Quick Answer
SAT formula rearrangement practice problems assess students’ ability to work with formulas from algebra, geometry, rates, percentages, and science, as well as to isolate a required variable, substitute known values, clarify fractions, and reverse operations. Seventy SAT-style questions are included in this tutorial, ranging from simple one-step rearrangement to more complex formulae including powers, roots, fractions, and multiple variables.
What Should You Know Before Practicing Formula Rearrangement?
- Identify the variable the question asks you to isolate.
- Use inverse operations in the reverse order of the original formula.
- Clear fractions by multiplying both sides by the complete denominator.
- Keep grouped expressions together when cross-multiplying.
- For squared or cubed variables, use the correct root after isolating the power.
- Keep negative integers in parenthesis and carefully substitute known values.
In This Guide – 70 SAT Formula Rearrangement Practice Questions
- What does the SAT test in formula rearrangement?
- How do basic formula rearrangement questions work?
- How are linear and coordinate formulas rearranged?
- How do geometry and measurement formulas appear?
- How are rates, percentages, and science formulas tested?
- What do hard mixed formula questions look like?
- What do student-produced response questions look like?
- What mistakes cost students points?
- How should students study this topic in 2 weeks?
- Frequently asked questions
Start With SAT Math Topic-Wise Practice
Along with equations, functions, geometry, rates, and advanced algebra, practice rearranging formulas.
Download the SAT Prep Guide E-Book
Organize formula practice, go over high-frequency SAT math concepts, and link each practice set to a specific score-improvement strategy by using the SAT Prep Guide E-Book.
Download SAT Prep Guide E-BookWhat Does the SAT Test in Formula Rearrangement Questions?
Formula rearrangement arises across SAT Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. The SAT may present a familiar formula and ask for a different variable, supply numerical values and ask for the missing quantity, or position the formula inside a short real-world context.
The most reliable way is to keep the required variable visible, undo operations one at a time, and defer decimal computation until the formula has been rearranged.
| Skill Area | What It Tests | Common SAT Trap | Practice Set |
|---|---|---|---|
| Basic rearrangement | Inverse operations and substitution | Using operations in the wrong order | Q1-Q15 |
| Linear and coordinate formulas | Slope, intercept, midpoint, and motion formulas | Substituting into the wrong variable | Q16-Q30 |
| Geometry and measurement | Area, volume, perimeter, and distance formulas | Forgetting powers or roots | Q31-Q45 |
| Rates and science formulas | Percent, density, energy, work, and unit rates | Using a percent instead of its decimal form | Q46-Q55 |
| Hard mixed formulas | Fractions, powers, roots, and grouped variables | Cross-multiplying incompletely | Q56-Q70 |
SAT strategy: Rearrange symbolically when possible, then substitute numbers. This reduces calculator errors and makes the relationship between variables easier to see.
Download Free SAT Study Resources For U.S. Students
To begin your preparation with organized practice, download our free SAT Prep E-Book, SAT Math Question Bank, and SAT English Question Bank. These tools are intended to assist students in comprehending the style of the Digital SAT, increasing their accuracy, and boosting their self-assurance prior to test day.
How Do Basic Formula Rearrangement Questions Work?
Inverse operations, substitution, and one-variable isolation are tested in these problems. Maintain equilibrium on both sides while working in reverse order.
Formula Rearrangement Basics
EASY
Question 1
Solve 3x + 7 = 25 for x.
Which choice is correct?
A) 4
B) 6
C) 8
D) 10
Show full solution
Correct answer: B) 6
Subtract 7 from both sides to get 3x = 18. Divide by 3, so x = 6.
SAT trap: Undo addition before undoing multiplication.
Formula Rearrangement Basics
EASY
Question 2
Solve 5y – 8 = 17 for y.
Which choice is correct?
A) 3
B) 4
C) 5
D) 6
Show full solution
Correct answer: C) 5
Add 8 to both sides: 5y = 25. Divide by 5, so y = 5.
SAT trap: The -8 moves by using the opposite operation, which is +8.
Formula Rearrangement Basics
EASY
Question 3
Solve p/4 + 6 = 11 for p.
Which choice is correct?
A) 5
B) 16
C) 20
D) 44
Show full solution
Correct answer: C) 20
Subtract 6 to get p/4 = 5. Multiply both sides by 4, so p = 20.
SAT trap: Dividing by 4 is undone by multiplying by 4.
Formula Rearrangement Basics
MEDIUM
Question 4
Solve 7 – 2m = 19 for m.
Which choice is correct?
