1,045 prompts matching "Why friction does not depend on the area of contact"
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Derive the quadratic formula
Act as my SS2 Further Maths tutor. Show me, step by step, how to derive the quadratic form
Quiz me on line and curve intersection conditions
Act as my SS2 Further Maths tutor. Quiz me with three different line-and-curve pairs, and
Teach me the universal and existential quantifiers
Act as my SS2 Further Maths tutor. Teach me the difference between the universal quantifie
Teach me the distance and midpoint formulas
Act as my SS2 Further Maths tutor. Teach me how to find the distance between two points an
Teach me finding the determinant of a 2x2 matrix
Act as my SS2 Further Maths tutor. Teach me how to find the determinant of a 2x2 matrix an
Teach me the dot product of two vectors
Act as my SS2 Further Maths tutor. Teach me how to calculate the dot product of two vector
Worked example: finding the angle between two vectors
Act as my SS2 Further Maths tutor. Show me a full worked example of finding the angle betw
Worked example: find the distance between the points (1,2) and (4,6)
Act as my SS2 Further Maths tutor. Show me a full worked example for this coordinate geome
Worked example: find the midpoint of the segment joining (-3,5) and (7,-1)
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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 modulus and argument of 3+4i
Act as my SS2 Further Maths tutor. Show me a full worked example for this complex numbers
Worked example: solve x^2+4x+13=0 giving the roots as complex numbers
Act as my SS2 Further Maths tutor. Show me a full worked example for this complex numbers
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]]
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Worked example: find the magnitude of the vector (3,4)
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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: 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
Show all your working command word: simultaneous equations
I am in SS 2. Set me a linear-quadratic simultaneous equations question that instructs 'sh
Structured question: classify a line-curve relationship
I am in SS 2. Give me three short parts, each with a different line and the same curve, as
Structured question: add and simplify two polynomials
I am in SS 2. Set me a structured Additional Maths question where I must add two given pol