This question asks the student to interpret a JSXGraph diagram to write three vectors in terms of the base vectors. Each vector has both a horizontal and vertical component. Further parts ask the student to add vectors and find a magnitude. 

Find angular speed and reaction force of a swinging pendulum.

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Linear combinations of $2 \times 2$ matrices. Three examples.

Linear combinations of $2 \times 2$ matrices. Three examples.

Cofactors Determinant and inverse of a 3x3 matrix.

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Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

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Integrate Paris Law equation to estimate life to failure.

This is a diagnostic test - we use it to determine where extra mathematical help is needed for the class as a whole and where you get to see specific areas where you may need to work on your mathematical skills. The diagnostic test DOES NOT count in any way towards your first year grade.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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