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

Simplify, if possible,
(a) $\frac{2}{3}x^2 + \frac{x^2}{3}$, (b) $0.5x^2 + \frac{3}{4}x^2 - \frac{11}{2}x$, (c) $3x^3 - 11x + 3yx + 11$, and (d) $-4\alpha x^2 + \beta x^2$ where $\alpha$ and $\beta$ are constants.

The numbers and letters are all randomised.

Part of HELM Book 1.3

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

This is the simplest demonstration of the "code" part type I could think of: write Python to assign x = 1.

An alternative answer gives a hint if the student's code doesn't define x at all.

Students are shown a bar chart. There is a slider that adjusts the height of one of the bars. Students are asked to adjust the slider to make that particular bar value the mode.

Practice question simplifying fractions for integration by using partial fractions.

The purpose of this question is to ask the students to go through one Rijndael round from the AES algorithm.

Part of HELM Book 1.4.2

Factorise a quadratic, x^2+bx+c. An exam can choose whether or not a=1. Part of HELM Book 1.3

Factorise a quadratic, ax^2+bx+c. An exam can choose whether or not a=1. Part of HELM Book 1.3

Factorise a quadratic. Part of HELM Book 1.3

Factorise a quadratic. Part of HELM Book 1.3

Explain why one variable is a factor but the other is not. Factorise the expression, whose factor is alphanumeric. Part of HELM Book 1.3

Factorise a 2-term expression where the gcd can be alphanumeric. Part of HELM Book 1.3

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

Expand (a+b)(c+d). a,b,c,d are random terms that can be +ve or -ve, and can consist of a number and/or a letter.

The answer must contain no brackets but will be accepted if it is not simplified from there.

Part of HELM Book 1.3

Factorise two algebraic terms that have a numerical gcd > 1. Part of HELM book 1.3

Factorise a 2-term expression by pulling out a numeric gcd. Part of HELM Book 1.3

Factorise a+bk where a and b are non-coprime integers, and k is a letter. Part of HELM Book 1.3.4

Expand something like a(b+c) or (b+c)a or a(bc), where a, b and c can be +ve or -ve expressions. Part of HELM Book 1.3

Expand a binomial. Part of HELM Book 1.3

In parts (a) and (b) rearrange linear inequalities to make $x$ the subject.

In the parts (c) and (d) correctly give the direction of the inequality sign after rearranging an inequality.

Shows how to retrieve the student's answer to another part from a custom marking script.

No description given

Shows how to retrieve the student's answer to another part from a custom marking script.

Removing brackets from expressions of the form (a+b)(c+d). Part of HELM Book 1.3