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

The suggested answer uses numpy.std.

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.

Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

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

No description given

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

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

A quick practice set of problems for education students to take in preparation for their numeracy test.

This question tests the student's ability to solve Linear Programming problems by hand using the Simplex Method.

This question tests the student's ability to solve Linear Programming problems by hand using the Simplex Method.

Solving binary optimisation problems using Computational Packages

Solving continuous optimisation problems using Computational Packages

Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised positive numbers.

Part of HELM Book 1.2

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

An order of operation question using +,-,* with signed integers, with up to 4 variables.

The questions are the exercises from Q3 of HELM Book 1.1.5

Simplify three expressions: (a^b)^c, a^b * a^c, a^b/a^c where a, b and c are randomised. a is a letter, and b and c are rational numbers.

Part of HELM Book 1.2

Given an expression 10^-k, rewrite it as a fraction with no index. k is a random positive integer from 1 to 6.

Part of HELM Book 1.2

Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised and can be positive or negative numbers.

Part of HELM Book 1.2

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Part of HELM Book 1.1

Part of HELM Book 1.1

Using indices rules to rewrite an expression from $\left(\frac{a^n}{b^n}\right)^{-1/n}$ to $\frac{b}{a}$.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $\frac{1}{b}$, for integers $a$, $b$, $m$ and $n$.

An experiment using a PhET applet. The student can attach masses of different weights to a spring, and is asked to measure and record how far it stretches. Their measurements are shown on a graph, and they're asked to estimate the formula for the length in terms of the mass.