A) -6
B) -3
C) 3
D) 6
Show full solution
Correct answer: A) -6
Subtract 7 from both sides: -2m = 12. Divide by -2, so m = -6.
SAT trap: Dividing by a negative changes the sign of the result.
Formula Rearrangement Basics
EASY
Question 5
Solve 4(a – 3) = 20 for a.
Which choice is correct?
A) 2
B) 5
C) 8
D) 12
Show full solution
Correct answer: C) 8
Divide both sides by 4 to get a – 3 = 5. Add 3, so a = 8.
SAT trap: You can divide first instead of distributing.
Formula Rearrangement Basics
EASY
Question 6
Solve (n + 5)/3 = 7 for n.
Which choice is correct?
A) 2
B) 16
C) 21
D) 26
Show full solution
Correct answer: B) 16
Multiply both sides by 3: n + 5 = 21. Subtract 5, so n = 16.
SAT trap: Clear the denominator before isolating n.
Formula Rearrangement Basics
MEDIUM
Question 7
Solve 6t + 4 = 2t + 24 for t.
Which choice is correct?
A) 4
B) 5
C) 6
D) 7
Show full solution
Correct answer: B) 5
Subtract 2t from both sides and subtract 4 from both sides: 4t = 20. Therefore t = 5.
SAT trap: Collect variable terms on one side and constants on the other.
Formula Rearrangement Basics
MEDIUM
Question 8
Solve 9k – 5 = 4k + 20 for k.
Which choice is correct?
A) 3
B) 4
C) 5
D) 6
Show full solution
Correct answer: C) 5
Subtract 4k from both sides and add 5: 5k = 25. Therefore k = 5.
SAT trap: Keep the sign attached to each term while moving terms.
Formula Rearrangement Basics
MEDIUM
Question 9
Solve 2(3x – 1) = 4x + 10 for x.
Which choice is correct?
A) 4
B) 5
C) 6
D) 8
Show full solution
Correct answer: C) 6
Distribute: 6x – 2 = 4x + 10. Subtract 4x and add 2 to get 2x = 12, so x = 6.
SAT trap: Distribute the 2 to both terms inside the parentheses.
Formula Rearrangement Basics
MEDIUM
Question 10
Solve (2y – 3)/5 = 3 for y.
Which choice is correct?
A) 6
B) 8
C) 9
D) 12
Show full solution
Correct answer: C) 9
Multiply by 5: 2y – 3 = 15. Add 3 to get 2y = 18. Divide by 2, so y = 9.
SAT trap: Clear the denominator before working with the numerator.
Formula Rearrangement Basics
EASY
Question 11
The formula A = bh gives the area A of a rectangle. If A = 56 and b = 8, what is h?
Which choice is correct?
A) 6
B) 7
C) 8
D) 9
Show full solution
Correct answer: B) 7
Substitute the known values: 56 = 8h. Divide by 8, so h = 7.
SAT trap: When solving A = bh for h, divide A by b.
Formula Rearrangement Basics
MEDIUM
Question 12
The formula P = 2l + 2w gives the perimeter of a rectangle. If P = 30 and l = 9, what is w?
Which choice is correct?
A) 3
B) 6
C) 9
D) 12
Show full solution
Correct answer: B) 6
Substitute: 30 = 18 + 2w. Subtract 18 to get 12 = 2w, so w = 6.
SAT trap: Do not divide the entire perimeter by 2 and stop before subtracting l.
Formula Rearrangement Basics
EASY
Question 13
Using d = rt, what is t when d = 180 and r = 60?
Which choice is correct?
A) 2
B) 3
C) 4
D) 120
Show full solution
Correct answer: B) 3
Rearrange d = rt to t = d/r. Then t = 180/60 = 3.
SAT trap: Time equals distance divided by rate.
Formula Rearrangement Basics
MEDIUM
Question 14
The simple interest formula is I = Prt. What is r when I = 240, P = 2,000, and t = 2?
Which choice is correct?
A) 0.03
B) 0.06
C) 0.12
D) 6
Show full solution
Correct answer: B) 0.06
Rearrange to r = I/(Pt). Then r = 240/(2000 x 2) = 0.06.
SAT trap: A rate of 6% is written as 0.06 in the formula.
Formula Rearrangement Basics
MEDIUM
Question 15
The temperature formula is C = (5/9)(F – 32). What is F when C = 20?
Which choice is correct?
A) 52
B) 68
C) 72
D) 84
Show full solution
Correct answer: B) 68
Multiply by 9/5: 36 = F – 32. Add 32, so F = 68.
