Two particles connected by a string which passes over a pulley at the top of an inclined plane. Find the acceleration of the masses and the tension in the string. Can not model the whole system as a single particle.

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 mass is hanging from a string, tethered to two points. A horizontal force applied to the mass holds it directly underneath one of the points. Given the magnitude of the force, find the tension in the string and the mass of the bag.

Three forces act on a particle. You're given the magnitude of one, and the directions of all three. Find the magnitudes of the other two forces.

A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.

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Applying trigonometry to find heughts and lengths.

Ball projected vertically within water of a swimming pool. Finding the acceleration, greatest height above the swimming pool floor reached, speed and time. Uses SUVAT equations and $F=ma$.

Finding Cosine and Tangent values for an angle if Sine value is given. 

Applying trigonometry to find heughts and lengths.

Finding domain and range of a given function. 

Finding the values which satisfy an inequality containing two linear factors. 

Finding values which satisfy an inequality.

Adding several rational functions.

Finding the derivative  of a simple polynomial function.

Find the equation of a straight line parrarell to a given straight line passes through a given point.

Find the domain of a function.

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

Give the student three points lying on a quadratic, and ask them to find the roots.

Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.

Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.

Find an integral by choosing a suitable substitution.

Using differentiation to find the tangent and normal to a line at a given point

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Given the vector equations of two straight lines, find the coordinates of the point of intersection

Given the vector equations of two straight lines, find the angle between them

$x_n=\frac{an^2+b}{cn^2+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$. Determine whether the sequence is increasing, decreasing or neither.