English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

English sentences are given and for each the appropriate statement involving quantifiers is to be chosen. Also choose whether the statements are true or false.

Quotient and remainder, polynomial division.

a) Given a recursively defined sequence $t(n)$, find $t(n)$ as a function of $n$.

b) Given a sequence $s(n),\;n \in \mathbb{N}$, find a recursive definition of $s(n)$

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$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

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Quotient and remainder, polynomial division.

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Given sentences involving propositions translate into logical expressions.

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

Various questions on predicates and sets.

Paired t-test to see if there is a difference between responses after treatment.

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Split $\displaystyle \frac{b}{(cx + d)(px+q)}$ into partial fractions.

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Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

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Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

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