A block of given mass is sliding down the plane, with given acceleration or a given coeff-of-friction. Find the normal reaction force, the parallel force and the missing value of a and mu.

A measurement is performed multiple times for the same object, the student will

• calculate the mean result
• calculate the standard error on the mean 
• write the mean±error to the correct precision as defined by the error written to 1 significant figure 

Advice is provided including on performing the calculations in Python or spreedsheets together with further reading. 

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.

A straightforward test of encrypting and decrypting an eight-bit message with the Vernam Cipher.  The message and the key are uniform and independently generated eight-bit strings.

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

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

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

DCS 2023 Maths Entrance Test to be used September 2023

1.5 hours with 3 randomised questions from each of these groups:

• Notation and Algebra
• Calculus - Differentiation
• Calculus - Integration
• Trigonometry

More difficult trigonometric equations with radians

Calculation of max design capacities of reinforced concrete beams with and without shear links

This question asks students to solve a discrete logarithm problem with Pollard's rho algorithm as exposed in the book "introduction to cryptography with open source software" by McAndrew.

Solving a pair of linear simultaneous equations with integer solutions.

The purpose of this question is to ask students to decrypt a message encrypted with a Hill cipher.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of amodulus function with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a polar function with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a modulus function with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Given an expression in one or two variables, with two or three terms, collect like terms, if possible. Part of HELM Book 1.3

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 (a^k1*a^k2)/(a^k3*a^k4) where a is a randomised variable and k1,k2,k3 and k4 are randomised fractions (k2 and/or k4 may be 0). They may be written in index form or in surd form, or even a combination of the two.

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