Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

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Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

Very good feedback and corresponds to instance of randomisation

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

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

Missing: Application with bacteria, turning points, difficult chain rule

Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

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

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Integration techniques for monomials and simple polynomials.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

More work on differentiation with fractional coefficients.

Differentiate

\[ \sqrt{a x^m+b})\]

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

This question provides practice at differentiating polynomials.

A basic introduction to differentiation

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

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Integration techniques for monomials and simple polynomials.

I created this question, and every other question in Multiple Integration, for my dissertation `Computer-Aided Assessment of Multiple Integration'.

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

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

Use a series of difference tables to determine the coefficients of a degree three polynomial function from a set of data values, equally spaced over the x-axis.

Find the leading coefficient of a degree 3 polynomial using a difference table.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

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

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

rebelmaths