Calculating the integral of a function of the form $a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of integrals. 

Calculating the derivative of a function of the form $a \ln(bx)$ using a table of derivatives.

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

A question which asks students to encrypt a number using RSA, then to factor a small public key and find the decryption exponent.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

rebelmaths

The subtraction algortihm using the borrow and pay back method with integers.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

Determine the moment of a force about a point by using $M= F d_\perp$ or $M = F_\perp d$.

Homework set.  Find 2-D moments or balance moments using Verignon's theorem:  $ M = \pm F_x d_y \pm F_y d_x$

Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

HELM Book 1.5.1: using formulae and substitution: task 1

Shows how to switch to the 3D graphics view of a geogebra applet using an extension function.

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

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

Two dimensional particle equilibrium problem.  Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

The student must write code to compute the standard deviation of an unknown list of measurements.

The suggested answer uses numpy.std.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. NC = Non-Calculator strand. Students are shown an image of a thermometer calibrated in degrees Celsius. Student must answer a question using the thermometer. The image is randomly selected from a pool of 4. There are two different potential questions for each thermometer. Hence 8 different questions in total.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. NC = Non-Calculator strand. Students are shown an image of a thermometer calibrated in both degrees Celsius and degrees Fahrenheit. Student must answer a question using the thermometer. The image is randomly selected from a pool of 3. There are two different potential questions for each thermometer. Hence 6 questions in total.

rebelmaths

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Practice question solving linear homogeneous second order differentials using the auxiliary equation method.

Practice question simplifying fractions for integration by using partial fractions.

A straightforward test of encrypting and decrypting an eight-letter message with the Vigenère Cipher using a four-letter key.  Message letters are generated uniformly at random from the English alphabet, as are the key letters.  Students are expected to be able to map English letters onto elements of $\mathbb{Z}_{26}$ in the usual order.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.