A particle is projected up a rough plane at a given speed. Given the angle of the slope and the coefficient friction, find the distance the particle travels before it comes to instantaneous rest.

A block of given mass is sits on a flat plane with defined static and kinetic friction values. Randomly, it does one of two things, it is either:

1) pushed with enough force to start it moving - calculate the force on the block or the static friction.

2) moving over a distance - calculate the work done or the kinetic friction

(are these uneven calculations)

A block of given mass is sits on a flat plane with defined static and kinetic friction values. Randomly, it does one of two things, it is either:

1) pushed with enough force to start it moving - calculate the force on the block or the static friction.

2) moving over a distance - calculate the work done or the kinetic friction

(are these uneven calculations)

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

Given an oracle function that will output its value given an input: first estimate the derivative, and second calculate its shape.

Given an oracle function that will output its value given an input: first estimate the derivative, and second calculate its shape.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

No description given

Given th original formula the student enters the transformed formula

READY TO USE

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Approximating integral of a quadratic by Riemann sums . Will include an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Express the equation of the given line in the form $y=mx+c$.

Express the equation of the given line in the form $y=mx+c$.

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Given polynomial $f(X)$, $g(X)$ over $\mathbb{Q}$, find polynomials $q(X)$ and $r(X)$ over $\mathbb{Q}$ such that $f(X)=q(X)g(X)+r(X)$ and $\operatorname{deg}r(X) \lt \operatorname{deg}g(X)$.

Questions testing understanding of numerators and denominators of numerical fractions.

Find the equation of the straight line perpendicular to the given line that passes through the given point $(a,b)$.

No description given

Implicit differentiation.

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

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$. The object starts from rest. Find its maximum speed. 

English sentences are given and for each the appropriate proposition involving quantifiers is to be chosen. Also choose whether the propositions are true or false.

English sentences are given and for each the appropriate proposition involving quantifiers is to be chosen. Also choose whether the propositions are true or false.

Given two propositions in mathematics using quantifiers, choose the corresponding negation of the proposition. For example, the negation of: $\displaystyle \exists a \in \mathbb{R^+},\;\exists b \in \mathbb{N},\;\exists c \in \mathbb{N}\;\left[(c \lt b+1) \land \left(\frac{1}{2^n} \geq 3a\right)\right]$