What SAT Math Formulas Are Provided on Test Day<\/strong><\/h2>\n\n\n\nThe Digital SAT provides a built-in Math Reference Sheet in the Bluebook app, accessible throughout both Math modules. It includes formulas for area, circumference, volume, the Pythagorean theorem, and special right triangles.<\/p>\n\n\n\n
However, important formulas such as the quadratic formula, slope formula, and exponent rules are not included.<\/p>\n\n\n\n
Here’s everything provided on the official SAT Math Reference Sheet.<\/p>\n\n\n\n![\"\"](\"https:\/\/i0.wp.com\/blog.panoprep.com\/wp-content\/uploads\/2026\/10\/sat-formula-sheet.jpg?resize=1024%2C768&ssl=1\")
<\/figure>\n\n\n\n1. Area and Circumference Formulas<\/strong><\/h3>\n\n\n\nShape<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Area of a Circle<\/td> A = \u03c0r\u00b2<\/td><\/tr> Circumference of a Circle<\/td> C = 2\u03c0r<\/td><\/tr> Area of a Rectangle<\/td> A = lw<\/td><\/tr> Area of a Triangle<\/td> A = \u00bdbh<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, (r) is the radius, (l) is the length, (w) is the width, (b) is the base, and (h) is the height.<\/p>\n\n\n\n
2. Right Triangle Formulas<\/strong><\/h3>\n\n\n\nPythagorean Theorem<\/strong><\/p>\n\n\n\na\u00b2 + b\u00b2 = c\u00b2<\/p>\n\n\n\n
Here, (a) and (b) are the legs of a right triangle, and (c) is the hypotenuse.<\/p>\n\n\n\n
Special Right Triangles<\/strong><\/p>\n\n\n\nTriangle<\/strong><\/th>Side Ratios<\/strong><\/th>Opposite Angles<\/strong><\/th><\/tr><\/thead>30\u00b0\u201360\u00b0\u201390\u00b0<\/td> 1 : \u221a3 : 2<\/td> 30\u00b0 : 60\u00b0 : 90\u00b0<\/td><\/tr> 45\u00b0\u201345\u00b0\u201390\u00b0<\/td> 1 : 1 : \u221a2<\/td> 45\u00b0 : 45\u00b0 : 90\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nThe side ratios correspond to the opposite angles in the order shown. These relationships help you find missing side lengths without using trigonometric functions.<\/p>\n\n\n\n
3. Volume Formulas<\/strong><\/h3>\n\n\n\nSolid<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Rectangular Prism<\/td> V = lwh<\/td><\/tr> Cylinder<\/td> V = \u03c0r\u00b2h<\/td><\/tr> Sphere<\/td> V = (4\/3)\u03c0r\u00b3<\/td><\/tr> Cone<\/td> V = \u2153\u03c0r\u00b2h<\/td><\/tr> Pyramid (Rectangular Base)<\/td> V = \u2153lwh<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, (V) represents volume, (r) is the radius, (h) is the height, and (l) and (w) represent length and width. For the pyramid, (h) is the perpendicular height.<\/p>\n\n\n\n
4. Geometry Facts<\/strong><\/h3>\n\n\n\n\n- A full circle contains 360 degrees or 2\u03c0 radians.<\/li>\n\n\n\n
- The interior angles of a triangle add up to 180 degrees.<\/li>\n<\/ul>\n\n\n\n
SAT Math Tip:<\/strong> Even though these formulas are provided, knowing the most common ones by heart can save time and help you focus on more challenging questions.<\/p>\n\n\n\nThe SAT Math Reference Sheet covers essential geometry formulas, but many important formulas are not provided. Let’s look at the additional SAT Math formulas you should memorize before test day.<\/p>\n\n\n\n
What SAT Math Formulas Should You Memorize?<\/strong><\/h2>\n\n\n\nWhile the official SAT Math Reference Sheet covers basic geometry, many important formulas are not provided. Here are the essential SAT Math formulas worth memorizing, organized by topic for quick review.<\/p>\n\n\n\n
1. Linear Equations and Slope Formulas<\/strong><\/h3>\n\n\n\nLinear equations are a major part of SAT Algebra. Understanding slopes, intercepts, and different equation forms can help you solve questions efficiently.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th>Purpose<\/strong><\/th><\/tr><\/thead>Slope<\/td> m = (y\u2082 \u2212 y\u2081)\/(x\u2082 \u2212 x\u2081)<\/td> Rate of change
between two points<\/td><\/tr> Slope-Intercept Form<\/td> y = mx + b<\/td> Identify slope and
y-intercept<\/td><\/tr> Point-Slope Form<\/td> y \u2212 y\u2081 = m(x \u2212 x\u2081)<\/td> Write a line from
