Questions and Answers
What is the first step of rearranging formulas?
Get rid of any square root signs by squaring both sides.
What do you need to do next after getting rid of square root signs?
Get rid of fractions.
What do you do about brackets in an equation?
Multiply them out.
What do you do to the subject terms when rearranging equations?
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What do you reduce the equation to?
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What happens after you reduce the equation to the form Ax=B?
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If you are left with x², what do you do?
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Make b the subject of the formula a=5b+3?
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Make u the subject of the formula v²=u²+2as?
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Make n the subject of the equation 2(m+3)=√n+3?
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Make p the subject of the formula q=p+1?
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Study Notes
Rearranging Equations Steps
- Start by eliminating square roots by squaring both sides of the equation.
- Remove any fractions present in the equation to simplify.
- Expand and multiply out any brackets within the equation.
- Consolidate all subject terms on one side while keeping non-subject terms on the opposite side.
- The resulting form should be structured as Ax = B, with A representing coefficients of the variable and B representing constants.
- Divide both sides by A to isolate the variable, resulting in the form x = (B/A).
- If encountering x², take the square root of both sides to find x = ±√(expression).
Example: Making b the Subject of a Formula
- For the equation a = 5b + 3, eliminate fractions by multiplying through by 4: 4a = 5b + 12.
- Gather all subject terms (b terms) to one side to achieve: 5b = 4a - 12.
- The equation is simplified to the form Ab = B, where A is 5 and B is the rearranged term.
- Divide by 5 to solve for b, yielding b = (4a - 12)/5.
Example: Making u the Subject of a Formula
- Given v² = u² + 2as, isolate u² by rearranging to u² = v² - 2as.
- This leads to the form Au² = B.
- To isolate u, take the square root of both sides resulting in: u = ±√(v² - 2as).
Example: Making n the Subject of a Formula
- For the equation 2(m+3) = √n + 3, first square both sides to eliminate the square root: 4m² + 24m + 36 = n + 5.
- Rearrange to isolate n, which gives n = 4m² + 24m + 31.
Example: Making p the Subject of a Formula
- In the formula q = (p + 1)/(p - 1), first eliminate fractions by multiplying by (p - 1): q(p - 1).
- Expand this to pq - q = p + 1.
- Rearrange and consolidate terms to form pq - p = q + 1.
- Factor similar terms leading to p(q - 1) = q + 1 and solve for p by dividing each side by (q - 1): p = (q + 1)/(q - 1).
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Description
This quiz tests your understanding of the steps involved in rearranging equations to isolate a variable. It covers the elimination of square roots, removal of fractions, and other essential techniques needed to solve for a variable efficiently. Get ready to sharpen your algebra skills with practical examples!