SAT trap: Undo the factor 5/9 before adding 32.
Build Stronger SAT Algebra Skills
Use topic-wise practice to connect formula rearrangement with equations, functions, and real SAT Math timing.
How Are Linear and Coordinate Formulas Rearranged?
Slope, intercept, midpoint, motion, and other formulas with several known variables are used in these problems.
Linear and Coordinate Formulas
EASY
Question 16
In y = mx + b, what is b when y = 17, m = 3, and x = 4?
Which choice is correct?
A) 3
B) 5
C) 7
D) 29
Show full solution
Correct answer: B) 5
Substitute: 17 = 3(4) + b = 12 + b. Therefore b = 5.
SAT trap: The y-intercept is what remains after subtracting mx from y.
Linear and Coordinate Formulas
EASY
Question 17
In y = mx + b, what is m when y = 22, b = 4, and x = 6?
Which choice is correct?
A) 2
B) 3
C) 4
D) 18
Show full solution
Correct answer: B) 3
Substitute: 22 = 6m + 4. Subtract 4 to get 18 = 6m, so m = 3.
SAT trap: Subtract the intercept before dividing by x.
Linear and Coordinate Formulas
EASY
Question 18
If 3x + 2y = 18 and x = 4, what is y?
Which choice is correct?
A) 2
B) 3
C) 5
D) 6
Show full solution
Correct answer: B) 3
Substitute x = 4: 12 + 2y = 18. Then 2y = 6, so y = 3.
SAT trap: Substitute the known variable before rearranging.
Linear and Coordinate Formulas
MEDIUM
Question 19
If 5x – 4y = 28 and y = 3, what is x?
Which choice is correct?
A) 6
B) 8
C) 10
D) 16
Show full solution
Correct answer: B) 8
Substitute y = 3: 5x – 12 = 28. Add 12 to get 5x = 40, so x = 8.
SAT trap: The term -4y becomes -12, not +12.
Linear and Coordinate Formulas
MEDIUM
Question 20
The point-slope formula is y – y1 = m(x – x1). What is m when y = 11, y1 = 5, x = 4, and x1 = 1?
Which choice is correct?
A) 1
B) 2
C) 3
D) 6
Show full solution
Correct answer: B) 2
Substitute: 11 – 5 = m(4 – 1). Thus 6 = 3m, so m = 2.
SAT trap: Evaluate both differences before dividing.
Linear and Coordinate Formulas
MEDIUM
Question 21
Using m = (y2 – y1)/(x2 – x1), find y2 when m = 3, y1 = 4, x1 = 2, and x2 = 6.
Which choice is correct?
A) 12
B) 16
C) 18
D) 22
Show full solution
Correct answer: B) 16
Substitute: 3 = (y2 – 4)/4. Multiply by 4 to get 12 = y2 – 4, so y2 = 16.
SAT trap: The slope multiplies the change in x, not the final x-coordinate.
Linear and Coordinate Formulas
EASY
Question 22
The x-coordinate of a midpoint is M = (x1 + x2)/2. If M = 7 and x1 = 3, what is x2?
Which choice is correct?
A) 4
B) 10
C) 11
D) 17
Show full solution
Correct answer: C) 11
Substitute: 7 = (3 + x2)/2. Multiply by 2: 14 = 3 + x2. Therefore x2 = 11.
SAT trap: Multiply the midpoint by 2 before subtracting the known endpoint.
Linear and Coordinate Formulas
EASY
Question 23
The average of x and y is A = (x + y)/2. If A = 12 and x = 9, what is y?
Which choice is correct?
A) 3
B) 12
C) 15
D) 24
Show full solution
Correct answer: C) 15
Substitute: 12 = (9 + y)/2. Multiply by 2 to get 24 = 9 + y, so y = 15.
SAT trap: An average must be multiplied by the number of values.
Linear and Coordinate Formulas
MEDIUM
Question 24
Using m = (y2 – y1)/(x2 – x1), find y2 when m = -2, y1 = 7, x1 = 1, and x2 = 5.
Which choice is correct?
A) -8
B) -1
C) 1
D) 15
Show full solution
Correct answer: B) -1
Substitute: -2 = (y2 – 7)/4. Multiply by 4: -8 = y2 – 7. Add 7, so y2 = -1.
SAT trap: A negative slope makes the y-value decrease as x increases.
Linear and Coordinate Formulas
EASY
Question 25
The circumference formula is C = 2πr. What is r when C = 18π?
Which choice is correct?