a point and slope<\/td><\/tr> Standard Form<\/td> Ax + By = C<\/td> Slope = \u2212A\/B, when B \u2260 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, m represents the slope and b represents the y-intercept in slope-intercept form.<\/p>\n\n\n\n
Here, (m) represents the slope and (b) represents the y-intercept in slope-intercept form.<\/p>\n\n\n\n
Remember:<\/strong><\/p>\n\n\n\n\n- Parallel lines have equal slopes when their slopes are defined.<\/li>\n\n\n\n
- Perpendicular lines have slopes whose product is (-1), when both slopes are defined.<\/li>\n\n\n\n
- In word problems, the slope represents the rate of change, while the y-intercept represents the starting value.<\/li>\n<\/ul>\n\n\n\n
Systems of Linear Equations<\/strong><\/p>\n\n\n\nFor two linear equations, compare their coefficients to determine the number of solutions.<\/p>\n\n\n\nCondition<\/strong><\/th>Number of Solutions<\/strong><\/th><\/tr><\/thead>Coefficients of x and y are not proportional<\/td> Exactly one<\/td><\/tr> Variable coefficients are proportional, but constants are not in the same proportion<\/td> No solution<\/td><\/tr> All corresponding coefficients and constants are proportional<\/td> Infinitely many<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nSAT Math Tip:<\/strong> When a system contains an unknown constant such as k, check whether the equations represent intersecting, parallel, or identical lines before solving.<\/p>\n\n\n\n2. Quadratic Formulas<\/strong><\/h3>\n\n\n\nQuadratic formulas help solve nonlinear equations and identify roots, vertices, and maximum or minimum values.<\/p>\n\n\n\n
Quadratic Formula<\/strong><\/p>\n\n\n\nFor ax\u00b2 + bx + c = 0, where a \u2260 0:<\/p>\n\n\n\n
x = (\u2212b \u00b1 \u221a(b\u00b2 \u2212 4ac))\/(2a)<\/p>\n\n\n\n
Discriminant<\/strong><\/p>\n\n\n\nD = b\u00b2 \u2212 4ac<\/p>\n\n\n\nDiscriminant<\/strong><\/th>Number of Real Solutions<\/strong><\/th><\/tr><\/thead>D > 0<\/td> Two distinct real solutions<\/td><\/tr> D = 0<\/td> Exactly one real solution<\/td><\/tr> D < 0<\/td> No real solutions<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nThree Forms of a Quadratic Function<\/strong><\/p>\n\n\n\nForm<\/strong><\/th>Equation<\/strong><\/th>What It Reveals<\/strong><\/th><\/tr><\/thead>Standard Form<\/td> y = ax\u00b2 + bx + c<\/td> Y-intercept<\/td><\/tr> Vertex Form<\/td> y = a(x \u2212 h)\u00b2 + k<\/td> Vertex (h, k)<\/td><\/tr> Factored Form<\/td> y = a(x \u2212 r\u2081)(x \u2212 r\u2082)<\/td> X-intercepts r\u2081, r\u2082,
when real<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nVertex Formula<\/strong><\/p>\n\n\n\nx = \u2212b\/(2a)<\/p>\n\n\n\n
This gives the x-coordinate of the vertex. If a > 0, the parabola opens upward and has a minimum; if a < 0, it opens downward and has a maximum.<\/p>\n\n\n\n
3. Exponent Rules<\/strong><\/h3>\n\n\n\nExponent rules are useful for simplifying expressions, solving equations, and recognizing equivalent mathematical forms.<\/p>\n\n\n\nRule<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Product Rule<\/td> a\u1d50 \u00b7 a\u207f = a\u1d50\u207a\u207f<\/td><\/tr> Quotient Rule<\/td> a\u1d50\/a\u207f = a\u1d50\u207b\u207f<\/td><\/tr> Power Rule<\/td> (a\u1d50)\u207f = a\u1d50\u207f<\/td><\/tr> Zero Exponent<\/td> a\u2070 = 1<\/td><\/tr> Negative Exponent<\/td> a\u207b\u207f = 1\/a\u207f<\/td><\/tr> Fractional Exponent<\/td> a\u1d50\u2044\u207f = \u207f\u221a(a\u1d50)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nThese rules apply wherever the expressions are defined. In particular, expressions involving division by a require a \u2260 0.<\/p>\n\n\n\n
4. Percentages and Exponential Models<\/strong><\/h3>\n\n\n\nPercentage formulas are essential for SAT Problem-Solving and Data Analysis, while exponential models describe growth and decay over time.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th><\/tr><\/thead>Percentage Change<\/td> (New \u2212 Original)\/Original \u00d7 100%<\/td><\/tr> Value After a p% Increase<\/td> x(1 + p\/100)<\/td><\/tr> Value After a p% Decrease<\/td> x(1 \u2212 p\/100)<\/td><\/tr> Exponential Growth<\/td> y = a(1 + r)\u1d57<\/td><\/tr> Exponential Decay<\/td> y = a(1 \u2212 r)\u1d57<\/td><\/tr> Growth Every k Time Units<\/td> y = a(1 + r)\u1d57\u2044\u1d4f<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, a is the initial amount, r is the positive rate of change expressed as a decimal, and t represents time. In the last formula, r is the growth rate per k time units.<\/p>\n\n\n\n
