Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Elementary examples of multiplication and powers of complex numbers. Four parts.

A question to test basic differentiation of functions, including powers of x, trig, log and exponential functions.

This question provides practice at differentiating polynomials.

Introductory exercise about power sets.

Find modulus and argument of two complex numbers.

Then use De Moivre's Theorem to find powers of the complex numbers.

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

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Although the statement has 4 power stations and 3 pits, when the question is run sometimes 3 power stations are given and sometimes 4 pits.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA

Power series solution of $y''+axy'+by=0$ about $x=0$.

Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$. Find least integer $N$ s.t.  $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$

$\displaystyle \int \frac{bx+c}{(ax+d)^n} dx=g(x)(ax+d)^{1-n}+C$  for a polynomial $g(x)$. Find $g(x)$.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Information on inputting powers

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.

Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient.

Round some large integers to the a given power of ten.

Questions on powers, the laws of indices, and exponential growth.

Fill in a table of powers of 10.

Introductory exercise about power sets.

Information on inputting powers

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). 

Using the chain rule with polynomials and negative powers

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