Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$. Find time to maximum height and the maximum height. Now includes an interactive plot.

Given the original price of a smartphone and the rate at which it decreases, calculate its price after a given number of months. In the second part, calculate the time remaining until the price goes below a certain point.

Multiplication of $2 \times 2$ matrices.

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Hello! This test an extra opportunity to complete some practice questions on the material we have covered so far. Your results will NOT count towards your final grade, and there is no time limit to complete the test. You can check your answers as you go along, and even try new examples of the same type. Full solutions are also available for most questions. If there are any questions you don't understand, take a photo and we can discuss it in class or at a one-to-one appointment. 

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other. 

A probability question

Linear combinations of $2 \times 2$ matrices. Three examples.

Linear combinations of $2 \times 2$ matrices. Three examples.

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

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Students are given a word problem with the distance travelled and the time taken by a cyclist. They need to choose the correct form for the linear equation, compute the gradient, and plot the line.

The distance travelled and time taken are randomised.

Speed, distance and time are all integer values.

Students need to substitute a value into an equation and solve it. The equation constant (gravity) and the value (time) are both randomised.

Nursing question. Calculate drip rate in drops per minute if there are 20 drops per minute. Time given in minutes.

Nursing question. Calculate drip rate in drops per minute if there are 20 drops per minute. Time given in minutes.

Converting between metres (m) and centimetres (cm). 

This question is a simple example to show how to input value from numbas to geogebra applet, and get a value back from geogebra to numbas for marking.

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. 

Find eigenvalues and eigenvectors of $A$ $2 \times 2$ matrix.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Find the determinant of three $2 \times 2$ invertible matrices.

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

Inverse and division of complex numbers.  Four parts.

Multiplication of complex numbers. Four parts.

Questions which try to emphasise that f(x) does not mean f times x.

Nursing question. IV question. Given volume and flow rate what time will is take for the bag to run dry? Student have to round to the nearest quarter of an hour.

- David Sherwood didn't think this was a question that should be asked