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Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

Demonstrates how to create variables containing LaTeX commands, and how to use them in the question text.

This quiz is designed to help you practise your integration techniques.

Improvements needed:

• Add some definite integrals to Q2
• Use different variables

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$. 

3 questions. Finding the stationary points of functions of 2 variables.

Partial differentiation.

Converting integers from one base to another. The numbers are non-variable.

Shows how to define variables to stop degenerate examples.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

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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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Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Linear equations, simultaneous linear equations in two variables

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rebelmaths

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

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Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Demonstrates how to create variables containing LaTeX commands, and how to use them in the question text.

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

Shows how to define variables to stop degenerate examples.

This exercise will help you rearrange a linear equation to find the value of a given variable

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This exercise will help you rearrange a linear equation to find the value of a given variable

Shows how to define variables to stop degenerate examples.

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.

Shows how to define variables to stop degenerate examples.

Calculate the expression $\frac{12}{4}a+\frac{3}{5}a$. One of the following is not correct, which one?

Seven standard elementary limits of sequences. 

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

3 questions. Finding the stationary points of functions of 2 variables.

Partial differentiation.

These basic questions will help you expand one set of brackets for linear variables