Shaheen Charlwood

Linear combinations of $2 \times 2$ matrices. Three examples.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

Find modulus and argument of two complex numbers.

Then use De Moivre's Theorem to find powers of the complex numbers.

AEP Y1 - Engineering Mathematics Assessment 1(i)

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

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Cramers Rule applied to 3 simultaneous equations

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

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 38 minutes to complete this test.

You may use rough paper for your calculations.

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. 

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by'+cy=0$.

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