Blathnaid Sheridan

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

This quiz contains questions on functions, limits, logs, exponential functions, simultaneous equations and quadratic equations.

Questions on powers, the laws of indices, and exponential growth.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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First- and second order recurrence equations, homogenous and nonhomogenous

Solving three simultaneous congruences using the Chinese Remainder Theorem:

\[\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*} \] where $\operatorname{gcd}(n_1,n_2,n_3)=1$

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

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Find the gcd $d$ of two positive integers $a$ and $b$ also find integers $x,y$ such that $ax+by=d$, using the extended Euclidean algorithm.

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find  $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

Questions on differentiating with the chain rule and product rule.

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

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Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

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

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Real life problems with differentiation

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

8 questions on the quotient rule in differentiation.

8 questions on the quotient rule in differentiation.

8 questions on the quotient rule in differentiation.

Practice dividing polynomials using the long division method.

Questions about logical predicates, and basic set theory concepts.

Questions about logical predicates, and basic set theory concepts.

4 questions. Qualitative, quantitative random variables, types of sampling, frequencies, stem and leaf plot, descriptive statistics.

Questions about logical predicates, and basic set theory concepts.

Calculations in $\mathbb{Z_n}$ for three values of $n$.