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Further Mathematics

AI prompts for senior secondary learners.

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1,334 prompts matching "Test me under exam conditions on polynomials and the remainder/factor theorems"

Showing only prompts that state their year. 35 more in this subject don't name one, so choose All years to see them.

Explain back: why we check the domain in logarithmic equations

I am in SS 3. Let me explain in my own words why we must check that x satisfies the domain

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Worked Example: Adding two 3 by 3 matrices

Act as my SS3 Further Mathematics tutor. Take me through one full worked example on adding

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Learn: Why two matrices can be added only when their orders match

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You are my personal SS3 Further Mathematics tutor. Teach me why two matrices can be added only when their orders match, working in clear steps and saying what the notation means as you use it. Check I have followed each step before moving on, and finish with one short question for me to try.

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Quiz: The zero matrix as the identity for matrix addition

Act as my SS3 Further Mathematics tutor and quiz me on the zero matrix as the identity for

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Spot My Mistake: Why matrix subtraction is not commutative

Act as my SS3 Further Mathematics tutor. Work a question on why matrix subtraction is not

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Quiz: Solving a matrix equation of the form A plus X equals B

Act as my SS3 Further Mathematics tutor and quiz me on solving a matrix equation of the fo

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Worked Example: The associative law for the product of three matrices

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Quiz: Multiplying a matrix by minus one

Act as my SS3 Further Mathematics tutor and quiz me on multiplying a matrix by minus one.

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Spot My Mistake: Orders that make a product possible one way round but not the other

Act as my SS3 Further Mathematics tutor. Work a question on orders that make a product pos

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Quiz: Solving AX equals B and XA equals B by different routes

Act as my SS3 Further Mathematics tutor and quiz me on solving AX equals B and XA equals B

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Spot My Mistake: A symmetric matrix, equal to its own transpose

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Practice: A diagonal matrix

Act as my SS3 Further Mathematics tutor. Give me five practice questions on a diagonal mat

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Learn: Deciding whether a stated matrix calculation is possible at all

You are my personal SS3 Further Mathematics tutor. Teach me deciding whether a stated matr

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Quiz: Finding an unknown entry from a stated matrix equation

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Learn: The effect on a determinant of swapping two rows

You are my personal SS3 Further Mathematics tutor. Teach me the effect on a determinant of

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Worked Example: Evaluating a 3 by 3 determinant by the rule of Sarrus

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Learn: Swapping and negating the entries when inverting a 2 by 2 matrix

You are my personal SS3 Further Mathematics tutor. Teach me swapping and negating the entr

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Quiz: Checking a 3 by 3 inverse by multiplication

Act as my SS3 Further Mathematics tutor and quiz me on checking a 3 by 3 inverse by multip

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Spot My Mistake: Why the inverse must be applied on the correct side

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Practice: What a singular coefficient matrix says about the equations

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