Using rules for roots and powers to write expressions with only powers

Using indices to write roots as fractional powers

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

simplifying, multiplication, fraction of square roots resulting in rational, square root of fraction resulting in rational, rationalising the denominator, simple rationalising the denominator conjugate

No description given

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Find roots and the area under a parabola

No description given

1) Randomiseer een waarde, bijvoorbeeld de prijs, en pas alles aan zodat het automatisch werkt.

Een nuttig commando is precround(...,2) wat een getal op 2 cijfers na de komma afrondt.

2) Randomiseer alle waardes. Het ideaalst lijkt mij het aantal initiële appels, de prijs van toen, en hoeveel appels je finaal zou kopen. Je kan dit doen door een lijst van goeie opties manueel in te geven, of door automatisch een goeie situatie te selecteren (moeilijker).

Een nuttig commando is gcd(a,b) wat de grootste gemene deler geeft van 2 getallen (voor de middelste kolom in de verhoudingstabel).

1) Randomiseer een waarde, bijvoorbeeld de prijs, en pas alles aan zodat het automatisch werkt.

Een nuttig commando is precround(...,2) wat een getal op 2 cijfers na de komma afrondt.

2) Randomiseer alle waardes. Het ideaalst lijkt mij het aantal initiële appels, de effectieve prijs per appel, en hoeveel appels je finaal zou kopen. Je kan dit doen door een lijst van goeie opties manueel in te geven, of door automatisch een goeie situatie te selecteren (moeilijker).

Een nuttig commando is gcd(a,b) wat de grootste gemene deler geeft van 2 getallen (voor de middelste kolom in de verhoudingstabel).

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

Simple questions on square numbers, square roots, cube number, cube roots and prime numbers.

The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.

When there's only one root, the student can only fill in one of the answer fields.

This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.

The marking corresponds to this table:

Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

No description given

Determining the number of real roots a quadratic equation has by evaluating and interpreting the discriminant.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Identify co-efficients, then use quadratic formula to find roots.

All set to be distinct and real. Some can be non-integer (0.5 steps)

Solve quadratic equations (non-simple case, two real, discrete integer roots) using the formula.