Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

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 particle is in equilibrium on an incline. Four forces are acting on it. You're given the angle of the incline and three forces. Resolve the forces to find the angle and magnitude of the other force.

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

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Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax

Using Pythagoras' theorem to determine the hypotenuse, where side lengths include surds and students enter using sqrt syntax

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

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.

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Given the graph of the line determine the equation of the line.

Students will locate and write the equation for the axis of symmetry of a quardatic function from graph.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Given three vectors with integer components, find the corresponding magnitude and direction.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Directional derivative of a scalar field.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.