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The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

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Simplifying an expression of the form $\frac{a^4b^3}{\sqrt{a^4b^2}}$ to $a^2b^2$, for integers $a$ and $b$.

Simplifying an expression of the form $a^3 \times (a^4)^{1/2}$ to $a^5$, where $a$ is an integer. 

Using indices rules to rewrite an expression from $\left(\frac{a^n}{b^n}\right)^{-1/n}$ to $\frac{b}{a}$.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $\frac{1}{b}$, for integers $a$, $b$, $m$ and $n$.

Simplifying expressions from $\left(\frac{x^m}{x^n}\right)^p$ to $x^{(m-n)p}$.

Simplifying expressions from $(ax^n)^m$ to $a^mx^{mn}$, where $a$, $m$ and $n$ are positive integers.

This question demonstrates how to use GeoGebra applets in explore mode.

The student must construct a polygon by adding points one at a time. At any point, they can answer the question, "Is the centroid inside the polygon?"

GeoGebra's IsInRegion command is used to decide if the centroid is inside the polygon.

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This exam collects some questions demonstrating different uses of the programming extension and the Code part type, to mark code written in Python and R.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

The student is asked to integrate a given function. The marking algorithm differentiates the student's answer, and checks that it is equivalent to the original function.

Evaluación de un polinomio

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Obtener el grado del resto de la división de polinomio

Aplique el teorema del factor para verificar cuáles de una lista de polinomios lineales son factores de otro polinomio.

Questions on Vector Calculus

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Encuentra la ecuación de la línea recta que pasa por los puntos $ (a, b) $ y $ (c, d) $.

These practice questions can help you revise basic mathematical concepts needed to succeed when studying STEM programs.

Natural numbers addition algorithm. 2 and 3 digit numbers. Carrying.

Decimals addition algorithm. 2 and 3 digit numbers. Carrying.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

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Questions on probability including tree and Venn diagrams