\n- SAT Math Tip:<\/strong> Use multipliers for percentage changes. A 15% increase means multiplying by 1.15, while a 20% decrease means multiplying by 0.80. For successive changes, multiply the factors rather than adding the percentages.<\/li>\n<\/ul>\n\n\n\n
5. Statistics and Probability Formulas<\/h3>\n\n\n\n
Statistics and probability questions focus on interpreting data, calculating averages, and understanding the likelihood of events.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th>Purpose<\/strong><\/th><\/tr><\/thead>Mean<\/td> x\u0304 = \u03a3x\u1d62\/n<\/td> Average of a data set<\/td><\/tr> Total from Mean<\/td> Sum = x\u0304 \u00d7 n<\/td> Find the total from an average<\/td><\/tr> Probability<\/td> P(A) = Favorable Outcomes \/ Total Outcomes<\/td> Probability when outcomes are equally likely<\/td><\/tr> Conditional Probability<\/td> P(A \u2223 B) = P(A \u2229 B) \/ P(B)<\/td> Probability of A given B, where P(B) > 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nKey Concepts:<\/strong><\/p>\n\n\n\n\n- Outliers:<\/strong> Can affect the mean more than the median.<\/li>\n\n\n\n
- Standard Deviation:<\/strong> Measures how spread out values are around the mean.<\/li>\n\n\n\n
- Margin of Error:<\/strong> Describes uncertainty in a sample-based estimate.<\/li>\n\n\n\n
- Correlation:<\/strong> Does not necessarily imply causation.<\/li>\n<\/ul>\n\n\n\n
SAT Math Tip:<\/strong> For conditional probability questions involving two-way tables, use the total for the given condition as the denominator.<\/p>\n\n\n\n6. Coordinate Geometry and Circle Formulas<\/h3>\n\n\n\n
These formulas help calculate distances, midpoints, and properties of circles on the coordinate plane.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th>Purpose<\/strong><\/th><\/tr><\/thead>Distance<\/td> d = \u221a[(x\u2082 \u2212 x\u2081)\u00b2 + (y\u2082 \u2212 y\u2081)\u00b2]<\/td> Distance between two points<\/td><\/tr> Midpoint<\/td> M = ((x\u2081 + x\u2082)\/2, (y\u2081 + y\u2082)\/2)<\/td> Midpoint of a segment<\/td><\/tr> Circle Equation<\/td> (x \u2212 h)\u00b2 + (y \u2212 k)\u00b2 = r\u00b2<\/td> Center (h, k), radius r<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nRemember:<\/strong> The center of a circle is (h, k), and the right side of the equation represents r\u00b2, not the radius itself.<\/p>\n\n\n\nOn the SAT, circle equations may appear in expanded form. Complete the square for both x and y to find the center and radius:<\/p>\n\n\n\n
x\u00b2 + 6x + y\u00b2 \u2212 4y = 12<\/p>\n\n\n\n
\u21d2 (x + 3)\u00b2 + (y \u2212 2)\u00b2 = 25<\/p>\n\n\n\n
The center is (\u22123, 2) and the radius is 5.<\/p>\n\n\n\n
7. Arcs, Sectors, and Scale Factors<\/h3>\n\n\n\n
Arc length, sector area, and scale factors are useful for solving geometry questions involving circles and similar figures.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th><\/tr><\/thead>Arc Length (Degrees)<\/td> s = (\u03b8\/360\u00b0) \u00d7 2\u03c0r<\/td><\/tr> Arc Length (Radians)<\/td> s = r\u03b8<\/td><\/tr> Sector Area (Degrees)<\/td> A = (\u03b8\/360\u00b0) \u00d7 \u03c0r\u00b2<\/td><\/tr> Sector Area (Radians)<\/td> A = \u00bdr\u00b2\u03b8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, \u03b8 is the central angle and r is the radius. Radian formulas require \u03b8 to be measured in radians.<\/p>\n\n\n\n
SAT Math Tip:<\/strong> When a figure’s dimensions change by a linear scale factor of k, its area changes by k\u00b2 and its volume by k\u00b3.<\/p>\n\n\n\n8. Trigonometric Ratios<\/h3>\n\n\n\n
