Taylor Approximation ofr $\cos(2x)$

Solving first order differentials by separation of variables.

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

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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-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.

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

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

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

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. 

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

Evaluating arithmetic operations, and the order of operations.

Students select the option which lists the four decimal weights of premature infants in order from smallest to highest.

This question was written by MESH (the Mathematics Education Support Hub) at Western Sydney University.

Students must match the decimals 0.1, 0.01 and 0.001 to their fraction equivalents. The order in which they appear is randomised but it is always the same three decimals.

All the answers in this question are equations. In order to mark each equation, Numbas needs to pick some values that satisfy the equation and some that don't, and check that the student's answer agrees with the expected answer.

Any equation with the same solution set as the expected answer will be marked correct.

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

This question is to practice order of precedence in mathematical expressions. 

Please use * for multiplication and / for division. 

Translating prefixes into orders of magnitude, e.g. kilo = 10^(3)

Stating orders of magnitude for real-world values, e.g. height of Everest, diameter of a atom.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

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. 

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