's area increases by a factor of 9. By what factor does its radius increase?”

The reference sheet gives (A=\pi r^2).

You still need to understand the relationship.

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Part 2: Algebra formulas and relationships worth knowing

Slope

[ m=\frac{y_2-y_1}{x_2-x_1} ]

Slope means:

change in y divided by change in x.

Example

Points:

[ (2,5),\ (6,13) ]

[ m=\frac{13-5}{6-2}=\frac84=2 ]

Slope-intercept form

[ y=mx+b ]

where:

• (m) = slope;
• (b) = y-intercept.

Point-slope form

[ y-y_1=m(x-x_1) ]

Useful when you know:

• one point;
• the slope.

Standard form of a linear equation

[ Ax+By=C ]

The SAT may present lines in any equivalent form.

Do not memorize one format so rigidly that you fail to recognize another.

Parallel lines

Parallel nonvertical lines have the same slope.

Perpendicular lines

For nonvertical, nonhorizontal lines:

[ m_1m_2=-1 ]

Their slopes are negative reciprocals.

Distance between two points

[ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} ]

This is really the Pythagorean theorem on the coordinate plane.

Midpoint

[ \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) ]

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Part 3: Advanced Math formulas and relationships

Quadratic standard form

[ y=ax^2+bx+c ]

Factored form

[ y=a(x-r_1)(x-r_2) ]

The roots are:

[ r_1,\ r_2 ]

Vertex form

[ y=a(x-h)^2+k ]

The vertex is:

[ (h,k) ]

Quadratic formula

[ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} ]

You can sometimes solve a quadratic faster by:

• factoring;
• graphing in Desmos;
• using structure.

But the quadratic formula is a reliable fallback.

Discriminant

[ b^2-4ac ]

Interpretation:

• positive → 2 distinct real solutions;
• zero → 1 repeated real solution;
• negative → no real solutions.

Difference of squares

[ a^2-b^2=(a-b)(a+b) ]

Example:

[ x^2-49=(x-7)(x+7) ]

Exponential growth

[ y=a(1+r)^t ]

where:

• (a) = initial value;
• (r) = growth rate as a decimal;
• (t) = number of periods.

A 6% increase:

[ 1+r=1.06 ]

Exponential decay

[ y=a(1-r)^t ]

A 20% decrease:

[ 1-r=0.80 ]

Exponent rules

Product

[ x^a x^b=x^{a+b} ]

Quotient

[ \frac{x^a}{x^b}=x^{a-b} ]

Power of a power

[ (x^a)^b=x^{ab} ]

Negative exponent

[ x^{-a}=\frac{1}{x^a} ]

Fractional exponent

[ x^{1/n}=\sqrt[n]{x} ]

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Part 4: Percentages, ratios and rates

Percent

[ \text{percent}=\frac{\text{part}}{\text{whole}}\times100 ]

Percent change

[ \text{percent change}

\frac{\text{new}-\text{original}}{\text{original}}\times100 ]

Use the original amount in the denominator.

Increase by r%

[ \text{new}=\text{original}(1+r) ]

Decrease by r%

[ \text{new}=\text{original}(1-r) ]

Proportion

[ \frac{a}{b}=\frac{c}{d} ]

If appropriate:

[ ad=bc ]

Rate

[ \text{rate}=\frac{\text{quantity}}{\text{time}} ]

Examples:

• miles per hour;
• dollars per item;
• liters per minute.

Density

[ \text{density}=\frac{\text{mass}}{\text{volume}} ]

Dimensional analysis

Treat units like algebra.

Example:

[ 72\frac{\text{km}}{\text{hour}} \times \frac{1\text{ hour}}{60\text{ min}}

1.2\frac{\text{km}}{\text{min}} ]

If the wrong unit does not cancel, your setup is probably wrong.

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Part 5: Statistics and data formulas

Mean

[ \text{mean}=\frac{\text{sum of values}}{\text{number of values}} ]

Weighted mean

[ \frac{\sum(\text{value}\times\text{weight})}{\sum\text{weights}} ]

Example:

40% at 80 and 60% at 90:

[ 0.4(80)+0.6(90)=86 ]

Probability

[ P(A)=\frac{\text{favorable outcomes}}{\text{total possible outcomes}} ]

when the outcomes are equally likely.

Complement

[ P(\text{not }A)=1-P(A) ]

Conditional probability

A useful way to think about:

[ P(A\mid B) ]

is:

restrict the denominator to the cases where B is true.

Residual

[ \text{residual}=\text{actual}-\text{predicted} ]

Positive residual: actual value is above the model.

Negative residual: actual value is below the model.

