Manipulation of an exponential function

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

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 $y_i-x_i,\;i=1,\dots 5$.

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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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 $y_i-x_i,\;i=1,\dots 5$.

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Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a right hyperbola.

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Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

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Find the gcd $d$ of two positive integers $a$ and $b$ also find integers $x,y$ such that $ax+by=d$, using the extended Euclidean algorithm.

Integration by Substitution

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Definite Integrals

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

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Definite Intgerals

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Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

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5 questions on indefinite integration. Includes integration by parts and integration by substitution.

Antiderivatives

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Finding the stationary points of a cubic with two turning points

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Differentiating the natural logarithm

Some questions which use JSXGraph to create interactive graphics.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Differentiating the natural logarithm

Differentiating further exponentials

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.