Inverse and division of complex numbers.  Four parts.

Compute the experimental probability of a particular score on a die given a sample of throws, and compare it with the theoretical probability.

The last part asks what you expect to happen to the experimental probability as the sample size increases.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

Questions on powers, the laws of indices, and exponential growth.

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

Inverse and division of complex numbers.  Four parts.

Inverse and division of complex numbers.  Four parts.

The expression $p\Rightarrow q\Rightarrow r$ is ambiguous.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

Applied questions that could be done with modulo arithmetic.

Credits to : Ben Brown.

used under a CC-BY 4.0 licence. https://creativecommons.org/licenses/by/4.0/

This question tests the students ability to use the logarithm equivalence law to make x the subject of a given equation and to check which of a list of logarithmic expressions are equivalent to x.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

$A$ 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 $\left(I_3 | A^{-1}\right)$.

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$. 

$A$ 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 $\left(I_3 | A^{-1}\right)$.

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When throwing a dice once what is the probability of ....

rebelmaths

Given two ordered sets of vectors $S,\;T$ in $\mathbb{R^5}$ find the reduced echelon form of the matrices given by $S$ and $T$ and hence determine whether or not they span the same subspace.

A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

Gitt vektorene  $\boldsymbol{A,\;B}$, finn vinkelen mellom dem.

$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min? 

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

$I$ compact interval, $g:I\rightarrow I$, $g(x)=(x-a)(x-b)^2$. Stationary points in interval. Find local and global maxima and minima of $g$ on $I$. 

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

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

Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.