A) 4.5
B) 9
C) 18
D) 36
Show full solution
Correct answer: B) 9
Divide both sides by 2π: r = 18π/(2π) = 9.
SAT trap: Cancel π only after dividing both sides by the full factor 2π.
Linear and Coordinate Formulas
EASY
Question 26
Using F = ma, what is a when F = 84 and m = 12?
Which choice is correct?
A) 6
B) 7
C) 8
D) 72
Show full solution
Correct answer: B) 7
Rearrange to a = F/m. Then a = 84/12 = 7.
SAT trap: Acceleration is force divided by mass.
Linear and Coordinate Formulas
MEDIUM
Question 27
Using v = u + at, what is a when v = 26, u = 8, and t = 6?
Which choice is correct?
A) 2
B) 3
C) 4
D) 18
Show full solution
Correct answer: B) 3
Subtract u: 18 = 6a. Divide by 6, so a = 3.
SAT trap: First isolate at by subtracting the initial velocity.
Linear and Coordinate Formulas
MEDIUM
Question 28
The arithmetic series formula is S = n(a + l)/2. What is l when S = 75, n = 5, and a = 10?
Which choice is correct?
A) 15
B) 20
C) 25
D) 30
Show full solution
Correct answer: B) 20
Substitute: 75 = 5(10 + l)/2. Multiply by 2 and divide by 5: 30 = 10 + l. Therefore l = 20.
SAT trap: Undo the division by 2 before isolating the final term.
Linear and Coordinate Formulas
EASY
Question 29
In q = mx + b, what is x when q = 31, m = 4, and b = 7?
Which choice is correct?
A) 4
B) 6
C) 7
D) 9.5
Show full solution
Correct answer: B) 6
Substitute: 31 = 4x + 7. Subtract 7 to get 24 = 4x, so x = 6.
SAT trap: Subtract the fixed value b before dividing by m.
Linear and Coordinate Formulas
HARD
Question 30
In y = a(x – h) + k, what is h when y = 17, a = 3, x = 8, and k = 2?
Which choice is correct?
A) 2
B) 3
C) 5
D) 7
Show full solution
Correct answer: B) 3
Substitute: 17 = 3(8 – h) + 2. Subtract 2 and divide by 3: 5 = 8 – h. Therefore h = 3.
SAT trap: After dividing, solve 8 – h = 5 carefully; h is positive 3.
How Do Geometry and Measurement Formulas Appear on the SAT?
Geometry formulas often require isolating a length, radius, height, or base area. Watch for squares, cubes, and positive roots.
Geometry and Measurement Formulas
EASY
Question 31
The area of a triangle is A = bh/2. What is b when A = 54 and h = 9?
Which choice is correct?
A) 6
B) 9
C) 12
D) 18
Show full solution
Correct answer: C) 12
Substitute: 54 = 9b/2. Multiply by 2 and divide by 9: b = 12.
SAT trap: Double the area before dividing by the height.
Geometry and Measurement Formulas
EASY
Question 32
The area of a circle is A = πr². What is r when A = 81π?
Which choice is correct?
A) 4.5
B) 9
C) 18
D) 81
Show full solution
Correct answer: B) 9
Divide by π: r² = 81. Since radius is positive, r = 9.
SAT trap: Take the positive square root for a geometric length.
Geometry and Measurement Formulas
EASY
Question 33
The volume of a rectangular prism is V = lwh. What is h when V = 360, l = 10, and w = 6?
Which choice is correct?
A) 4
B) 6
C) 8
D) 60
Show full solution
Correct answer: B) 6
Rearrange to h = V/(lw). Then h = 360/(10 x 6) = 6.
SAT trap: Divide by the product of length and width.
Geometry and Measurement Formulas
MEDIUM
Question 34
The volume of a cone is V = πr²h/3. What is h when V = 48π and r = 4?
Which choice is correct?
A) 3
B) 6
C) 9
D) 12
Show full solution
Correct answer: C) 9
Substitute: 48π = 16πh/3. Multiply by 3 and divide by 16π: h = 9.
SAT trap: The factor 1/3 must be undone by multiplying by 3.
Geometry and Measurement Formulas
MEDIUM
Question 35
The surface area of a rectangular prism is S = 2lw + 2lh + 2wh. What is h when S = 148, l = 5, and w = 4?
Which choice is correct?
A) 4
B) 5
C) 6
D) 8
Show full solution
Correct answer: C) 6
Substitute: 148 = 40 + 10h + 8h. Then 108 = 18h, so h = 6.
