Given the moment of inertia of an area about an arbitrary axis, find the centroidal moment of inertia and the moment of inertia about a second axis.

This question relies on using information in the pie chart to find a ratio.

These questions focus on finding a ratio (or fraction) from the information given.

Implicit differentiation.

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

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Implicit differentiation.

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

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

Finding the stationary points of a cubic with two turning points

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Given vector $\boldsymbol{v}$  find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.

Given vector $\boldsymbol{v}$  find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.

Find the size of a matrix.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Not randomized because it's the same as in our workbook. But the variables are made in a way that it should be easy to randomise the size of the matrix, and the to change the formula for the input in not too many places.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

Asking the student to create examples of two matrices which multiply to zero but are not themselves the zero matrix. Then getting the student to think about some features of these examples.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

Find the determinant of a $3 \times 3$ matrix.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

rebelmaths

Lets a student practice finding percentage changes.

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

Given an ascending sequence of numbers, finds the index in the sequence of the first number greater than or equal to a given value.

indefinite integration

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

rebel

rebelmaths

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Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Find an interior angle and length of a diagonal of a random parallelogram.

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.