Several questions on expanding double brackets

Expand two brackets involving powers of $x$.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Use double angle an pythagorean identities to manipulate before integrating.

Using double angle and pythagorean identities (2 parts)

Divisor is double digit. There is a remainder which we express as a fraction. 

Nice easy case except divisor is a double digit. There is no remainder. 

Expand two brackets involving powers of $x$.

Expanding two linear brackets multiplied together.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

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Double integral in polar coordinates - concentric circles

Draw the annulus given by a double inequality. The user moves circles on an interactive jsxgraph.

set of exercises on double and triple integrals

Nice easy case except divisor is a double digit. There is no remainder. 

Divisor is double digit. There is a remainder which we express as a fraction. 

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Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

3 Repeated integrals of the form $\int_a^b\;\int_c^{f(x)}g(x,y)\;dy \;dx$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;\int_0^{x^{m-1}}mf(x^m+a)dy \;dx$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Two cube-shaped flowerpots are shown, and their lengths given. The larger pot is either double or triple the length of the smaller pot. Students must work out the volume of the larger pot given the smaller one. There are eight potential questions.

Given an equation of the form $T=T_0 e^{kt}$ to model temperature, calculate the temperature after a given time, the time taken to reach a certain temperature, and the time taken for the temperature to double.

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Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

This test checks that students understand the principles of double entry bookkeeping