SAT trap: Combine both h-terms before dividing.
Geometry and Measurement Formulas
EASY
Question 36
The perimeter of a rectangle is P = 2l + 2w. What is l when P = 50 and w = 9?
Which choice is correct?
A) 8
B) 16
C) 25
D) 32
Show full solution
Correct answer: B) 16
Substitute: 50 = 2l + 18. Then 32 = 2l, so l = 16.
SAT trap: Subtract 2w before dividing by 2.
Geometry and Measurement Formulas
MEDIUM
Question 37
The area of a trapezoid is A = (a + b)h/2. What is b when A = 84, a = 8, and h = 7?
Which choice is correct?
A) 8
B) 12
C) 16
D) 24
Show full solution
Correct answer: C) 16
Substitute: 84 = 7(8 + b)/2. Multiply by 2 and divide by 7: 24 = 8 + b. Therefore b = 16.
SAT trap: The two bases are added before multiplying by height.
Geometry and Measurement Formulas
HARD
Question 38
The distance formula is d = √((x2 – x1)² + (y2 – y1)²). If d = 13, x2 – x1 = 5, and y2 > y1, what is y2 – y1?
Which choice is correct?
A) 8
B) 10
C) 12
D) 18
Show full solution
Correct answer: C) 12
Square both sides: 169 = 25 + (y2 – y1)². Thus the squared vertical change is 144, so y2 – y1 = 12.
SAT trap: Use the positive square root because y2 is greater than y1.
Geometry and Measurement Formulas
EASY
Question 39
In the Pythagorean formula c² = a² + b², what is b when c = 17 and a = 8?
Which choice is correct?
A) 9
B) 15
C) 17
D) 25
Show full solution
Correct answer: B) 15
Substitute: 289 = 64 + b². Then b² = 225, so b = 15.
SAT trap: A side length is positive, so use the positive square root.
Geometry and Measurement Formulas
HARD
Question 40
The area of an annulus is A = π(R² – r²). What is r when A = 36π and R = 10?
Which choice is correct?
A) 6
B) 8
C) 9
D) 64
Show full solution
Correct answer: B) 8
Divide by π: 36 = 100 – r². Then r² = 64, so r = 8.
SAT trap: After isolating r², take the positive square root.
Geometry and Measurement Formulas
MEDIUM
Question 41
The volume of a cylinder is V = πr²h. What is r when V = 200π and h = 8?
Which choice is correct?
A) 4
B) 5
C) 8
D) 25
Show full solution
Correct answer: B) 5
Divide by 8π: r² = 25. Therefore r = 5.
SAT trap: Do not stop at r² = 25; take the square root.
Geometry and Measurement Formulas
EASY
Question 42
The arc-length formula in radians is s = rθ. What is θ when s = 15 and r = 6?
Which choice is correct?
A) 2
B) 2.5
C) 6
D) 90
Show full solution
Correct answer: B) 2.5
Rearrange to θ = s/r. Then θ = 15/6 = 2.5 radians.
SAT trap: The angle is found by dividing arc length by radius.
Geometry and Measurement Formulas
HARD
Question 43
The surface area of a cylinder is S = 2πr² + 2πrh. What is h when S = 70π and r = 5?
Which choice is correct?
A) 2
B) 4
C) 7
D) 10
Show full solution
Correct answer: A) 2
Substitute: 70π = 50π + 10πh. Subtract 50π and divide by 10π, so h = 2.
SAT trap: The two circular bases contribute 2πr² before the height term.
Geometry and Measurement Formulas
MEDIUM
Question 44
The volume of a sphere is V = 4πr³/3. What is r when V = 36π?
Which choice is correct?
A) 3
B) 6
C) 9
D) 27
Show full solution
Correct answer: A) 3
Multiply by 3 and divide by 4π: r³ = 27. Therefore r = 3.
SAT trap: Use a cube root, not a square root.
Geometry and Measurement Formulas
EASY
Question 45
Density is ρ = m/V. What is V when m = 540 and ρ = 2.7?
Which choice is correct?
A) 20
B) 200
C) 540
D) 1,458
Show full solution
Correct answer: B) 200
Rearrange to V = m/ρ. Then V = 540/2.7 = 200.
SAT trap: Volume equals mass divided by density.
Need a Faster SAT Math Score Plan?
Combine practice questions with live instruction, mock-test review, and a weekly correction plan.
How Are Rates, Percentages, and Science Formulas Tested?
These questions connect algebra to rates, percentages, density, energy, work, and unit relationships.