The official SAT Reference Sheet provides special right triangle relationships, but students should also know the three basic trigonometric ratios.<\/p>\n\n\n\nRatio<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Sine<\/td> sin \u03b8 = Opposite\/Hypotenuse<\/td><\/tr> Cosine<\/td> cos \u03b8 = Adjacent\/Hypotenuse<\/td><\/tr> Tangent<\/td> tan \u03b8 = Opposite\/Adjacent<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nRemember these ratios using SOH\u2013CAH\u2013TOA<\/strong>.<\/p>\n\n\n\nFor complementary acute angles:<\/p>\n\n\n\n
sin \u03b8 = cos(90\u00b0 \u2212 \u03b8)<\/p>\n\n\n\n
If sin x\u00b0 = cos y\u00b0 and both x and y are acute angles, then x + y = 90\u00b0.<\/p>\n\n\n\n
Final Thoughts: Master SAT Math Formulas Through Practice<\/strong><\/h2>\n\n\n\nThe SAT Math Reference Sheet provides only a portion of the formulas you may need. Focus on three priorities: memorize formulas that aren’t provided, recognize when to apply them, and practice solving questions under timed conditions.<\/strong><\/p>\n\n\n\nThe built-in Desmos calculator can help you graph functions and check answers, but understanding the underlying math is just as important. For more strategies, check out our SAT Math Tips and Tricks.<\/p>\n\n\n\n
Ready to test your SAT Math skills?<\/strong><\/h2>\n\n\n\nPractice with PanoPrep’s full-length Digital SAT mock tests, review detailed answer explanations, and use performance analytics to identify areas for improvement.<\/p>\n\n\n\n
<\/figure>\n\n\n\n1. Area and Circumference Formulas<\/strong><\/h3>\n\n\n\nShape<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Area of a Circle<\/td> A = \u03c0r\u00b2<\/td><\/tr> Circumference of a Circle<\/td> C = 2\u03c0r<\/td><\/tr> Area of a Rectangle<\/td> A = lw<\/td><\/tr> Area of a Triangle<\/td> A = \u00bdbh<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, (r) is the radius, (l) is the length, (w) is the width, (b) is the base, and (h) is the height.<\/p>\n\n\n\n
2. Right Triangle Formulas<\/strong><\/h3>\n\n\n\nPythagorean Theorem<\/strong><\/p>\n\n\n\na\u00b2 + b\u00b2 = c\u00b2<\/p>\n\n\n\n
Here, (a) and (b) are the legs of a right triangle, and (c) is the hypotenuse.<\/p>\n\n\n\n
Special Right Triangles<\/strong><\/p>\n\n\n\nTriangle<\/strong><\/th>Side Ratios<\/strong><\/th>Opposite Angles<\/strong><\/th><\/tr><\/thead>30\u00b0\u201360\u00b0\u201390\u00b0<\/td> 1 : \u221a3 : 2<\/td> 30\u00b0 : 60\u00b0 : 90\u00b0<\/td><\/tr> 45\u00b0\u201345\u00b0\u201390\u00b0<\/td> 1 : 1 : \u221a2<\/td> 45\u00b0 : 45\u00b0 : 90\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nThe side ratios correspond to the opposite angles in the order shown. These relationships help you find missing side lengths without using trigonometric functions.<\/p>\n\n\n\n
3. Volume Formulas<\/strong><\/h3>\n\n\n\nSolid<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Rectangular Prism<\/td> V = lwh<\/td><\/tr> Cylinder<\/td> V = \u03c0r\u00b2h<\/td><\/tr> Sphere<\/td> V = (4\/3)\u03c0r\u00b3<\/td><\/tr> Cone<\/td> V = \u2153\u03c0r\u00b2h<\/td><\/tr> Pyramid (Rectangular Base)<\/td> V = \u2153lwh<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, (V) represents volume, (r) is the radius, (h) is the height, and (l) and (w) represent length and width. For the pyramid, (h) is the perpendicular height.<\/p>\n\n\n\n
4. Geometry Facts<\/strong><\/h3>\n\n\n\n\n- A full circle contains 360 degrees or 2\u03c0 radians.<\/li>\n\n\n\n
- The interior angles of a triangle add up to 180 degrees.<\/li>\n<\/ul>\n\n\n\n
SAT Math Tip:<\/strong> Even though these formulas are provided, knowing the most common ones by heart can save time and help you focus on more challenging questions.<\/p>\n\n\n\nThe SAT Math Reference Sheet covers essential geometry formulas, but many important formulas are not provided. Let’s look at the additional SAT Math formulas you should memorize before test day.<\/p>\n\n\n\n
What SAT Math Formulas Should You Memorize?<\/strong><\/h2>\n\n\n\nWhile the official SAT Math Reference Sheet covers basic geometry, many important formulas are not provided. Here are the essential SAT Math formulas worth memorizing, organized by topic for quick review.<\/p>\n\n\n\n
