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Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.

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

Missing: Application with bacteria, turning points, difficult chain rule

A 2D linear programming problem: optimise the profit from producing two different kinds of product, which both use the same limited resources.

A JSXGraph diagram illustrates the problem and can be used to find an answer.

Integrate the product of two functions by the method of integration by parts.

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Differentiate $f(x) = x^m(a x+b)^n$.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Differentiate $x^m\cos(ax+b)$

Differentiate $ \sin(ax+b) e ^ {nx}$.

Using the chain rule within product rule problems

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Matrix multiplication. Contains a function that will let you print the calculation steps of matrix multiplication, e.g. in the Advice.

checking by size whether two matrices can be multiplied. Student either gives size of resulting product, or NA if matrices can't be multiplied.

checking by size whether two matrices can be multiplied. Student either gives size of resulting product, or NA if matrices can't be multiplied.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

Student can choose one of all possible matrix products from the matrices given. Meant for voluntary extra practice. No extensive solutions: referred to other questions for this.