Rates, Percentages, and Science Formulas
EASY
Question 46
Using I = Prt, what is t when I = 450, P = 3,000, and r = 0.05?
Which choice is correct?
A) 2
B) 3
C) 5
D) 30
Show full solution
Correct answer: B) 3
Rearrange to t = I/(Pr). Then t = 450/(3000 x 0.05) = 3.
SAT trap: Convert 5% to 0.05 before substitution.
Rates, Percentages, and Science Formulas
MEDIUM
Question 47
The simple growth formula is A = P(1 + rt). What is r when A = 1,320, P = 1,200, and t = 2?
Which choice is correct?
A) 0.02
B) 0.05
C) 0.10
D) 5
Show full solution
Correct answer: B) 0.05
Divide by 1,200: 1.1 = 1 + 2r. Then 0.1 = 2r, so r = 0.05.
SAT trap: Subtract 1 after dividing by the principal.
Rates, Percentages, and Science Formulas
MEDIUM
Question 48
Percent increase is p = 100(new – old)/old. What is the new value when old = 80 and p = 25?
Which choice is correct?
A) 85
B) 95
C) 100
D) 105
Show full solution
Correct answer: C) 100
Write 25 = 100(new – 80)/80. This means new – 80 = 20, so new = 100.
SAT trap: A 25% increase adds 25% of the original value, not 25 units.
Rates, Percentages, and Science Formulas
EASY
Question 49
Average speed is v = d/t. What is d when v = 55 and t = 4?
Which choice is correct?
A) 13.75
B) 59
C) 220
D) 275
Show full solution
Correct answer: C) 220
Rearrange to d = vt. Then d = 55 x 4 = 220.
SAT trap: Distance equals rate multiplied by time.
Rates, Percentages, and Science Formulas
EASY
Question 50
Unit price is c = C/n. What is n when C = 42 and c = 3.5?
Which choice is correct?
A) 7
B) 12
C) 38.5
D) 147
Show full solution
Correct answer: B) 12
Rearrange to n = C/c. Then n = 42/3.5 = 12.
SAT trap: Number of items equals total cost divided by cost per item.
Rates, Percentages, and Science Formulas
EASY
Question 51
Ohm's law is V = IR. What is R when V = 24 and I = 3?
Which choice is correct?
A) 7
B) 8
C) 21
D) 72
Show full solution
Correct answer: B) 8
Rearrange to R = V/I. Then R = 24/3 = 8.
SAT trap: Resistance is voltage divided by current.
Rates, Percentages, and Science Formulas
MEDIUM
Question 52
Kinetic energy is E = mv²/2. What is v when E = 144 and m = 8?
Which choice is correct?
A) 3
B) 6
C) 12
D) 36
Show full solution
Correct answer: B) 6
Substitute: 144 = 4v². Then v² = 36, so v = 6.
SAT trap: After isolating v², take the positive square root for speed.
Rates, Percentages, and Science Formulas
EASY
Question 53
Using C = (5/9)(F – 32), what is C when F = 95?
Which choice is correct?
A) 30
B) 35
C) 45
D) 63
Show full solution
Correct answer: B) 35
Compute F – 32 = 63. Then C = (5/9)(63) = 35.
SAT trap: Subtract 32 before multiplying by 5/9.
Rates, Percentages, and Science Formulas
EASY
Question 54
Population density is D = P/A. What is A when P = 180,000 and D = 1,200?
Which choice is correct?
A) 120
B) 150
C) 1,500
D) 216,000,000
Show full solution
Correct answer: B) 150
Rearrange to A = P/D. Then A = 180000/1200 = 150.
SAT trap: Area equals population divided by population per unit area.
Rates, Percentages, and Science Formulas
EASY
Question 55
Work is W = Fd. What is d when W = 750 and F = 125?
Which choice is correct?
A) 5
B) 6
C) 8
D) 625
Show full solution
Correct answer: B) 6
Rearrange to d = W/F. Then d = 750/125 = 6.
SAT trap: Distance equals work divided by force.
What Do Hard SAT Formula Rearrangement Questions Look Like?
Hard questions combine fractions, roots, powers, grouped expressions, or variables in denominators.
Hard Mixed Formula Rearrangement
HARD
Question 56
If 1/p + 1/q = 1/r, what is r when p = 6 and q = 3?
Which choice is correct?
A) 1
B) 2
C) 3
D) 9
Show full solution
Correct answer: B) 2
Substitute: 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. Therefore 1/r = 1/2, so r = 2.
SAT trap: Add the fractions before taking the reciprocal.
