Literal Equations Quiz
Questions: 16 · 10 minutes
1. A calibration formula is Q = (a + b)/c. If Q = 7, c = 3, and a = 5, what value of b follows from rearranging the formula?
Multiply 7 by 3 and subtract 5, giving b = 16
Subtract 5 from 7 before multiplying, giving b = 6
Divide 7 by 3 and subtract 5, giving b = −8/3
Subtract the product from 5, giving b = −16
2. A transformed measurement satisfies z = (x − q)/r + s. Assuming r ≠ 0, which expression isolates q?
Distribute r to z but not s: q = x − rz − s
Reverse the final difference: q = r(z − s) − x
Subtract s from z, multiply by r, and subtract from x: q = x − r(z − s)
Divide the adjusted value by r: q = x − (z − s)/r
3. Which description best defines a literal equation?
An equation relating multiple variables that can be rearranged for a selected variable
An equation whose only possible solution must be a whole number
An equation that contains letters but cannot include numerical constants
An equation that requires numerical substitution before any algebra is performed
4. For parallel resistors, 1/R = 1/R₁ + 1/R₂. Which formula isolates R₂, assuming all required denominators are nonzero?
Subtract the two resistances: R₂ = R₁ − R
Divide the product RR₁ by the difference R₁ − R: R₂ = RR₁/(R₁ − R)
Divide the product RR₁ by the opposite difference R − R₁: R₂ = RR₁/(R − R₁)
Divide the difference R₁ − R by the product RR₁: R₂ = (R₁ − R)/(RR₁)
5. The area of an annulus is A = π(R² − r²). If r is nonnegative, which formula gives r?
Reverse the terms under the radical: r = √(A/π − R²)
Subtract A/π from R² and take the principal square root: r = √(R² − A/π)
Subtract a radius based on the area: r = R − √(A/π)
Omit division by π outside the area term: r = √(πR² − A)
6. Solve A = lw for w, assuming l ≠ 0.
Divide by twice the length: w = A/(2l)
Reverse the ratio: w = l/A
Subtract the length: w = A − l
Divide both sides by the length: w = A/l
7. Simple interest is modeled by I = Prt. If P and t are nonzero, which expression gives the rate r?
Invert the interest ratio: r = Pt/I
Treat the product as a term to subtract: r = I − Pt
Multiply by P but divide by t: r = IP/t
Divide interest by both factors: r = I/(Pt)
8. Average-velocity motion is modeled by d = (vᵢ + v_f)t/2. Which expression gives v_f when t ≠ 0?
Double d but subtract the full product: v_f = 2d − vᵢt
Double d, divide by t, then subtract vᵢ: v_f = 2d/t − vᵢ
Divide 2d by both velocity and time: v_f = 2d/(vᵢt)
Halve d/t before subtracting: v_f = d/(2t) − vᵢ
9. Celsius and Fahrenheit temperatures satisfy C = 5(F − 32)/9. Which formula converts C to F?
Scale C by 9/5, then subtract 32: F = 9C/5 − 32
Scale C by 5/9, then add 32: F = 5C/9 + 32
Add 32 before scaling: F = 9(C + 32)/5
Scale C by 9/5, then add 32: F = 9C/5 + 32
10. The volume of a pyramid is V = Bh/3. Solve for h, assuming B ≠ 0.
Divide V by 3B: h = V/(3B)
Divide B by 3V: h = B/(3V)
Multiply V by 3, then divide by B: h = 3V/B
Multiply B by 3, then divide by V: h = 3B/V
11. A lab formula is K = (M − N)/p. Which expression correctly isolates N?
Multiply the entire difference M − K by p: N = p(M − K)
Reverse the subtraction after multiplying: N = pK − M
Divide K by p before subtracting: N = M − K/p
Multiply K by p and subtract from M: N = M − pK
12. Displacement under constant acceleration can be modeled by s = ut + at²/2. Solve for a, assuming t ≠ 0.
Remove ut, double the result, and divide by t²: a = 2(s − ut)/t²
Double only s before dividing: a = (2s − ut)/t²
Divide by t rather than t²: a = 2(s − ut)/t
Leave the time factor attached to u: a = 2s − ut²
13. The perimeter of a rectangle is P = 2l + 2w. Which formula gives l?
Remove 2w and divide by 2: l = (P − 2w)/2
Remove one w and halve: l = (P − w)/2
Subtract 2w without halving: l = P − 2w
Divide the perimeter by 2w: l = P/(2w)
14. A line is described by y = mx + b. Assuming m ≠ 0, which rearrangement isolates x?
Add b before dividing: x = (y + b)/m
Divide y first, then subtract b: x = y/m − b
Subtract b, then divide by m: x = (y − b)/m
Multiply the difference by m: x = m(y − b)
15. The equation 3a − 2b = 7 relates a and b. Which sequence correctly solves for b?
Move 3a with the wrong sign, then halve: b = (7 − 3a)/2
Divide only the constant term by 2: b = 3a − 7/2
Subtract 7 from 3a, then divide the full difference by 2: b = (3a − 7)/2
Add 7 to 3a before dividing: b = (3a + 7)/2
16. In ax + b = cx + d, the x-terms occur on both sides. Assuming a ≠ c, which formula correctly combines and isolates them?
Add the constant terms in the numerator: x = (d + b)/(a − c)
Subtract the constants and coefficients consistently: x = (d − b)/(a − c)
Add the coefficients in the denominator: x = (d − b)/(a + c)
Invert the required quotient: x = (a − c)/(d − b)