Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $\frac{1}{b}$, for integers $a$, $b$, $m$ and $n$.

An experiment using a PhET applet. The student can attach masses of different weights to a spring, and is asked to measure and record how far it stretches. Their measurements are shown on a graph, and they're asked to estimate the formula for the length in terms of the mass.

Using some passages of text, fill in a product fact sheet.

A simple example showing how to mark entries in a spreadsheet.

This question demonstrates how to use GeoGebra applets in explore mode.

The student must construct a polygon by adding points one at a time. At any point, they can answer the question, "Is the centroid inside the polygon?"

GeoGebra's IsInRegion command is used to decide if the centroid is inside the polygon.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

This question demonstrates how to construct a JSXGraph diagram using JessieCode.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

The student must write code to compute the standard deviation of an unknown list of measurements.

The suggested answer uses numpy.std.

Using Pythagoras' Theorem to find a missing side. Illustrated using simple Eukleides diagram

rebelmaths

A collection of information and activities to introduce students to Numbas. There is some information on how Numbas works, information on how to write answers to mathematical expression and number entry parts, and a "test yourself" explore mode activity.

Note: This exam was written for students accessing Numbas exams through the Numbas LTI tool. Some of the information does not apply to exams accessed standalone or through a generic SCORM player.

sin vertically shifted Working 1_11_16

This question is the one described in method 2 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.

Choose one from a list to identify the function shown in a graph. The function is a randomly selected sin, cos, or tan graph with random scale factor.

Simple application of "Power Rule" to differentiate single term functions.

All co-efficients and powers are integer (though some may be negative.

Questions using Pythagoras' theorem involving integers and surds. 

Replace two parallel forces with an equivalent single force

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of people that are fed with 200g of rice (randomised), and the total number of people to be fed (randomised). They need to calculate the weight of rice using proportional reasoning.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of pages read (randomised) and number of pages remaining (randomised), and asked to write the proportion read as a simple fraction.

Finding the confidence interval at either 90%, 95% or 99% for the population variance of a sample. $\chi^2$ tables are used. A single scenario is given.

Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Volume of a tetrahedron using integrals

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Calculating the missing side-length of a triangle using the cosine rule.