Hard Mixed Formula Rearrangement
MEDIUM
Question 57
The compound growth formula is A = P(1 + r)^t. What is P when A = 1,331, r = 0.10, and t = 3?
Which choice is correct?
A) 900
B) 1,000
C) 1,100
D) 1,210
Show full solution
Correct answer: B) 1,000
Compute (1.10)^3 = 1.331. Then P = 1331/1.331 = 1000.
SAT trap: Divide by the complete growth factor, including the exponent.
Hard Mixed Formula Rearrangement
MEDIUM
Question 58
If y = (ax + b)/c, what is x when y = 7, a = 4, b = 5, and c = 3?
Which choice is correct?
A) 3
B) 4
C) 5
D) 8
Show full solution
Correct answer: B) 4
Substitute: 7 = (4x + 5)/3. Multiply by 3: 21 = 4x + 5. Then 4x = 16, so x = 4.
SAT trap: Clear the denominator before subtracting b.
Hard Mixed Formula Rearrangement
HARD
Question 59
Parallel resistance is R = (R1R2)/(R1 + R2). What is R2 when R = 6 and R1 = 10?
Which choice is correct?
A) 12
B) 15
C) 16
D) 60
Show full solution
Correct answer: B) 15
Substitute: 6 = 10R2/(10 + R2). Cross-multiply: 60 + 6R2 = 10R2. Thus 60 = 4R2, so R2 = 15.
SAT trap: Cross-multiply both terms in the denominator.
Hard Mixed Formula Rearrangement
HARD
Question 60
The lens formula is 1/f = 1/u + 1/v. What is v when f = 12 and u = 20?
Which choice is correct?
A) 8
B) 20
C) 30
D) 32
Show full solution
Correct answer: C) 30
Compute 1/v = 1/12 – 1/20 = 5/60 – 3/60 = 2/60 = 1/30. Therefore v = 30.
SAT trap: Subtract the fractions first, then take the reciprocal.
Hard Mixed Formula Rearrangement
MEDIUM
Question 61
The lateral-plus-base area formula is A = πr(r + l). What is l when A = 45π and r = 5?
Which choice is correct?
A) 4
B) 5
C) 9
D) 20
Show full solution
Correct answer: A) 4
Substitute: 45π = 5π(5 + l). Divide by 5π: 9 = 5 + l. Therefore l = 4.
SAT trap: Divide by πr before subtracting r.
Hard Mixed Formula Rearrangement
HARD
Question 62
The pendulum formula is T = 2π√(L/g). What is L when T = 4π and g = 9?
Which choice is correct?
A) 9
B) 18
C) 36
D) 81
Show full solution
Correct answer: C) 36
Divide by 2π: 2 = √(L/9). Square both sides: 4 = L/9. Therefore L = 36.
SAT trap: Remove the coefficient before squaring.
Hard Mixed Formula Rearrangement
HARD
Question 63
Using v² = u² + 2as, what is s when v = 20, u = 8, and a = 6?
Which choice is correct?
A) 14
B) 28
C) 32
D) 56
Show full solution
Correct answer: B) 28
Substitute: 400 = 64 + 12s. Then 336 = 12s, so s = 28.
SAT trap: Subtract u² before dividing by 2a.
Hard Mixed Formula Rearrangement
HARD
Question 64
If y = k/(x – h) + c, what is h when y = 7, k = 12, x = 10, and c = 4?
Which choice is correct?
A) 4
B) 6
C) 7
D) 14
Show full solution
Correct answer: B) 6
Subtract c: 3 = 12/(10 – h). Cross-multiply: 3(10 – h) = 12. Then 10 – h = 4, so h = 6.
SAT trap: Keep x – h grouped while cross-multiplying.
Hard Mixed Formula Rearrangement
HARD
Question 65
If z = √((x – a)/b), what is x when z = 3, a = 5, and b = 4?
Which choice is correct?
A) 17
B) 29
C) 36
D) 41
Show full solution
Correct answer: D) 41
Square both sides: 9 = (x – 5)/4. Multiply by 4: 36 = x – 5. Therefore x = 41.
SAT trap: Square before multiplying by b, then add a.
What Do Student-Produced Response Formula Questions Look Like?
These questions do not provide answer choices. Rearrange carefully and enter the final numerical value.
Student-Produced Response
MEDIUM
Question 66
The area of a trapezoid is A = h(b1 + b2)/2. If A = 96, h = 8, and b1 = 10, what is b2?
Enter your answer in the student-produced response box.
