28 results authored by Matthew Mears - search across all users.

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Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

• Question

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• Question in Class 20

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

• Question

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

• Question

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

• Question

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

• Question in Class 18

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

• Question

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

• Question

Addition, subtraction and multiplication of 2 x 2 matrices and multiplication by a scalar.

(Last three parts of original question removed.)

• Question in Class 12

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

• Question in Class 10

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

• Question

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• Question in Class 5

Antiderivatives

rebel

rebelmaths

• Question

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

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Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

• Exam (2 questions)

Find the first few terms of the Maclaurin and Taylor series of given functions.

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• Exam (8 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

• Question

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

• Question

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• Question

Given a randomised rational function select the possible ways of writing the domain of the function.

• Question

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

• Question

Given a randomised square root function select the possible ways of writing the domain of the function.