Questions on the construction $t+U$ where $K$ is a field, $t\in K^n$, $U\subseteq K^n$ (in parts a) - d), $K=\mathbb R$ and $n=2$ so that we can draw pictures). Part e) is a bit more abstract and probably more difficult.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. SP = Statistics & Probability strand. Students are given the experimental probability in ratio form in a sentence, and asked to write it as a decimal. There are 7 different versions of this question.

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.

EEE8120 Formative Assessment

Two slightly more complicated questions on handling fractions.

Three lines given with different information provided. Equation of the line is asked for.

This tests the student's ability to understand the components of formula.

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. 

Apply formulas to calculate the areas of various shapes.

Solve exponential equation of the form \[ a^{kx}=b^{kx+m}. \]

Solve exponential equation of the form \[ a^{kx}=a^{m}. \]

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. 

Differentiate $\displaystyle (ax^m+bx^2+c)^{n}$.

Differentiate $\displaystyle \ln((ax+b)^{m})$

En Teoría de la Información, se provee una matriz de probabilidades conjuntas P(ai,bj) de un canal 2x2.

Se trata de hallar la matriz del canal.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

Given the formula for BMI, students are asked to determine a patient's BMI given their height in cm (as people usually do) and their mass in kg.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

No description given

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 line equation (where the coefficient of y is 1) and asked to rearrange it into gradient-intercept form.

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 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.

Describe a given linear transformation as a vector in Cartesian coordinates.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.