Show full solution
Correct answer shown in the solution
Substitute: 96 = 8(10 + b2)/2 = 4(10 + b2). Divide by 4: 24 = 10 + b2. Therefore b2 = 14.
SAT trap: Enter only the numerical value 14.
Student-Produced Response
MEDIUM
Question 67
If q = (a + b)/(c – d), what is d when q = 5, a = 8, b = 12, and c = 7?
Enter your answer in the student-produced response box.
Show full solution
Correct answer shown in the solution
Substitute: 5 = 20/(7 – d). Cross-multiply: 35 – 5d = 20. Then -5d = -15, so d = 3.
SAT trap: Keep c – d together when clearing the denominator.
Student-Produced Response
HARD
Question 68
If m = (y – k)/(x – h), what is h when m = -3, y = 5, k = 14, and x = 2?
Enter your answer in the student-produced response box.
Show full solution
Correct answer shown in the solution
Substitute: -3 = (5 – 14)/(2 – h) = -9/(2 – h). Cross-multiply: -3(2 – h) = -9. Then 2 – h = 3, so h = -1.
SAT trap: A negative final answer is allowed in a student-produced response.
Student-Produced Response
MEDIUM
Question 69
The formula A = P(1 + rt) gives simple growth. What is t when A = 1,800, P = 1,500, and r = 0.04?
Enter your answer in the student-produced response box.
Show full solution
Correct answer shown in the solution
Substitute: 1800 = 1500(1 + 0.04t). Divide by 1500: 1.2 = 1 + 0.04t. Then 0.2 = 0.04t, so t = 5.
SAT trap: Divide by P before subtracting 1.
Student-Produced Response
EASY
Question 70
The volume of a pyramid is V = Bh/3. What is B when V = 240 and h = 12?
Enter your answer in the student-produced response box.
Show full solution
Correct answer shown in the solution
Substitute: 240 = 12B/3 = 4B. Therefore B = 60.
SAT trap: The base area is found by multiplying the volume by 3 and dividing by height.
What Mistakes Cost Students Points on Formula Rearrangement?
| Mistake | Why It Happens | Better SAT Method |
|---|---|---|
| Reversing operations incorrectly | Students follow the original formula order | Undo operations in reverse order |
| Clearing only part of a denominator | A grouped denominator is treated as separate terms | Multiply by the complete denominator |
| Forgetting a square or cube root | Students stop after isolating r² or r³ | Apply the matching root as the final step |
| Using 5 instead of 0.05 | Percent notation is entered directly into a decimal formula | Divide a percent by 100 before substitution |
| Substituting too early | The equation becomes cluttered with numbers | Rearrange first when the symbolic steps are simple |
How Should Students Study SAT Formula Rearrangement in 2 Weeks?
| Days | Focus | Practice Goal |
|---|---|---|
| Days 1-3 | One-step and two-step rearrangement | Solve Q1-Q15 and rewrite every missed formula |
| Days 4-6 | Linear and coordinate formulas | Solve Q16-Q30 with limited calculator use |
| Days 7-9 | Geometry and measurement | Review powers, roots, π, and units |
| Days 10-11 | Rates, percent, and science formulas | Practice decimal rates and unit interpretation |
| Days 12-13 | Hard mixed questions | Solve Q56-Q70 under timed conditions |
| Day 14 | Mixed review | Redo every missed question without notes |
Frequently Asked Questions About SAT Formula Rearrangement
Does the Digital SAT test formula rearrangement?
Yes. Formula rearrangement appears across algebra, advanced math, geometry, data analysis, and real-world modeling questions.
Should I rearrange the formula before substituting numbers?
Usually yes. Rearranging first keeps the algebra cleaner and reduces calculator mistakes, especially when several values are given.
Do I need to memorize every formula for the SAT?
No. Many formulas are provided in the question or reference sheet, but you still need to understand how to isolate a requested variable.
How do I clear a fraction in a formula?
Multiply both sides by the complete denominator. Keep grouped terms in parentheses so every term is handled correctly.
When do I use a square root or cube root?
Use a square root after isolating a squared variable and a cube root after isolating a cubed variable.
Can formula rearrangement questions be solved with Desmos?
Some can, but symbolic rearrangement is often faster. Desmos is useful for checking numerical solutions or solving an equation after substitution.
What is the biggest SAT trap in formula questions?
The most common trap is performing the right operation on only one term or one side of the equation.
How many formula rearrangement questions should I practice?
Practice enough to cover linear, geometry, rate, percent, and harder fraction or root formulas. This 70-question set provides a broad progression.
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