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Precedence of operators - everything except brackets
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Question by Newcastle University Mathematics and Statistics

Questions testing understanding of the precedence of operators using BIDMAS applied to integers. These questions only test IDMAS. That is Indices, Division/Multiplication and Addition/Subtraction.
Precedence of operators - everything except indices
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Question by Newcastle University Mathematics and Statistics

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.
Pigeonhole principle - greatest number of people with birthdays in the same month,
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Question by Newcastle University Mathematics and Statistics

No description given
Quotient rule - differentiate exponential over exponential
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Question by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$ . Find $p$ .
Quotient rule - differentiate linear over quadratic
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Question by Newcastle University Mathematics and Statistics and 1 other

The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$ . Find $g(x)$ .
Quotient rule - differentiate linear over square root
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Question by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$ . Find $g(x)$ .
Quotient rule - differentiate quadratic over quadratic
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Question by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$ . Find $g(x)$ .
Quotient rule - differentiate quotient of linear terms
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Question by Newcastle University Mathematics and Statistics

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$ . Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$ .
Simple combinations,
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Question by Newcastle University Mathematics and Statistics

Two shops each have different numbers of jumper designs and colours. How many choices of jumper are there?
Polar form of a complex number
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Question by Newcastle University Mathematics and Statistics and 1 other

Polar form of a complex number.
Principle value of a complex number
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Question by Newcastle University Mathematics and Statistics

Calculate the principal value of a complex number.
Roots of a quartic real polynomial
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Question by Newcastle University Mathematics and Statistics

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.
Second order ODE with constant coefficients and boundary conditions
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Question by Newcastle University Mathematics and Statistics

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .
Separable first order ODE with boundary condition
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Question by Newcastle University Mathematics and Statistics

Solve for $x(t)$ , $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
Solve a second order ODE with repeated roots,
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Question by Newcastle University Mathematics and Statistics and 1 other

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example).
Taylor series (three terms)
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Question by Newcastle University Mathematics and Statistics

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
Divide Polynomials
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Question by Newcastle University Mathematics and Statistics

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.
Probability, expectation and standard deviation of binomial distribution
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Question by Newcastle University Mathematics and Statistics

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.
Probability, expectation and variance of exponential distribution
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Question by Newcastle University Mathematics and Statistics

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.
Probability, expectation and variance of uniform distribution
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Question by Newcastle University Mathematics and Statistics

Exercise using a given uniform distribution $X$ , calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$ .
Rearrange linear equations to find value of an unknown
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Question by Newcastle University Mathematics and Statistics

Finding the value of a variable
Simplify logarithms
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Question by Newcastle University Mathematics and Statistics

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$ . Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$
Simplifying fractions
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Question by Newcastle University Mathematics and Statistics

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$ .
Solve a pair of simultaneous equations
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Question by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Solve an equation in logarithms
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Question by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$ .

Make sure that your choice is a solution by substituting back into the equation.
Solve an equation with a reciprocal
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Question by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solving equations
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Question by Newcastle University Mathematics and Statistics

Solve $\displaystyle ax + b = cx + d$ for $x$ .
Solving equations
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Question by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$
Substitute a value into an expression
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Question by Newcastle University Mathematics and Statistics

What is the value of the expression given a choice of n?
Solve linear equations in the rationals and Z_n
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Question by Newcastle University Mathematics and Statistics

Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$ .

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