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

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Integration by Parts

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Integration using partial fractions

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Draws a triangle based on 3 side lengths.

Another transposition question, which requires (basic) factorisation.

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Scores  in 20 games and frequency given -- calculate mean.

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Scores  in 20 games and frequency given -- calculate mean.

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Another transposition question, which requires (basic) factorisation.

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Quiz covering basic arithmetic with complex numbers and solving roots for a quadratic with complex solutions

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

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Simple Percentages

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Finding the cost including VAT

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

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Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

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A student selects a card from a deck of 52 and rolls a dice once.

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When throwing a dice once what is the probability of ....

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Multiplication and addition of complex numbers. Four parts.

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.

Factorising algebraic expressions

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Currency Conversion

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

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

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

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