Maria Aneiros

Questions on matrix arithmetic.

Approximate the integral of a function by Riemann sums.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Solve a system of linear equations using Gaussian elimination.

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4 questions on integrating by parts.

5 questions on using substitution to find indefinite integrals.

Implicit differentiation including finding tangents

Find eigenvalues and eigenvectors of a $2 \times 2$ matrix.

5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.

Find the determinants of three $2 \times 2$ invertible matrices.

Two questions on solving systems of simultaneous equations.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

Find the modulus and argument of complex numbers.

Find the inverses of three $2 \times 2$ invertible matrices.

Three questions on linear combinations and products of matrices.

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

Solve a pair of linear equations by writing an equivalent matrix equation.

Integration by Substitution

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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This quiz is designed to help you practise your integration techniques.

Improvements needed:

• Add some definite integrals to Q2
• Use different variables

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

Using the unit circle definition of sin, cos and tan, to calculate the exact value of trig functions evaluated at angles that depend on 0, 30, 45, 60 or 90 degrees.

Questions on manipulating logarithms.

Questions on powers, the laws of indices, and exponential growth.