Christian Lawson-Perfect

Christian Lawson-Perfect on Finding the missing value of a constant in a polynomial, using the Factor Theorem 8 years, 6 months ago

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Christian Lawson-Perfect on Finding the missing value of a constant in a polynomial, using the Factor Theorem 8 years, 6 months ago

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Christian Lawson-Perfect commented on Solve quadratic inequalities 8 years, 6 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 on Solve quadratic inequalities 8 years, 6 months ago

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Christian Lawson-Perfect commented on Solve quadratic inequalities 8 years, 6 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 $x^2-ax-b \gt 0$.

Christian Lawson-Perfect on Expansion of brackets 8 years, 6 months ago

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Christian Lawson-Perfect commented on Expansion of brackets 8 years, 6 months ago

Very nearly there!

Add restrictions to the parts forbidding brackets, to make sure the student has expanded in some way. It'll be too much effort to make sure they've collected like terms in the later parts.

In the parts with more than one variable, make sure you set the "expected variable names" field, so that mistakes like typing ab instead of a*b get caught.