Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient. By Newcastle University

Given the original formula the student enters the transformed formula

Finding lengths of sides of triangles

$2e^{x^3}+x^2$

$2e^{x^3}+sin{x}$

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Calculate the functional value at a point.

A detailed look at how algebraic fractions can be manipulated and simplified.

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

Composite functions.

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

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Multiplication of $2 \times 2$ matrices.

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Find $\displaystyle I=\int \frac{2 a x +b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

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

Finding areas under graphs using definite integration.

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Integration by Substitution

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Indices in their simples form

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Indices in their simples form

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Use the chain rule to differentiate various functions.

Using trig identities to find solutions to equations

Use the quotient rule to differentiate various functions.

Use the product rule to differentiate various functions.

Questions on differentiation from first principles, and continuity and differentiability.

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

Use the chain rule to differentiate various functions.

Questions on differentiation from first principles, and continuity and differentiability.

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

Implicit differentiation including finding tangents