Selection of questions on substituting values into simple expressions

Substituting a values of $x$ and $z$ into $\frac{ax+bz}{c}$

Substituting a values of $x$ and $z$ into $a(x+z)$

Substituting a values of $x$ and $z$ into $ax+bz$

Substituting a value of $x$ into $ax+b$

Substituting a value of $x$ into $x^2$ or $x^3$.

Substituting a value of $x$ into $x/a$.

Substituting a value of $x$ into $ax$

Substituting a value of $x$ into $x+a$.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Collecting like terms, expanding a bracket (distributive law), substitution of values, finding factors, simplifying algebraic fractions.

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.

Substitute values into an algebraic expression and calculate the result.

Simple substitution into an algebraic expression. Includes powers, division, mulitplication, brackets.  Includes subscripts.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 2 with parts' by Joshua Boddy.

This shows how to define a list of LaTeX strings, and pick a couple of them at random to display.

The "JSON data" type is used to define the available strings, so they're automatically marked as "safe" and curly braces aren't interpreted as variable substitution.

HELM Book 1.5 Formulae and substitution exercises.

HELM Book 1.5.1: using formulae and substitution: task 1

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

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.

Calculating the integral of a function of the form $4ax(ax^2+b)^n$ using integration by substitution.

Use a substitution to simplify an integral.

Integration by susbtitution. Use the letter C for the constant.

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

Calculating the integral of a function of the form $2ax(ax^2+b)^n$ using integration by substitution.

Calculating the integral of a function of the form $x(ax^2+b)^n$ using integration by substitution.

Calculating the integral of a function of the form $kx e^{ax^2}$ using integration by substitution, where $k=2a$.

Calculating the integral of a function of the form $kx e^{ax^2}$ using integration by substitution, where $k=2na$.

Calculating the integral of a function of the form $n x e^{ax^2}$ using integration by substitution.

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.