Indices and Roots

Questions based on Exercise Intro(b) from the Textbook "Engineering Maths through Applications" by Kuldeep Singh.

Intended for use as Homework Exercises.

Indices and Roots

Questions based on Exercise Intro(b) from the Textbook "Engineering Maths through Applications" by Kuldeep Singh.

Intended for use as Homework Exercises.

Indices and Roots

Questions based on Exercise Intro(b) from the Textbook "Engineering Maths through Applications" by Kuldeep Singh.

Intended for use as Homework Exercises.Indices and Roots

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Calculations in $\mathbb{Z_n}$ for three values of $n$.     

Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

Express various integers and rationals mod $\mathbb{Z}_3, \;\mathbb{Z}_5,\;\mathbb{Z}_7,\;\mathbb{Z}_{11}$

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

English sentences which are propositions are given and for each the appropriate proposition  involving quantifiers is to be chosen. 

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

Intorduces strong induction and uses it to verify the solutions of a second order linear recurrence.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

The custom function rectangle(width,height) draws a rectangle with the given dimensions, along with some labels.

The student must perform an indefinite integration, and include a constant of integration.

A custom marking algorithm identifies the name of the student's constant of integration, and replaces it with 'c' before comparing with the expected answer.

If the student enters something like '2c' instead of 'c', it'll be marked wrong, which is an error in the marking.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Multiplication of $2 \times 2$ matrices.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

This question aims to test understanding and ability to use the laws of indices.

Differentiate

\[ \sqrt{a x^m+b})\]

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Questions about volumes of shapes, and some surface areas.

Calculating the volumes of different containers

rebelmaths

Recall and use of formulae for volume and surface area of a sphere.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

Finding surface area and volume, given formulae.