Graphing $y=a\log_{b}(\pm x+d)+c$

Given an equation or a worded formula determine if it is a function or not

A quick practice set of problems for education students to take in preparation for their numeracy test.

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Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

The greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250

Calculating the derivative of a function of the form $\frac{(x-a)^2}{bx} + c$, finding its stationary points and determining their nature.

Given a graph of the form either a.cos(bx) or a.sin(bx), identify the amplitude and period.

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

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This question tests students' ability to use repeated squaring to perform modular exponentiation.  Moduli are random numbers between 30 and 70, the base is a number between 10 and 29.  To generate questions of approximately uniform difficult the exponent is taken to be 256 plus two smaller powers of 2. 

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land$.

For example $\neg q \to \neg p$.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

A question to test understanding of set cardinality and intersections when limited information is known about the size of certain sets.

An application of quadratic functions based on the Golden Gate Bridge in San Francisco, USA. Student is given an equation representing the suspension cable of the bridge and asked to find the width between the towers and the minimum height of the cable above the roadway. Requires and understanding of the quadratic function and where and how to apply correct formulae.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

Convert numbers greater than 1 into standard form/scientific notation.

This is a copy of a question from the Numbas demos project, with references to the editor removed.

The student is shown a plot of a mystery function. They can enter values of $x$ check, within the bounds of the plot.

They're asked to give the formula for the function, and then asked for its value at a very large value of $x$.

A plot of the student's function updates automatically as they type. Adaptive marking is used for the final part to award credit if the student gives the right value for their incorrect function.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

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This question tests if a students understands when matrices are conformable

Information on inputting powers

GIve a random linear program and ask the students to convert it to canonical form.

Putting algebraic fractions into their simplest forms

Simplifying indices

Simplifying indices

Simplifying indices