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

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Simple Definite Integrals

Simple Definite Integrals

Simple Definite Integrals

Simple Definite Integrals

Simple Definite Integrals

Ask for the square of each number from 0 to 15, in random order.

The shuffle function puts a list in random order.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Calculate the cube roots of a complex number using De Moivre.

Calculating the square root of a complex number using De Moivre.

Calculating complex numbers raised to an natural number exponent

Euler's identity \(e^{j\theta}=cos(\theta)+jsin(\theta)\)

modulus & argument of a complex number

Complex number multiplication & division

Differential equations.

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Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

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Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^3-y^3$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Partial Fractions

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Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.

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 $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Given the pdf  $f(x)=\frac{a-bx}{c},\;r \leq x \leq s,\;f(x)=0$ else, find $P(X \gt p)$, $P(X \gt q | X \gt t)$.

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Tests the ability to match a quadratic function to a given parabola.

multiple choice testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees