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Q1
Answer
Factorise $\;9x^2 - 16$.
[1]
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$(3x+4)(3x-4)$
Q2
Answer
Expand and then differentiate $\;y = (x + 3)(x - 5)$.
[2]
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$y = x^2 - 2x - 15$, so $\dfrac{\mathrm{d}y}{\mathrm{d}x} = 2x - 2$.
Q3
Answer
Differentiate $\;y = x^3 + 4x^2 - 7x + 2$.
[2]
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$\dfrac{\mathrm{d}y}{\mathrm{d}x} = 3x^2 + 8x - 7$.
Q4
Answer
The curve has equation $\;y = x^2 - 4x + 1$.
Find the gradient of the curve at the point where $x = 3$.
[2]
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$\dfrac{\mathrm{d}y}{\mathrm{d}x} = 2x - 4$, gradient $= 2(3) - 4 = 2$.
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