Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

Shows how to define variables to stop degenerate examples.

Shows how to define variables to stop degenerate examples.

Shows how to define variables to stop degenerate examples.

Shows how to define variables to stop degenerate examples.

Crear una tabla de verdad para una expresión lógica de la forma :

                $( a \ {op1} \ b) \ {op2} \ (c \ {op} \ d) \ {op4} \ e $

donde cada una de $a, \; b, \; c, \; d, \; e, \; f $ puede ser una de las variables booleanas $ p, \; q, \; \neg q, \; \neg p $ y cada uno de los operados $\{op}$  puede ser uno de los operadores $\lor, \; \land, \; \to$.

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

A simple ideal gas law question, using number of molecules, that asks the student to calculate one of the four variables. he question can ask for either L atm, or kPa m3, and either K or C for temp. As such the boltzmann constant is in either J/K or L atm/K.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. SP = Statistics & Probability strand.This question provides a list of data to the student. They are asked to find the difference between the mean and the median. This question was based on a Newcastle Uni question which also asked the mode, hence the surplus legacy variables (too tricky to delete).

This question demonstrates how to use the "Download a text file" extension to create a link to download a file containing text created from question variables.

Exercises in solving simultaneous equations with 2 variables.

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

Finding probabilities using the Poisson distribution.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

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

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Choosing whether given random variables are qualitiative or quantitative.

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

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Finding areas under graphs using definite integration.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.