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.

Calculate the dot products of (a) two 2D vectors and (b) two 3D vectors.

This creates a 4x4 times table grid using numbers from 2 to 9. The step gives some advice on how to work out times tables (products, multiplications) if you can't remember them.

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Simplify a fraction where the numerator and denominator are factorised and have common products, and one of the common factors is powered. Part of HELM book 1.4

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Demonstration of randomisation: many elements in this question are randomised. The names of the products and clients are randomly chosen, as are the prices and order amounts.

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.

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.

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Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

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Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

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Some more questions on set theory - covering set builder notation, cartesian products, complements.

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Expanding products of 3 linear  polynomials over $\mathbb{Z}_3,\;\mathbb{Z}_5,\;\mathbb{Z}_7$

Simplify fractions involving the products of factorials.

How to input x^2 and x*y.

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

This creates a 4x4 times table grid using numbers from 2 to 9. The step gives some advice on how to work out times tables (products, multiplications) if you can't remember them.