Multiplication of  matrices of different sizes.

Simplifying indices.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Simplifying indices.

Solve a quadratic equation by completing the square. The roots are not pretty!

Rearrange equations to make $x$ the subject. 

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rearranging the Michelas-Menten equation to make the substrate the subject.

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Decimal Places and Significant Figures

rebelmaths

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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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

Calculating particular harmonic components of a Fourier series expansion.

Several quadratics are given and students are asked to factorise them.

Introductory exercise about subsets using custom grading code.

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Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Use the quotient rule to differentiate various functions.

Use the product rule to differentiate various functions.

Practice using the log rules to add and subtract logarithms

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

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.