1. Linear Equations and Slope Formulas<\/strong><\/h3>\n\n\n\nLinear equations are a major part of SAT Algebra. Understanding slopes, intercepts, and different equation forms can help you solve questions efficiently.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th>Purpose<\/strong><\/th><\/tr><\/thead>Slope<\/td> m = (y\u2082 \u2212 y\u2081)\/(x\u2082 \u2212 x\u2081)<\/td> Rate of change
between two points<\/td><\/tr> Slope-Intercept Form<\/td> y = mx + b<\/td> Identify slope and
y-intercept<\/td><\/tr> Point-Slope Form<\/td> y \u2212 y\u2081 = m(x \u2212 x\u2081)<\/td> Write a line from
a point and slope<\/td><\/tr> Standard Form<\/td> Ax + By = C<\/td> Slope = \u2212A\/B, when B \u2260 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, m represents the slope and b represents the y-intercept in slope-intercept form.<\/p>\n\n\n\n
Here, (m) represents the slope and (b) represents the y-intercept in slope-intercept form.<\/p>\n\n\n\n
Remember:<\/strong><\/p>\n\n\n\n\n- Parallel lines have equal slopes when their slopes are defined.<\/li>\n\n\n\n
- Perpendicular lines have slopes whose product is (-1), when both slopes are defined.<\/li>\n\n\n\n
- In word problems, the slope represents the rate of change, while the y-intercept represents the starting value.<\/li>\n<\/ul>\n\n\n\n
Systems of Linear Equations<\/strong><\/p>\n\n\n\nFor two linear equations, compare their coefficients to determine the number of solutions.<\/p>\n\n\n\nCondition<\/strong><\/th>Number of Solutions<\/strong><\/th><\/tr><\/thead>Coefficients of x and y are not proportional<\/td> Exactly one<\/td><\/tr> Variable coefficients are proportional, but constants are not in the same proportion<\/td> No solution<\/td><\/tr> All corresponding coefficients and constants are proportional<\/td> Infinitely many<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nSAT Math Tip:<\/strong> When a system contains an unknown constant such as k, check whether the equations represent intersecting, parallel, or identical lines before solving.<\/p>\n\n\n\n2. Quadratic Formulas<\/strong><\/h3>\n\n\n\nQuadratic formulas help solve nonlinear equations and identify roots, vertices, and maximum or minimum values.<\/p>\n\n\n\n
Quadratic Formula<\/strong><\/p>\n\n\n\nFor ax\u00b2 + bx + c = 0, where a \u2260 0:<\/p>\n\n\n\n
x = (\u2212b \u00b1 \u221a(b\u00b2 \u2212 4ac))\/(2a)<\/p>\n\n\n\n
Discriminant<\/strong><\/p>\n\n\n\nD = b\u00b2 \u2212 4ac<\/p>\n\n\n\nDiscriminant<\/strong><\/th>Number of Real Solutions<\/strong><\/th><\/tr><\/thead>D > 0<\/td> Two distinct real solutions<\/td><\/tr> D = 0<\/td> Exactly one real solution<\/td><\/tr> D < 0<\/td> No real solutions<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nThree Forms of a Quadratic Function<\/strong><\/p>\n\n\n\nForm<\/strong><\/th>Equation<\/strong><\/th>What It Reveals<\/strong><\/th><\/tr><\/thead>Standard Form<\/td> y = ax\u00b2 + bx + c<\/td> Y-intercept<\/td><\/tr> Vertex Form<\/td> y = a(x \u2212 h)\u00b2 + k<\/td> Vertex (h, k)<\/td><\/tr> Factored Form<\/td> y = a(x \u2212 r\u2081)(x \u2212 r\u2082)<\/td> X-intercepts r\u2081, r\u2082,
when real<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nVertex Formula<\/strong><\/p>\n\n\n\nx = \u2212b\/(2a)<\/p>\n\n\n\n
This gives the x-coordinate of the vertex. If a > 0, the parabola opens upward and has a minimum; if a < 0, it opens downward and has a maximum.<\/p>\n\n\n\n
3. Exponent Rules<\/strong><\/h3>\n\n\n\nExponent rules are useful for simplifying expressions, solving equations, and recognizing equivalent mathematical forms.<\/p>\n\n\n\nRule<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Product Rule<\/td> a\u1d50 \u00b7 a\u207f = a\u1d50\u207a\u207f<\/td><\/tr> Quotient Rule<\/td> a\u1d50\/a\u207f = a\u1d50\u207b\u207f<\/td><\/tr> Power Rule<\/td> (a\u1d50)\u207f = a\u1d50\u207f<\/td><\/tr> Zero Exponent<\/td> a\u2070 = 1<\/td><\/tr> Negative Exponent<\/td> a\u207b\u207f = 1\/a\u207f<\/td><\/tr> Fractional Exponent<\/td> a\u1d50\u2044\u207f = \u207f\u221a(a\u1d50)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nThese rules apply wherever the expressions are defined. In particular, expressions involving division by a require a \u2260 0.<\/p>\n\n\n\n
