823 prompts matching "Showing a set is not closed by a single counter-example"
Showing only prompts that state their year. 35 more in this subject don't name one, so choose All years to see them.
Form a quadratic from a given sum and product
Set me a structured question: given the sum and product of the roots of a quadratic equati
Structured question: new equation with roots 1/alpha and 1/beta
I am in SS 2. Set me a multi-part question where I first find the sum and product of the r
Teach me solving quadratic inequalities
Teach me how to solve a quadratic inequality like x^2-5x+6>0 using a sketch of the curve a
Quiz me on quadratic inequalities
I am in SS 2. Quiz me with five short quadratic inequality questions of increasing difficu
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: find coordinates of intersection points
I am in SS 2. Give me a multi-part question where I solve a linear-quadratic system and th
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
Show that command word: polynomial identity
I am in SS 2. Give me a 'show that' polynomial question where I must expand and simplify b
Worked Example: Halving the coefficient of x and squaring it
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on halvin
Worked Example: Substituting a, b and c into the quadratic formula correctly
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on substi
Worked Example: The product of the roots as c over a
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on the pr
Worked Example: The identity linking alpha squared plus beta squared to the sum and product
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on the id
Worked Example: Substituting into the quadratic and tidying up
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on substi
Worked Example: The degree of a polynomial in one variable
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on the de
Worked Example: How many roots a cubic equation has
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on how ma
Worked Example: Conjunction in a three-variable truth table
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on conjun
Worked Example: The truth table for the conditional
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on the tr
Worked Example: The truth table for the biconditional
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on the tr
Worked Example: Arranging r of n objects in a line
Act as my SS2 Further Mathematics tutor. Take me through one full worked example on arrang