Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

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!

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Rearranging equations to change the subject

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, changes in position, distances are to be calculated.

Use the specific heat capacity of an object and the change in temperature to calculate the heat added to that object.

Uses Custom marking to allow partial credit for common student errors (mal rules).

Thermochemistry Revision Sheet Q 5

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

Double integrals (2) with numerical limits

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.

Four questions on finding least upper bounds and greatest lower bounds of various sets.

Find a regression equation given 12 months data on temperature and sales of a drink. 

Two factor ANOVA example

Paired t-test to see if there is a difference between times take in a task.

Simple probability question. Counting number of occurences of an event in a sample space with given size and finding the probability of the event.

Given sample data find mean, standard deviation, median, interquartile range,

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.

Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

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.

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

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find  $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.