Multiplication of $2 \times 2$ matrices.

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

You are allowed 31 minutes to complete this test.

You may use rough paper for your calculations.

Two parts.

Content assessed : complex arithmetic; argument and modulus of complex numbers; de Moivre's theorem.

This complex numbers in-class assesment counts 20% towards your final maths grade for WM104.

Note that although questions are randomised for each student, all questions test the same learning outcomes at the same level for each student.  

If you have any questions during the test, please put up your hand to alert the invigilator that you need attention. 

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

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, definite integrals of v ar eto be determined.

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Find the first few terms of the Maclaurin and Taylor series of given functions.

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

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Find the determinant of a $4 \times 4$ matrix.

Find the determinant of a $3 \times 3$ matrix.

Given a randomised log function select the possible ways of writing the domain of the function.

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Add, subtract, multiply and divide algebraic fractions.