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A question which asks students to encrypt a number using RSA, then to factor a small public key and find the decryption exponent.

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Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

The greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250

Practice factorising different types of quadratics. Repeat as many times as you want. 

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Asks students to find the partil fraction decomposition for a rational function Denominator is a quadratic with distinct factors.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

Cofactors Determinant and inverse of a 3x3 matrix.

Statistics and probability. A question on two factor ANOVA.

Quotient and remainder, polynomial division.

Factorising polynomials using the highest common factor

Quadratic factorisation that does not rely upon pattern matching.

One could also use the pattern matching syntax to check automatically; this is programatically harder.

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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.

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A mathematical expression part with a pattern restriction to ensure that the student has extracted the highest common factor of two terms.

The answer must be of the form $a(b+cx)$, where $b$ and $c$ are coprime.

Simplify (a) a fully-factorised fraction with common factors, and (b) a fraction where the numerator is a product and the denominator a sum sharing the same variables (that cannot be simplified). The variables are randomised. Part of HELM book 1.4

Simplify an algebraic fraction where both numerator and denominator must first be factorised. Part of HELM Book 1.4

Simplify an algebraic fraction where the numerator is a factor of the quadratic on the denominator. Posed as a yes/no question, is this fraction equivalent to this simplified form? The answer is always yes. Part of HELM Book 1.4

Simplify an algebraic fraction where the numerator and denominator first need to be factorised (the common factor is an integer). Part of HELM book 1.4

Simplify an algebraic fraction that is fully factorised with common factors between the numerator and denominator, and one of the variables has a larger index on the denominator. Part of HELM Book 1.4

Simplify a fraction where the numerator and denominator are factorised and have common products, and one of the common factors is powered. Part of HELM book 1.4

This question tests the student's ability to identify the factors of some composite numbers and the highest common factors of two numbers. 

Apply the factor and remainder theorems to manipulate polynomial expressions

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