Flashcards · Maths · Algebra
Substitution and Rearranging Formulae
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How do you substitute a negative number safely?
Put it in brackets. If \(a = -3\), then \(a^2 = (-3)^2 = 9\).
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What is the value of \(3x^2\) when \(x = -2\)?
12. Square first (\((-2)^2 = 4\)), then multiply by 3.
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What is the difference between \(3x^2\) and \((3x)^2\)?
\(3x^2 = 3 \times x^2\), but \((3x)^2 = 9x^2\).
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What is the formula for speed?
Speed \(=\) distance \(\div\) time.
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What is the formula for the area of a trapezium?
\(A = \tfrac{1}{2}(a + b)h\).
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How do you write a formula for a \(\pounds 35\) call-out plus \(\pounds 22\) per hour?
\(C = 35 + 22h\).
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What does the subject of a formula mean?
The letter on its own on one side of the equals sign, such as \(y\) in \(y = 3x + 5\).
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How do you rearrange a formula?
Undo the operations in reverse order, using inverse operations and doing the same to both sides.
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Make \(x\) the subject of \(y = 3x + 5\).
\(x = \dfrac{y - 5}{3}\).
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Make \(t\) the subject of \(v = u + at\).
\(t = \dfrac{v - u}{a}\).
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Make \(x\) the subject of \(y = \dfrac{2x - 1}{3}\).
\(x = \dfrac{3y + 1}{2}\).
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Make \(a\) the subject of \(P = 2(a + b)\).
\(a = \dfrac{P}{2} - b\).
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Make \(m\) the subject of \(E = \tfrac{1}{2}mv^2\).
\(m = \dfrac{2E}{v^2}\).
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Make \(r\) the subject of \(A = \pi r^2\) (Higher tier).
\(r = \sqrt{\dfrac{A}{\pi}}\).
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What do you do when the subject appears twice (Higher tier)?
Collect every term containing the subject on one side, factorise it out, then divide.
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If \(C = 12 + 8d\) and \(C = 84\), how do you find \(d\)?
\(84 = 12 + 8d\), so \(72 = 8d\) and \(d = 9\).
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What is wrong with writing \(-3^2\) when you mean \((-3)^2\)?
\(-3^2\) means \(-(3^2) = -9\). The bracket is what makes the answer 9.