4. Percentages and Exponential Models<\/strong><\/h3>\n\n\n\nPercentage formulas are essential for SAT Problem-Solving and Data Analysis, while exponential models describe growth and decay over time.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th><\/tr><\/thead>Percentage Change<\/td> (New \u2212 Original)\/Original \u00d7 100%<\/td><\/tr> Value After a p% Increase<\/td> x(1 + p\/100)<\/td><\/tr> Value After a p% Decrease<\/td> x(1 \u2212 p\/100)<\/td><\/tr> Exponential Growth<\/td> y = a(1 + r)\u1d57<\/td><\/tr> Exponential Decay<\/td> y = a(1 \u2212 r)\u1d57<\/td><\/tr> Growth Every k Time Units<\/td> y = a(1 + r)\u1d57\u2044\u1d4f<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, a is the initial amount, r is the positive rate of change expressed as a decimal, and t represents time. In the last formula, r is the growth rate per k time units.<\/p>\n\n\n\n
\n- SAT Math Tip:<\/strong> Use multipliers for percentage changes. A 15% increase means multiplying by 1.15, while a 20% decrease means multiplying by 0.80. For successive changes, multiply the factors rather than adding the percentages.<\/li>\n<\/ul>\n\n\n\n
5. Statistics and Probability Formulas<\/h3>\n\n\n\n
Statistics and probability questions focus on interpreting data, calculating averages, and understanding the likelihood of events.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th>Purpose<\/strong><\/th><\/tr><\/thead>Mean<\/td> x\u0304 = \u03a3x\u1d62\/n<\/td> Average of a data set<\/td><\/tr> Total from Mean<\/td> Sum = x\u0304 \u00d7 n<\/td> Find the total from an average<\/td><\/tr> Probability<\/td> P(A) = Favorable Outcomes \/ Total Outcomes<\/td> Probability when outcomes are equally likely<\/td><\/tr> Conditional Probability<\/td> P(A \u2223 B) = P(A \u2229 B) \/ P(B)<\/td> Probability of A given B, where P(B) > 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nKey Concepts:<\/strong><\/p>\n\n\n\n\n- Outliers:<\/strong> Can affect the mean more than the median.<\/li>\n\n\n\n
- Standard Deviation:<\/strong> Measures how spread out values are around the mean.<\/li>\n\n\n\n
- Margin of Error:<\/strong> Describes uncertainty in a sample-based estimate.<\/li>\n\n\n\n
- Correlation:<\/strong> Does not necessarily imply causation.<\/li>\n<\/ul>\n\n\n\n
SAT Math Tip:<\/strong> For conditional probability questions involving two-way tables, use the total for the given condition as the denominator.<\/p>\n\n\n\n6. Coordinate Geometry and Circle Formulas<\/h3>\n\n\n\n
These formulas help calculate distances, midpoints, and properties of circles on the coordinate plane.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th>Purpose<\/strong><\/th><\/tr><\/thead>Distance<\/td> d = \u221a[(x\u2082 \u2212 x\u2081)\u00b2 + (y\u2082 \u2212 y\u2081)\u00b2]<\/td> Distance between two points<\/td><\/tr> Midpoint<\/td> M = ((x\u2081 + x\u2082)\/2, (y\u2081 + y\u2082)\/2)<\/td> Midpoint of a segment<\/td><\/tr> Circle Equation<\/td> (x \u2212 h)\u00b2 + (y \u2212 k)\u00b2 = r\u00b2<\/td> Center (h, k), radius r<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nRemember:<\/strong> The center of a circle is (h, k), and the right side of the equation represents r\u00b2, not the radius itself.<\/p>\n\n\n\nOn the SAT, circle equations may appear in expanded form. Complete the square for both x and y to find the center and radius:<\/p>\n\n\n\n
x\u00b2 + 6x + y\u00b2 \u2212 4y = 12<\/p>\n\n\n\n
\u21d2 (x + 3)\u00b2 + (y \u2212 2)\u00b2 = 25<\/p>\n\n\n\n
The center is (\u22123, 2) and the radius is 5.<\/p>\n\n\n\n
7. Arcs, Sectors, and Scale Factors<\/h3>\n\n\n\n
