861 prompts matching "Explain why a complex number times its conjugate is real"
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Teach me combinations
Act as my SS2 Further Maths tutor. Teach me what a combination is and how it differs from
Teach me approximating powers using binomial expansion
Act as my SS2 Further Maths tutor. Teach me how to use the binomial expansion to evaluate
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: 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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Worked example: find the centre and radius of the circle x^2+y^2-4x+6y-3=0
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Worked example: find the magnitude of the vector (3,4)
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Worked example: find a+b where a=(2,-1) and b=(-3,5)
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Worked example: find the angle between the vectors (1,2) and (3,-1) using the dot product
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Worked example: find the unit vector in the direction of (6,8)
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Worked example: find 2a-3b where a=(4,1) and b=(-2,3)
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Worked example: construct the truth table for (p AND q) OR (NOT p)
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Worked example: construct the truth table for NOT(p OR q) and compare it to (NOT p) AND (NOT q)
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Real-life application of quadratic equations
Act as my SS2 Further Maths tutor. Explain a real-life or practical situation where quadra
Real-life application of completing the square
Act as my SS2 Further Maths tutor. Explain a real-life or practical situation where comple
Real-life application of the quadratic formula
Act as my SS2 Further Maths tutor. Explain a real-life or practical situation where the qu
Real-life application of polynomials
Act as my SS2 Further Maths tutor. Explain a real-life or practical situation where polyno