Use $\cos^2\theta+\sin^2\theta=1$ and/or an understanding on the unit circle definitions to determine $\sin\theta$ given $\cos\theta$ and the quadrant theta is in.

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

Given a randomised log function select the possible ways of writing the domain of the function.

Given a randomised rational function select the possible ways of writing the domain of the function.

A block of given mass is sliding down the plane, with given acceleration or a given coeff-of-friction. Find the normal reaction force, the parallel force and the missing value of a and mu.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

In this question the students are given the public and private keys for El Gamal through Elliptic Curve and a message to decrypt. They have to decrypt the message.

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

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

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.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

A quartic is given and the student is asked whether the gradient is positive or negative at various values of x.

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

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given. 

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given a proportion of students who DO speak a language other than English at home, and are asked to find the percentage who do NOT. The fraction denominator is either 20 or 25, and the numerator is randomised.

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.

Given either (a) ax+bx+cy+dy, or (b) ax^2+bx+c, (c) ax^2+bx^2+cx^2, where a,b,c,d are randomised constants, and x and y are randomised letters, simplify by collecting like terms (if possible).

Part of HELM Book 1.3

Given an expression in one or two variables, with two or three terms, collect like terms, if possible. Part of HELM Book 1.3

State if a function is increasing at given points or on given intervals

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Given an expression 10^-k, rewrite it as a fraction with no index. k is a random positive integer from 1 to 6.

Part of HELM Book 1.2

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Given an arbitrary polynomial, identify its degree. Part of HELM Book 1.2

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Recovering original function given some information such as derivative and value at some point.

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.