Find the sum of the first n terms of a Geometric progression

Find the nth term of a Geometric progression

Find the sum of the first n terms of an arithmetic progression

Find the nth term of an Arithmetic progression

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

Given a table of data, calculate the mean, mode and median, and complete a frequency table.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

rebelmaths

Find the determinant of a $3 \times 3$ matrix.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Find roots and the area under a parabola

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Find the nth term of an Arithmetic progression

Find the solution of a first order separable differential equation of the form $(a+y)y'=b+x$.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

For a sample of size n from a normal distribution and given the mean of the sample and the standard deviation of the distribution, find the MLE for the mean. Also the expected information and a confidence interval for the mean.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

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.

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A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

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

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.