Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

This question asks students to solve a discrete logarithm problem with Pollard's rho algorithm as exposed in the book "introduction to cryptography with open source software" by McAndrew.

These are some questions on graph theory, pulled from a module on groups and graphs.

Use your calculator to calculate a factorial between 5 and 11

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.

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Calculating the definite integral $\int_{n_1}^{n_2}ax^b dx$.

The purpose of this question is to test student's understanding of the Elliptic curves version of El Gamal encryption. It asks them to go through two steps: the publication of the public key, and the use of this public key to encrypt a message.

Solving a pair of linear simultaneous equations with integer solutions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

The purpose of this question is to ask students to decrypt a message encrypted with a Hill cipher.

Shows how to use the bin function to group data into equal-sized intervals.

Tests the ability to find the gradient and intercept of a straight line graph.

No description given

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

No description given

When are vectors $\boldsymbol{v,\;w}$ orthogonal?

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

No description given

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

No description given

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Given a graph of some function f, the student is asked for values of $f$ and its inverse. Function is cubic and invertible.

Given a graph of some line or curve - the student is asked about the nature of the map and whether it constitutes a function.

Given a graph of some line or curve - the student is asked about the nature of the map and whether it constitutes a function.