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A variety of trigonometric equations which can be solved using inverse operations.

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

Solve equations involving logs and exponential functions, by using inverse operations.

Order of Operations

rebelmaths

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AMRC Skills Audit - covering the following programmes:

Shows how to mark a boolean expression, by checking all possible values of the free variables. There's an information step containing a reminder of the syntax for boolean operations.

MCQ for basic order of operations

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Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

These questions deal with vector operations and its application in geology.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Add, subtract, multiply and divide numerical fractions.

Evaluate pi / (2r+s) given values for r and s (r>0, s positive or negative)

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A quick practice set of problems for education students to take in preparation for their numeracy test.

Part of HELM Book 1.1

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

A quick practice set of problems for education students to take in preparation for their numeracy test.

Evaluating arithmetic operations, and the order of operations.

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

Example of an explore mode question. Student is given a 2x2 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvector is recognised by the marking algorithm, also multiples of the "obvious" one(s) (given the reduced row echelon form that we use to calculate them).

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.