Algebra

Harder inequalities that involve terms like $\frac{1}{x}$ where multiplication by the denominator requires you to split into cases for positive or negative, or you multiply by the square of the denominator.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Solving inequalities that involve a quadratic and where the right-hand side is 0.

Solving inequalities that involve a quadratic and where the right-hand side is not 0. 

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Students seem to freak out when their answer is not written exactly the same as the answer provided. This question tries to enforce that $(x-y)=-(y-x)$ and $\frac{a-b}{c-d}=\frac{b-a}{d-c}$

Multiply two algebraic fractions (unfortunately their appearance doesn't really change) and cancel. 

Fractions don't have a common denominator. Need to find one. Addition and subtraction 50:50 split.

Fractions already have a common denominator. Addition and subtraction 50:50 split. Students shouldn't have to worry about reducing fractions by design.

A whole number divided by a very simple algebraic fraction. No cancelling is required by design.

A very simple algebraic fraction multiplied by a whole number. No cancelling is required by design. 

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A simple algebraic fraction dividing by another. Cancelling is recommended.

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