883 prompts matching "Proving that a quadratic expression is positive for every real x"
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Worked example: an AP where the 4th term is 15 and the 9th term is 35, find the first term and common difference
Act as my SS2 Further Maths tutor. Show me a full worked example for this sequences and se
Worked example: a GP where the 2nd term is 6 and the 5th term is 162, find the first term and common ratio
Act as my SS2 Further Maths tutor. Show me a full worked example for this sequences and se
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 the condition for a line to be tangent to a curve
Act as my SS2 Further Maths tutor. Explain a real-life or practical situation where the co
Multi-part exam question on factorising trinomials
I am in SS 2. Give me a three-part exam-style question, (a) (b) (c), where each part asks
Mark scheme walkthrough: factorising a trinomial
I am in SS 2. Walk me through a Cambridge-style mark scheme for factorising a quadratic tr
Hence solve command word: quadratic equations
I am in SS 2. Explain what 'hence solve' means in an exam question, using an example where
Spot the examiner's trick in a factorisation question
I am in SS 2. Give me a quadratic equation exam question that has a common trap, such as a
Discriminant classification exam question
I am in SS 2. Give me a short structured question where I must use the discriminant to sta
Find the range of values command word: quadratic inequality
I am in SS 2. Set me an exam question phrased 'find the range of values of x for which...'
Quiz me on quadratic inequalities
I am in SS 2. Quiz me with five short quadratic inequality questions of increasing difficu
Common command word mistakes SS2 students make
Tell me the most common mistakes SS2 Further Maths students make when responding to comman
Worked Example: Substituting into the quadratic and tidying up
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Show All Working: A simultaneous pair in which the second equation is a circle
Act as my Further Mathematics examiner. I am in SS 2. Set me a question on a simultaneous
Show All Working: Synthetic division as a shorter route
Act as my Further Mathematics examiner. I am in SS 2. Set me a question on synthetic divis
Worked Example: Testing a list of candidates to find a factor
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on testin
Learn: Factorising a cubic into three linear factors
You are my personal SS2 Further Mathematics tutor. Teach me factorising a cubic into three
Show All Working: Factorising a polynomial with fractional roots
Act as my Further Mathematics examiner. I am in SS 2. Set me a question on factorising a p
Learn: Solving a cubic once it has been factorised
You are my personal SS2 Further Mathematics tutor. Teach me solving a cubic once it has be
Show All Working: Solving a cubic that must first be rearranged
Act as my Further Mathematics examiner. I am in SS 2. Set me a question on solving a cubic