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.

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.

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Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

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Given two sets of data, sample mean and sample standard deviation, on performance on the same task, make a decision as to whether or not the mean times differ. Population variance not given, so the t test has to be used in conjunction with the pooled sample standard deviation.

Link to use of t tables and p-values in Show steps.

Introductory exercise about set equality

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Introductory exercise about power sets.

Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

Slightly harder introductory exercises about the power set.

Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

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Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

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.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

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

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

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

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

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.