of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Find a regression equation.

Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

Also includes an updated SSE to see how the sum of the squares of the residuals varies with the regression line.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given two probabilities in ratio form, and are required to select the higher probability. There are 7 different versions of this question.

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Useful for students' revision. Assesses ability to apply the algorithms correctly. Question has randomised values.

Calculate the z-score and percentile of an observation. The question uses the random person extension.

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

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

Semi-worked example of solving simultaneous equations using matrices. Equation values are randomly generated. The student is walked through the steps needed to solve the equations.

This question is the one described in method 1 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

Students are given a line equation in the form y=mx+b and asked to graph it.

m and b are randomised.

The question is not auto-marked, students need to "reveal answers" to see a sample graph that they can compare to their own.

Students are given a word problem and are asked to construct a line equation, evaluate it at a given point, and graph the line.

The line parameters and the given point are randomised.

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.

A bill (for a random amount) is divided equally between a number of people.

Students evaluate the per-person cost for a random number of people.

They then complete a table showing the cost per person for various numbers of people.

Finally they are asked to identify the shape of the graph that represents this function. They are given 2 exponentials, a hyperbola and a line to choose from.

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

Students are given 2 equations of the form y=mx+b and asked to solve them using either the substitution or the elimination method. The lines are randomised but the solution coordinates are always integers.

Students are shown a graph that simultaneously plots cost and revenue lines. They are asked to identify the break-even point.

They are asked to give the x- and y- coordinate values.

The graph is randomised, but it is set up so that the point of intersection lies on gridlines.