139 results for "theorem".

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• Parallel Axis Theorem
Question

Write expressions for the moment of inertia of simple shapes about various axes.

• Polynomial Quiz
Needs to be tested
Exam (2 questions)
A quick quiz on dividing polynomials and using the factor theorem.
• Question

Find the moment of inertia of semi and quarter circles using the parallel axis theorem.

• Question

Use the parallel axis theorem to find the area moment of inertia of a triangle and a rectangle about various axes.

• Question

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

• Question

Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the x-axis. Shapes rest on the x-axis so the parallel axis theorem is not required.

• Question

Calculate the moment of inertia of a composite shape consiting of two rectangles about the x or y-axis.  Parallel axis theorem is often required.

• Question

Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

• Question

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

• Question

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

• Question

Find modulus and argument of two complex numbers.

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

• Exam (7 questions)

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.

• Question

No description given

• Question

Quotient and remainder, polynomial division.

• Question

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

• Question

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$

• Question

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$

• Question

Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

• Question

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

• Question

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

• Question

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

• Exam (13 questions)

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

• Question

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

• Question

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

• Question

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

• Question

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

• Question

This question tests the student's ability to find remainders using the remainder theorem.

• Exam (5 questions)

Apply the factor and remainder theorems to manipulate polynomial expressions

• Question

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$

• Question

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