789 prompts matching "Structured question: polynomial with a given remainder pattern"
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Why simultaneous linear-quadratic systems can have two solutions
Act as my SS2 Further Maths tutor. Explain to me why solving a linear equation together wi
Teach me conditions for a line and a curve to intersect
Act as my SS2 Further Maths tutor. Teach me how to determine whether a given straight line
Quiz me on line and curve intersection conditions
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Find the value of k for a line to be tangent to a curve
Act as my SS2 Further Maths tutor. Teach me how to find an unknown constant k in a line's
Worked example: using the factor theorem to factorise a cubic
Act as my SS2 Further Maths tutor. Show me a full worked example of using the factor theor
Quiz me on solving cubic equations
Act as my SS2 Further Maths tutor. Quiz me with three cubic equations to solve completely,
Give me practice solving cubic equations
Act as my SS2 Further Maths tutor. Give me six practice cubic equations to solve completel
Sum and product of roots of a cubic equation
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Give me practice identifying compound propositions
Act as my SS2 Further Maths tutor. Give me eight sentences and ask me to classify each as
Teach me the truth table for negation
Act as my SS2 Further Maths tutor. Teach me how to construct the truth table for negation
Teach me the truth table for conjunction
Act as my SS2 Further Maths tutor. Teach me how to construct the truth table for conjuncti
Teach me the truth table for disjunction
Act as my SS2 Further Maths tutor. Teach me how to construct the truth table for disjuncti
Teach me converse and inverse propositions
Act as my SS2 Further Maths tutor. Teach me how to form the converse and the inverse of a
Give me practice on converse and inverse propositions
Act as my SS2 Further Maths tutor. Give me six conditional statements and ask me to form a
Teach me logically equivalent propositions
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Quiz me on biconditional statements
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Give me practice on logical equivalence
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Quiz me on tautologies
Act as my SS2 Further Maths tutor. Quiz me with four compound statements and ask me each t
Teach me what a logical argument is
Act as my SS2 Further Maths tutor. Teach me what a logical argument is in propositional lo
Worked example: testing an argument for validity
Act as my SS2 Further Maths tutor. Show me a full worked example of testing a simple logic