Inverse and division of complex numbers.  Four parts.

Multiplication of complex numbers. Four parts.

Differentiate

\[ \sqrt{a x^m+b})\]

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

The student is asked to enter an approximation to $\sqrt{n}$, where $n$ is not a square number, to 20 decimal places.

This question is a demonstration of the high precision arithmetic in Numbas v4.

The student is asked to give the Avogadro constant in scientific form, calculate the mass of a number of moles of carbon, in grams, and then calculate the number of molecules in that mass.

This is a demonstration of the high-precision decimal arithmetic in Numbas v4.0.

The student must calculate the number of digits a given decimal number would have when written in a different base. Alternative answers catch some common mal-rules and give appropriate feedback.

Based on table 2 from "diagnosing student errors in e-assessment questions" by Philip Walker, D. Rhys Gwynllyw and Karen L. Henderson.

Given some numbers in standard index form, convert to decimal form.

Welcome the the first stats quiz! It's very short. 

• You have 25 minutes.
• There are 3 questions (with parts). The topics are measures of central tendency and measures of spread.
• Enter all of your answers and keep 2 decimal places. 
• Submit them as you go to make sure you don't carry mistakes. You can't change your answer once you've submitted it.
  

Write down on a sheet of paper the data you are given, along with your detailed calculations. Submit a picture on google classroom. 

Let me know if you have any questions!

Good luck!

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Given sum of sample from a Normal distribution with unknown mean $\mu$ and known variance $\sigma^2$. Find MLE of $\mu$ and one of four functions of $\mu$.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Converting odds to probabilities.

Find $\displaystyle\int \frac{ax^3-ax+b}{1-x^2}\;dx$. Input constant of integration as $C$.

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$. Enter the constant of integration as $C$.

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$. Enter the constant of integration as $C$.

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $ 

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

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

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

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given subset $T \subset S$ of $m$ objects in $n$ find the probability of choosing without replacement $r\lt n-m$ from $S$ and not choosing any element in $T$.