Arc length, sector area, and scale factors are useful for solving geometry questions involving circles and similar figures.<\/p>\n\n\n\nFormula<\/strong><\/th>Equation<\/strong><\/th><\/tr><\/thead>Arc Length (Degrees)<\/td> s = (\u03b8\/360\u00b0) \u00d7 2\u03c0r<\/td><\/tr> Arc Length (Radians)<\/td> s = r\u03b8<\/td><\/tr> Sector Area (Degrees)<\/td> A = (\u03b8\/360\u00b0) \u00d7 \u03c0r\u00b2<\/td><\/tr> Sector Area (Radians)<\/td> A = \u00bdr\u00b2\u03b8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nHere, \u03b8 is the central angle and r is the radius. Radian formulas require \u03b8 to be measured in radians.<\/p>\n\n\n\n
SAT Math Tip:<\/strong> When a figure’s dimensions change by a linear scale factor of k, its area changes by k\u00b2 and its volume by k\u00b3.<\/p>\n\n\n\n8. Trigonometric Ratios<\/h3>\n\n\n\n
The official SAT Reference Sheet provides special right triangle relationships, but students should also know the three basic trigonometric ratios.<\/p>\n\n\n\nRatio<\/strong><\/th>Formula<\/strong><\/th><\/tr><\/thead>Sine<\/td> sin \u03b8 = Opposite\/Hypotenuse<\/td><\/tr> Cosine<\/td> cos \u03b8 = Adjacent\/Hypotenuse<\/td><\/tr> Tangent<\/td> tan \u03b8 = Opposite\/Adjacent<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nRemember these ratios using SOH\u2013CAH\u2013TOA<\/strong>.<\/p>\n\n\n\nFor complementary acute angles:<\/p>\n\n\n\n
sin \u03b8 = cos(90\u00b0 \u2212 \u03b8)<\/p>\n\n\n\n
If sin x\u00b0 = cos y\u00b0 and both x and y are acute angles, then x + y = 90\u00b0.<\/p>\n\n\n\n
Final Thoughts: Master SAT Math Formulas Through Practice<\/strong><\/h2>\n\n\n\nThe SAT Math Reference Sheet provides only a portion of the formulas you may need. Focus on three priorities: memorize formulas that aren’t provided, recognize when to apply them, and practice solving questions under timed conditions.<\/strong><\/p>\n\n\n\nThe built-in Desmos calculator can help you graph functions and check answers, but understanding the underlying math is just as important. For more strategies, check out our SAT Math Tips and Tricks.<\/p>\n\n\n\n
Ready to test your SAT Math skills?<\/strong><\/h2>\n\n\n\nPractice with PanoPrep’s full-length Digital SAT mock tests, review detailed answer explanations, and use performance analytics to identify areas for improvement.<\/p>\n\n\n\n
Shape<\/strong><\/th>| Formula<\/strong><\/th><\/tr><\/thead> | Area of a Circle<\/td> | A = \u03c0r\u00b2<\/td><\/tr> | Circumference of a Circle<\/td> | C = 2\u03c0r<\/td><\/tr> | Area of a Rectangle<\/td> | A = lw<\/td><\/tr> | Area of a Triangle<\/td> | A = \u00bdbh<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n | Here, (r) is the radius, (l) is the length, (w) is the width, (b) is the base, and (h) is the height.<\/p>\n\n\n\n 2. Right Triangle Formulas<\/strong><\/h3>\n\n\n\na\u00b2 + b\u00b2 = c\u00b2<\/p>\n\n\n\n Here, (a) and (b) are the legs of a right triangle, and (c) is the hypotenuse.<\/p>\n\n\n\n Special Right Triangles<\/strong><\/p>\n\n\n\n The side ratios correspond to the opposite angles in the order shown. These relationships help you find missing side lengths without using trigonometric functions.<\/p>\n\n\n\n Here, (V) represents volume, (r) is the radius, (h) is the height, and (l) and (w) represent length and width. For the pyramid, (h) is the perpendicular height.<\/p>\n\n\n\n SAT Math Tip:<\/strong> Even though these formulas are provided, knowing the most common ones by heart can save time and help you focus on more challenging questions.<\/p>\n\n\n\n The SAT Math Reference Sheet covers essential geometry formulas, but many important formulas are not provided. Let’s look at the additional SAT Math formulas you should memorize before test day.<\/p>\n\n\n\n While the official SAT Math Reference Sheet covers basic geometry, many important formulas are not provided. Here are the essential SAT Math formulas worth memorizing, organized by topic for quick review.<\/p>\n\n\n\n Linear equations are a major part of SAT Algebra. Understanding slopes, intercepts, and different equation forms can help you solve questions efficiently.<\/p>\n\n\n\n Here, m represents the slope and b represents the y-intercept in slope-intercept form.<\/p>\n\n\n\n Here, (m) represents the slope and (b) represents the y-intercept in slope-intercept form.