Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

First part: Express  $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d},\;a=-c$. Numerator is an integer.

Second part: $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d}+ \frac{r}{sx+t}$ as single fraction 

First part: express as a single fraction: $\displaystyle \frac{a}{x + b} +  \frac{c}{x + d},\; a \neq -c$.

Second part: Find $\displaystyle \frac{a}{x + b} + \frac{c}{x + d}+\frac{r}{x+t}$ as a single fraction.

First part: express as a single fraction: $\displaystyle \frac{a}{px + b} +  \frac{c}{qx + d}$.

Second part: Find $\displaystyle \frac{a}{px + b} + \frac{c}{qx + d}+\frac{r}{sx+t}$ as a single fraction.

Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{x + b} +\frac{c}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{x + b} +\frac{cx+d}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

Contains a video in Show steps.

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

Find minimum distance between a point and a line in 3-space. The line goes through a given point in the direction of a given vector.

The correct solution is given, however the accuracy of 0.001  is not enough as in some cases answers near to the correct solution are also marked as correct.

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

Minitab was used to fit both an AR(1) model and an AR(2) to a stationary series. A  table is given summarising the results obtained from Minitab. Choose the most appropriate model and make a forecast based on that model.

Four questions on finding least upper bounds and greatest lower bounds of various sets.

Minitab was used to fit an AR(1) model to a stationary time series. Given the output answer the following questions about the model and use the model to make forecasts.

Asking users to interpret a minitab output to give the coefficients of a multiple regression together with a prediction based on the subsequent equation.

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

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

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.

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 $(x=1)$.

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Given five fractions, identify the one which is not equivalent to the others by reducing to lowest terms.