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Implication sign and 'if, then' construction.

Implication sign and 'if, then' construction.

poles of a transfer function

Gain & Phase of a transfer function

This question summarizes the definitions of surjective and injective, and applies them to prove the existance of an inverse.

Multiples, factors, lowest common multiples and highest common factors.

5 indefinite integrals containing exponential functions

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Solve $p - t < \text{or}> q$

These practice questions cover:

• resolving axial forces in a truss structure
• stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
• use of Mohr's circle for determining principal stresses for a 2D plane stress case
• calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses

Basic calculation of 3D stresses.

Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.

Deicde whether each of the described sets of data is drawn from a discrete or continuous distribution.

Deicde whether each of the described sets of data is drawn from a discrete or continuous distribution.

Deicde whether each of the described sets of data is drawn from a discrete or continuous distribution.

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Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Manipulation of algebraic fractions

Manipulation of algebraic fractions

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Draws a triangle based on 3 side lengths.

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Students seem to miss the fact that division is actually multiplication by the reciprocal or the inverse of multiplication. This question attempts to address that.

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

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Cos, Sin and Tan

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Find angle and side in a right angled triangle.

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Pythagoras' Theorem and naming sides of right angled triangle

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