657 prompts matching "Why matrix subtraction is not commutative"
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Solve the logarithmic equation log(x+1) - log(x-1) = 2
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Solve the logarithmic equation 2log(x) = log(x+6) + log(4)
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Solve the logarithmic equation log3(x^2) - log3(x+2) = 1
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Solve the logarithmic equation log5(x+3) + log5(2) = 2
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Simplify the surd expression sqrt(72) + sqrt(18)
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Simplify the surd expression sqrt(50) - sqrt(8)
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Simplify the surd expression (3+sqrt2)(3-sqrt2)
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Simplify the surd expression 5/(1+sqrt3)
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Simplify the surd expression (2+sqrt5)^2
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Worked example: an AP with first term 5 and common difference 3, find the 20th term and the sum of the first 20 terms
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Worked example: a GP with first term 4 and common ratio 2, find the 8th term and the sum of the first 8 terms
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Worked example: a GP with first term 100 and common ratio 0.5, find the sum to infinity
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Worked example: differentiate y = 3x^4 - 2x^3 + x - 7
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Worked example: find the gradient of y = x^3 - 4x at the point where x = 2
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Worked example: find the stationary points of y = x^3 - 3x^2 - 9x + 5 and classify each one
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Worked example: find the equation of the tangent to y = x^2 - 5x + 6 at the point where x = 1
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Worked example: differentiate y = (2x-1)(x+3) after expanding it first
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Worked example: find the equation of the line through (2,3) and (5,9)
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Worked example: find the midpoint of the segment joining (-3,5) and (7,-1)
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Worked example: find the equation of a circle with centre (2,-1) and radius 4
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