Algebraic Formula Manipulation
Grade 12 math worksheet on manipulating and rearranging algebraic formulas to solve for different variables.
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Algebraic Formula Manipulation
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Read each question carefully and manipulate the given formula to solve for the indicated variable. Show all your work.
1. The formula for the area of a trapezoid is A = \( \frac{1}{2}h(b_1 + b_2) \). Rearrange this formula to solve for \( b_1 \).
2. The formula for compound interest is \( A = P(1 + \frac{r}{n})^{nt} \). Rearrange this formula to solve for P.
3. Given the formula \( V = \frac{1}{3}\pi r^2 h \) for the volume of a cone, if we want to solve for \( h \), the rearranged formula would be \( h = \) .
4. If the formula for kinetic energy is \( E_k = \frac{1}{2}mv^2 \), and we need to solve for \( v \), the steps would involve multiplying by 2, dividing by \( m \), and then taking the square root. The final rearranged formula for \( v \) is \( v = \) .
Match each original formula with its correctly rearranged form.
5. \( P = 2l + 2w \) (solve for \( l \))
a. \( x = \frac{y}{m} - b \)
6. \( y = mx + b \) (solve for \( x \))
b. \( l = \frac{P - 2w}{2} \)
7. \( F = ma \) (solve for \( m \))
c. \( m = \frac{F}{a} \)
8. Which of the following correctly rearranges \( d = vt + \frac{1}{2}at^2 \) to solve for \( a \)?
\( a = \frac{2(d - vt)}{t^2} \)
\( a = \frac{d - vt}{2t^2} \)
\( a = \frac{2d - vt}{t^2} \)
\( a = 2(d - vt)t^2 \)