139 results for "theorem".

Question in Engineering Statics
Write expressions for the moment of inertia of simple shapes about various axes.

Exam (2 questions) in Brad's workspaceA quick quiz on dividing polynomials and using the factor theorem.

Question in Engineering Statics
Find the moment of inertia of semi and quarter circles using the parallel axis theorem.

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

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

Question in Engineering Statics
Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the xaxis. Shapes rest on the xaxis so the parallel axis theorem is not required.

Question in Engineering Statics
Calculate the moment of inertia of a composite shape consiting of two rectangles about the x or yaxis. Parallel axis theorem is often required.

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

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

Question in Andrew's workspace
Finding the lengths and angles within a rightangled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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

Exam (7 questions) in Shaheen's workspace
Content assessed : complex arithmetic; argument and modulus of complex numbers; de Moivre's theorem.
This complex numbers inclass 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 in Ruth's workspace
No description given

Question in Analytical Methods: LO1  Algebraic
Quotient and remainder, polynomial division.

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

Question in Content created by Newcastle University
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 in Content created by Newcastle University
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 in Content created by Newcastle University
Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

Question in Content created by Newcastle University
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 in Content created by Newcastle University
Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.

Question in Content created by Newcastle University
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) in Content created by Newcastle University
Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

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

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

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

Finding the full factorisation of a polynomial, using the Factor Theorem and long division Ready to useQuestion in Transition to university
Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Question in Transition to university
This question tests the student's ability to find remainders using the remainder theorem.

Exam (5 questions) in Transition to university
Apply the factor and remainder theorems to manipulate polynomial expressions

Question in Blathnaid's workspace
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 in NC PreCalculus
No description given