<\/p>\n\n\n\n Remember:<\/strong><\/p>\n\n\n\n Systems of Linear Equations<\/strong><\/p>\n\n\n\n For two linear equations, compare their coefficients to determine the number of solutions.<\/p>\n\n\n\n SAT Math Tip:<\/strong> When a system contains an unknown constant such as k, check whether the equations represent intersecting, parallel, or identical lines before solving.<\/p>\n\n\n\n Quadratic formulas help solve nonlinear equations and identify roots, vertices, and maximum or minimum values.<\/p>\n\n\n\n Quadratic Formula<\/strong><\/p>\n\n\n\n For ax\u00b2 + bx + c = 0, where a \u2260 0:<\/p>\n\n\n\n x = (\u2212b \u00b1 \u221a(b\u00b2 \u2212 4ac))\/(2a)<\/p>\n\n\n\n Discriminant<\/strong><\/p>\n\n\n\n D = b\u00b2 \u2212 4ac<\/p>\n\n\n\n Three Forms of a Quadratic Function<\/strong><\/p>\n\n\n\n Vertex Formula<\/strong><\/p>\n\n\n\n x = \u2212b\/(2a)<\/p>\n\n\n\n This gives the x-coordinate of the vertex. If a > 0, the parabola opens upward and has a minimum; if a < 0, it opens downward and has a maximum.<\/p>\n\n\n\n Exponent rules are useful for simplifying expressions, solving equations, and recognizing equivalent mathematical forms.<\/p>\n\n\n\n These rules apply wherever the expressions are defined. In particular, expressions involving division by a require a \u2260 0.<\/p>\n\n\n\n Percentage formulas are essential for SAT Problem-Solving and Data Analysis, while exponential models describe growth and decay over time.<\/p>\n\n\n\n Here, a is the initial amount, r is the positive rate of change expressed as a decimal, and t represents time. In the last formula, r is the growth rate per k time units.<\/p>\n\n\n\n Statistics and probability questions focus on interpreting data, calculating averages, and understanding the likelihood of events.<\/p>\n\n\n\n Key Concepts:<\/strong><\/p>\n\n\n\n SAT Math Tip:<\/strong> For conditional probability questions involving two-way tables, use the total for the given condition as the denominator.<\/p>\n\n\n\n These formulas help calculate distances, midpoints, and properties of circles on the coordinate plane.<\/p>\n\n\n\n Remember:<\/strong> The center of a circle is (h, k), and the right side of the equation represents r\u00b2, not the radius itself.<\/p>\n\n\n\n On the SAT, circle equations may appear in expanded form. Complete the square for both x and y to find the center and radius:<\/p>\n\n\n\n x\u00b2 + 6x + y\u00b2 \u2212 4y = 12<\/p>\n\n\n\n \u21d2 (x + 3)\u00b2 + (y \u2212 2)\u00b2 = 25<\/p>\n\n\n\n The center is (\u22123, 2) and the radius is 5.<\/p>\n\n\n\n Arc length, sector area, and scale factors are useful for solving geometry questions involving circles and similar figures.<\/p>\n\n\n\n Here, \u03b8 is the central angle and r is the radius. Radian formulas require \u03b8 to be measured in radians.<\/p>\n\n\n\n SAT Math Tip:<\/strong> When a figure’s dimensions change by a linear scale factor of k, its area changes by k\u00b2 and its volume by k\u00b3.<\/p>\n\n\n\n The official SAT Reference Sheet provides special right triangle relationships, but students should also know the three basic trigonometric ratios.<\/p>\n\n\n\n Remember these ratios using SOH\u2013CAH\u2013TOA<\/strong>.<\/p>\n\n\n\n For complementary acute angles:<\/p>\n\n\n\n sin \u03b8 = cos(90\u00b0 \u2212 \u03b8)<\/p>\n\n\n\n If sin x\u00b0 = cos y\u00b0 and both x and y are acute angles, then x + y = 90\u00b0.<\/p>\n\n\n\n The SAT Math Reference Sheet provides only a portion of the formulas you may need. Focus on three priorities: memorize formulas that aren’t provided, recognize when to apply them, and practice solving questions under timed conditions.<\/strong><\/p>\n\n\n\n The built-in Desmos calculator can help you graph functions and check answers, but understanding the underlying math is just as important. For more strategies, check out our SAT Math Tips and Tricks.<\/p>\n\n\n\n Practice with PanoPrep’s full-length Digital SAT mock tests, review detailed answer explanations, and use performance analytics to identify areas for improvement.<\/p>\n\n\n\n |
|---|