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

Apply the factor and remainder theorems to manipulate polynomial expressions

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 $\operatorname{gcd}(n_1,n_2,n_3)=1$

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Quotient and remainder, polynomial division.

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

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

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

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

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Basic question on limit laws and the squeeze theorem for sequences.

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

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

Using Pythagoras' Theorem to find a missing side. Illustrated using simple Eukleides diagram

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Calculating the square root of a complex number using De Moivre.

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

Pythagoras' Theorem and naming sides of right angled triangle

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

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

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.

Calculating complex numbers raised to an natural number exponent

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

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

This homework counts 10% towards your final Engineering Mathematics mark.

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

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

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

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

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

Pythagoras' Theorem and naming sides of right angled triangle

rebelmaths