Margin of error

For SAT purposes, the important relationship is usually conceptual:

Larger well-designed random samples generally produce smaller margins of error.

You normally do not need an advanced margin-of-error formula.

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Part 6: Geometry and trigonometry relationships worth knowing

Even when the formula appears on the reference sheet, know what each variable means.

Arc length

[ \text{arc length}

\frac{\theta}{360^\circ}(2\pi r) ]

for (\theta) measured in degrees.

Sector area

[ \text{sector area}

\frac{\theta}{360^\circ}(\pi r^2) ]

Circle equation

[ (x-h)^2+(y-k)^2=r^2 ]

Center:

[ (h,k) ]

Radius:

[ r ]

Right-triangle trigonometry

Sine

[ \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} ]

Cosine

[ \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} ]

Tangent

[ \tan\theta=\frac{\text{opposite}}{\text{adjacent}} ]

A familiar memory aid is:

SOH-CAH-TOA

Similar figures

If lengths scale by (k):

• lengths scale by (k);
• areas scale by (k^2);
• volumes scale by (k^3).

That relationship is more useful than memorizing dozens of separate shape problems.

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Part 7: Formulas that students often misuse

Mistake 1: wrong percent denominator

Price changes from 80 to 100.

Increase:

[ 20 ]

Percent increase:

[ \frac{20}{80}\times100=25% ]

Not 20%.

Mistake 2: confusing growth rate with growth factor

8% growth:

[ r=0.08 ]

growth factor:

[ 1.08 ]

Mistake 3: using diameter as radius

If diameter = 10:

[ r=5 ]

Circle area:

[ 25\pi ]

not:

[ 100\pi ]

Mistake 4: applying Pythagorean theorem to a non-right triangle

[ a^2+b^2=c^2 ]

requires a right triangle.

Mistake 5: treating slope as y/x

Slope is:

[ \frac{\Delta y}{\Delta x} ]

not automatically:

[ \frac yx ]

unless the context happens to make that valid.

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Part 8: Original SAT-style formula practice

These questions are MastaPrep-created practice examples, not official College Board questions.

1. Linear model

A water tank contains 420 liters and loses 18 liters per minute.

Which equation models the amount (V) after (t) minutes?

A. (V=420+18t)
B. (V=420-18t)
C. (V=18-420t)
D. (V=18t)

Answer: B

The starting value is 420 and the rate of change is (-18).

2. Percent decrease

A jacket priced at $160 is discounted 25%.

New price:

[ 160(0.75)=120 ]

Answer: $120

3. Quadratic roots

[ x^2-11x+24=0 ]

Factor:

[ (x-3)(x-8)=0 ]

Answer: 3 and 8

4. Exponential growth

A population starts at 2,000 and grows 4% per year.

Model:

[ P(t)=2000(1.04)^t ]

5. Circle equation

[ (x-2)^2+(y+5)^2=49 ]

Center:

[ (2,-5) ]

Radius:

[ 7 ]

6. Residual

Model predicts 72.

Actual value is 68.

[ 68-72=-4 ]

Answer: -4

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Do you need to memorize every formula?

No.

A stronger approach is:

Memorize automatically useful relationships

Such as:

• slope;
• percent change;
• growth/decay factors;
• quadratic forms;
• probability basics;
• SOH-CAH-TOA.

Recognize reference-sheet formulas instantly

Do not waste time hunting for:

[ A=\pi r^2 ]

if you already know it.

Practice choosing the formula

The SAT rewards setup more than formula recitation.

Use Desmos intelligently

Bluebook includes Desmos throughout SAT Math.

It can be excellent for:

• systems;
• roots;
• intersections;
• graph behavior;
• regressions.

But do not graph:

[ 2x+3=11 ]

if solving it mentally takes five seconds.

The best Math strategy combines:

algebra + formula fluency + Desmos judgment.

For the complete set of Math topics, browse our SAT Math guides.

Next useful SAT Math guides

• Linear equations
• Quadratics
• Functions
• Percentages
• Probability and statistics
• Exponents and radicals
• Ratios, rates and units
• Right-triangle trigonometry
• Desmos guide

How MastaPrep can help

Knowing a formula is only step one.

MastaPrep can give you fresh questions from the same skill, increase the challenge as you improve, and bring the skill back later so you can check whether the method still sticks.

Practice SAT Math free in MastaPrep when you are ready to move from reading formulas to actually using them.

Official sources

• Bluebook Testing Tools: https://bluebook.collegeboard.org/students/tools
• College Board Math content domains: https://satsuite.collegeboard.org/practice/content-domains
• College Board Student Question Bank — Math: https://satsuite.collegeboard.org/practice/student-question-bank/math

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