1,008 prompts matching "Structured question: find fg(x) and gf(x)"
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Summarise sequences and series for quick revision
Act as my SS2 Further Maths tutor. Give me a concise summary of the key formulas and metho
Summarise logarithms and indices for quick revision
Act as my SS2 Further Maths tutor. Give me a concise summary of the key formulas and metho
Worked example: find the gradient of y = x^3 - 4x at the point where x = 2
Act as my SS2 Further Maths tutor. Show me a full worked example for this differentiation
Worked example: find the equation of the tangent to y = x^2 - 5x + 6 at the point where x = 1
Act as my SS2 Further Maths tutor. Show me a full worked example for this differentiation
Worked example: differentiate y = (2x-1)(x+3) after expanding it first
Act as my SS2 Further Maths tutor. Show me a full worked example for this differentiation
Worked example: find the determinant of [[5,2],[3,4]]
Act as my SS2 Further Maths tutor. Show me a full worked example for this matrices problem
Worked example: find the inverse of [[2,1],[5,3]]
Act as my SS2 Further Maths tutor. Show me a full worked example for this matrices problem
Worked example: use matrices to solve the simultaneous equations 2x+y=8 and x-y=1
Act as my SS2 Further Maths tutor. Show me a full worked example for this matrices problem
Worked example: how many ways can a president and secretary be chosen from 8 people
Act as my SS2 Further Maths tutor. Show me a full worked example for this permutations and
Worked example: expand (x+2)^5 fully using the binomial theorem
Act as my SS2 Further Maths tutor. Show me a full worked example for this binomial theorem
Worked example: find the term in x^3 in the expansion of (2x-1)^6
Act as my SS2 Further Maths tutor. Show me a full worked example for this binomial theorem
Worked example: find the coefficient of x^4 in the expansion of (1+3x)^7
Act as my SS2 Further Maths tutor. Show me a full worked example for this binomial theorem
Worked example: expand (1-x)^4 fully and use it to estimate (0.98)^4
Act as my SS2 Further Maths tutor. Show me a full worked example for this binomial theorem
Worked example: construct the truth table for (p AND q) OR (NOT p)
Act as my SS2 Further Maths tutor. Show me a full worked example for this propositional lo
Worked example: construct the truth table for NOT(p OR q) and compare it to (NOT p) AND (NOT q)
Act as my SS2 Further Maths tutor. Show me a full worked example for this propositional lo
Worked example: write the converse, inverse and contrapositive of 'if a number is even, then it is divisible by 2'
Act as my SS2 Further Maths tutor. Show me a full worked example for this propositional lo
Real-life application of sequences and series
Act as my SS2 Further Maths tutor. Explain a real-life or practical situation where sequen
Real-life application of sum and product of roots
Act as my SS2 Further Maths tutor. Explain a real-life or practical situation where sum an
Give me a 5-minute recap of propositions and compound statements
Act as my SS2 Further Maths tutor. Give me a quick 5-minute recap of propositions and comp
Give me a 5-minute recap of converse and inverse propositions
Act as my SS2 Further Maths tutor. Give me a quick 5-minute recap of converse and inverse