Christian Lawson-Perfect 7 years, 4 months ago

Gave some feedback: Ready to use

Christian Lawson-Perfect 7 years, 4 months ago

Saved a checkpoint:

I've fixed a couple of typos, but otherwise this is OK!

Restore this checkpoint

Bradley Bush commented 7 years, 4 months ago

Thank you for the feedback, I can see your logic, so I've changed it to your way of asking.

The inequality signs have been swapped to make sure the student is paying attention to their direction because of it's significance to the question.

Both graphs struggled to fit on the same figure so I have added another graph at the end with an brief bit of text to justify that both x ranges are the same.

Bradley Bush 7 years, 4 months ago

Gave some feedback: Needs to be tested

Christian Lawson-Perfect commented 7 years, 5 months ago

(I realise I contradicted Vicky's suggestion. Not sure if what you've done is exactly what she imagined, but it doesn't read clearly to me!)

Christian Lawson-Perfect 7 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented 7 years, 5 months ago

I've changed "sketch the quadratic" to "sketch each quadratic".

The prompt doesn't actually say what should go in the first gap for each part. I know the statement says factorise first, but you should be absolutely clear what you want.

I'd have:

"Factorise $f(x)$:

$x^2+ax+b = $ [[gap]]

Hence, find the range of values for $x$ such that $x^2+ax+b \gt 0$."

You need a conjunction between the two inequalities at the end of parts a and b: "$x \gt ??$ OR $x \lt ??$" in part a, and $x \gt ??$ AND $x \lt ??$" for part b. If you want, you can make that a dropdown.

The inequality signs for part b are the other way round to part a. Why?

Part c doesn't make sense - you can't rearrange an inequality to get an equality. I'd ask them to rearrange to get something $\gt 0$ - this also makes sure they don't give the negation of what you're expecting - and then say "by factorising or otherwise, give the range of values for which $ax + b \gt x^2$. Keeping track of the inequality makes it easier to work out which way round the upper and lower bounds should go.

In the advice, I'd give examples of some values of $x$ that satisfy the inequality - in part a, a big negative value and a big positive value, and in part b a vlaue between the roots. For part c, I think it would be very helpful to show the graphs of $x^2$ and $ax+b$ on top of the graph of $x^2-ax-b$ to show that the inequality holds for the same values in both arrangements - i.e., $x^2 \gt ax+b$ exactly when $x^2-ax-b \gt 0$.

Bradley Bush 7 years, 5 months ago

Gave some feedback: Needs to be tested

Bradley Bush 7 years, 5 months ago

Gave some feedback: Has some problems

Bradley Bush 7 years, 5 months ago

Gave some feedback: Needs to be tested

Bradley Bush commented 7 years, 5 months ago

Thank you for the feedback, those typos were careless and hopefully they are all sorted now, I have also reworded the question for you.

I hate to disagree but I think that it would be useful for students who are struggling in particular to have the factorise step left in the question to give the student a mid way point. But if there is more logic behind removing the gap, I am happy to take it out.

Vicky Hall 7 years, 5 months ago

Gave some feedback: Has some problems

Vicky Hall commented 7 years, 5 months ago

Reword the questions here to say something like: find the range of values of $x$ for which ${function}>0$. You have told the student to factorise in the statement so you don't need to say it again. I would also remove the gap asking them to give the factorised form. 

Have a check through the advice as I noticed a couple of typos and a rogue part d).

Bradley Bush 7 years, 5 months ago

Gave some feedback: Needs to be tested

Bradley Bush commented 7 years, 5 months ago

How do I allow either or answers for the gap in part a?