Simple exercise in collecting terms in different powers of \(x\)

Expand two brackets involving powers of $x$.

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

Question Covering AC power and frquency response

Question Covering AC power and frquency response

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Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

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Most of the standard prefixes (not hecto, deca though), abbreviations, powers of 10, converting between prefixes for distance, capacity, mass.

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This question tests students' ability to use repeated squaring to perform modular exponentiation.  Moduli are random numbers between 30 and 70, the base is a number between 10 and 29.  To generate questions of approximately uniform difficult the exponent is taken to be 256 plus two smaller powers of 2. 

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Information on inputting powers

Using the chain rule with polynomials and negative powers.

Using the chain rule with polynomials and negative powers

More work on differentiation with fractional coefficients and powers