Calculate the hypotenuse of a right triangle, given the other two side lengths.

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

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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 $(c,d)$.

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A small sequence of questions on calculating percentage increases and decreases. Moving from percentages of 100, to percentages of some random whole number, and onto calculating percentage changes in applied financial situations.

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This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
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$A$ 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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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 $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Solving inequalities that involve a quadratic and where the right-hand side is 0.

Solving inequalities that involve a quadratic and where the right-hand side is not 0. 

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

Draws a triangle based on 2 angles and a side length.

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

Given two propositions in mathematics using quantifiers, choose the corresponding negation of the proposition. For example, the negation of: $\displaystyle \exists a \in \mathbb{R^+},\;\exists b \in \mathbb{N},\;\exists c \in \mathbb{N}\;\left[(c \lt b+1) \land \left(\frac{1}{2^n} \geq 3a\right)\right]$

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

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 $(c,d)$.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.